Are you looking to level up your forex trading game to maximize your profits? One of the most popular and effective techniques is the use of Fibonacci numbers. This powerful tool can help traders predict market trends and identify the best entry and exit points. Whether you’re a beginner or an experienced trader, mastering the Fibonacci sequence can give you the edge you need to succeed in the ever-evolving world of forex trading.
The Fibonacci numbers, named after an Italian mathematician, are a sequence of numbers generated by adding the two preceding numbers to create the next number in the sequence. The pattern goes 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. Traders use these numbers to plot key levels of support and resistance on a price chart. By identifying these levels, they can make informed decisions about when to buy or sell a currency pair. This strategy works particularly well in volatile markets, where prices tend to move in repetitive cycles.
But how exactly does one use Fibonacci numbers in forex trading? It all starts by identifying the highs and lows of a price chart. From there, traders can use the Fibonacci ratios to identify key levels to watch for a potential breakout. By setting stop-loss orders just below these levels, traders can minimize their risk and increase their chances of success. With practice and persistence, even beginner traders can master this powerful tool and start making more informed and profitable trades.
What are Fibonacci numbers and ratios?
Fibonacci numbers are a series of numbers where each number is the sum of the two preceding numbers. The series starts with 0, 1, 1, 2, 3, 5, 8, 13, and continues infinitely. These numbers were first introduced in the book Liber Abaci by Italian mathematician Leonardo Fibonacci in the 13th century, which described various problems involving arithmetic, algebra, and geometry.
Fibonacci ratios are the values that are derived from the series of Fibonacci numbers. These ratios are used for technical analysis in various financial markets, including forex trading. The most popular ratios are 0.236, 0.382, 0.500, 0.618, and 0.786. The inverse of these ratios, which are 1.618, 2.618, and 4.236, are also commonly used in forex trading.
Fibonacci retracements as a trading tool
One of the most popular ways to use Fibonacci numbers in forex trading is through the use of Fibonacci retracements. These retracements are based on the idea that after a significant price move in one direction, the price will often retrace a certain percentage of that move before continuing in the original direction.
Fibonacci retracements are calculated by taking two extreme points on a price chart, typically a swing high and a swing low, and dividing the vertical distance between them by the key Fibonacci ratios of 23.6%, 38.2%, 50%, 61.8%, and 100%. These ratios are based on the Fibonacci sequence, which states that each number in the sequence is the sum of the two preceding numbers (i.e. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.).
Using Fibonacci retracements in forex trading
- Identifying potential support and resistance levels: By plotting Fibonacci retracements on a price chart, traders can identify potential levels of support and resistance where the price is likely to stall or reverse. For example, the 38.2% and 61.8% retracement levels are often considered key levels to watch, as the price will often test these levels before continuing in the original direction.
- Setting profit targets and stop loss levels: Fibonacci retracements can also be used to set profit targets and stop loss levels. For example, a trader might set a profit target at the 61.8% retracement level, where there is a higher likelihood that the price will stall or reverse. Likewise, a trader might set a stop loss at the 38.2% retracement level, which would indicate that the trade is likely to be unsuccessful.
- Confirming other technical analysis: Fibonacci retracements can also be used to confirm other technical analysis indicators, such as trend lines or moving averages. If a Fibonacci retracement level coincides with a trend line or moving average, it is more likely to serve as a significant support or resistance level.
Fibonacci retracement levels table
Overall, Fibonacci retracements are a powerful tool for forex traders looking to identify potential levels of support and resistance, set profit targets and stop loss levels, and confirm other technical analysis indicators. With the help of these retracements, traders can more effectively navigate the complex world of forex trading and increase their chances of success.
How to Draw Fibonacci Retracement Levels on a Trading Chart
Fibonacci retracement levels are used in forex trading to identify potential support and resistance levels. These levels are based on the Fibonacci sequence of numbers and are widely used by traders to determine entry and exit points for currency trades.
Drawing Fibonacci retracement levels on a trading chart is a simple process that traders can easily learn and apply. Here are the steps to follow:
- Step 1: Identify the trend – Before drawing the Fibonacci retracement levels, you need to identify the trend of the currency pair you are trading. You can do this by analyzing the price movement over a period of time and looking for the direction of the trend.
- Step 2: Select the swing high and swing low – Once you have identified the trend, you need to select the swing high and swing low points. The swing high is the highest point reached by the currency pair during an uptrend, while the swing low is the lowest point reached during a downtrend
- Step 3: Draw the retracement levels – To draw the Fibonacci retracement levels, you need to use a Fibonacci retracement tool. This tool is usually available on most trading platforms. Click on the tool and then click on the swing low and drag it to the swing high point. The tool will automatically draw the retracement levels for you.
The Key Fibonacci Retracement Levels
The retracement levels that traders commonly use are 38.2%, 50%, and 61.8%. Traders also use the 23.6% and 78.6% levels, although they are not as significant as the three key levels. Here is how to interpret the retracement levels:
|38.2%||This is the first retracement level and is considered to be a shallow retracement. If the price retraces to this level, it is a sign that the trend is still strong and is likely to continue in the same direction.|
|50%||This is the second retracement level and is considered to be a moderate retracement. If the price retraces to this level, it is a sign that the trend is likely to continue, but may be losing momentum.|
|61.8%||This is the third and final retracement level and is considered to be a deep retracement. If the price retraces to this level, it is a sign that the trend is losing momentum and may be reversing.|
Tips and Tricks for Using Fibonacci Retracement Levels
Here are some tips and tricks for using Fibonacci retracement levels in forex trading:
- Don’t rely solely on Fibonacci retracement levels. They are just one tool that traders use and should be used in conjunction with other indicators and analysis.
- Use Fibonacci retracement levels in combination with support and resistance levels. This will help you identify potential entry and exit points for your trades.
- Practice drawing Fibonacci retracement levels on a demo trading account to get comfortable with the process before you begin trading with real money.
By following these steps and tips, traders can effectively use Fibonacci retracement levels to identify potential support and resistance levels for their forex trades. Remember to always practice risk management and never risk more than you can afford to lose.
Fibonacci extensions and their use in trading
Fibonacci extensions are another powerful tool in forex trading. They are used to help traders identify potential profit targets on trades. Once a trader has identified a trend, they can use Fibonacci extensions to predict where the price may move in the future.
- First, the trader identifies the swing high and swing low points of the trend.
- Then, they apply Fibonacci extensions levels to the chart.
- The levels indicate where the price may potentially reach, based on the length of the trend.
There are different levels of Fibonacci extensions, including 127.2%, 161.8%, and 261.8%. These levels can be used as potential exit points for traders, as the price may encounter resistance or support at these levels.
Fibonacci extensions can also be used in conjunction with other technical analysis tools, such as trend lines and moving averages, to confirm potential price targets.
Example of Fibonacci extensions in trading
|Date||Swing High||Swing Low||Price Target|
|January 1st||1.2000||1.1000||1.2720 (127.2% extension)|
|January 15th||1.4000||1.2500||1.6170 (161.8% extension)|
|February 1st||1.8000||1.6000||2.0860 (261.8% extension)|
In this example, the trader has identified the swing high and swing low points of three different trends. They have then applied Fibonacci extensions levels to the chart, with the levels indicating where the price may potentially reach. The trader can use these levels as potential profit targets, or as points to exit the trade.
Common Fibonacci levels used by traders
Fibonacci levels are widely used by traders in forex trading to identify potential support and resistance levels. Understanding these levels is crucial for traders to make informed decisions when it comes to placing trades. The most commonly used Fibonacci levels in trading are:
The Number 5
The number 5 is an important Fibonacci level that is used in trading. This level is not directly related to the actual Fibonacci sequence, but it is still important for traders to understand its significance. The number 5 is derived from the relationship between adjacent numbers in the Fibonacci sequence. The ratio of any two adjacent numbers in the Fibonacci sequence approaches the golden ratio of 1.618. When we add two adjacent Fibonacci numbers together, we get the next number in the sequence. For example, 3 + 2 = 5, and 5 + 3 = 8.
Traders use the 5 level as a potential reversal point. When prices break above or below this level, it often indicates a potential reversal in the direction of the trend. This level is also used in combination with other Fibonacci levels to identify potential support and resistance levels. For example, the 50% level is often used in combination with the 5 level to identify a potential reversal point.
In addition to its use in Fibonacci retracements, the number 5 is also important in other aspects of trading. For example, some traders use a 5-period moving average to identify short-term trends in the market. This moving average is calculated by taking the average closing price of the last 5 periods.
Overall, understanding the significance of the number 5 in trading can help traders make more informed decisions when it comes to placing trades. By combining this level with other Fibonacci levels, traders can identify potential support and resistance levels and make more accurate predictions about future price movements.
Identifying support and resistance levels with Fibonacci
One of the most popular ways to use Fibonacci numbers in forex trading is to identify support and resistance levels. Support levels are price points that a currency pair tends to bottom out at, while resistance levels are price points that a currency pair tends to peak at. By identifying these levels, traders can use them as indicators of potential future price movements and make more informed trading decisions.
- To use Fibonacci levels to identify support and resistance, traders first need to locate the most recent high and low points on a chart. These points will be used to draw Fibonacci retracement levels. These levels are drawn by placing horizontal lines at the appropriate Fibonacci ratios.
- Once the retracement levels are drawn, traders can look for support or resistance at these levels. Price action that shows a strong bounce off of a Fibonacci level can suggest that the level is acting as support or resistance.
- Traders should also be on the lookout for multiple Fibonacci levels that occur close to each other. This confluence can provide additional evidence that a particular level is acting as support or resistance.
For example, suppose a currency pair has recently been trending upwards and has reached a high point of 1.4500. The pair then begins to retrace downwards, with a low point of 1.4000. To draw Fibonacci levels, traders would draw a horizontal line between these two points and place horizontal lines at the appropriate Fibonacci ratios, such as 38.2%, 50%, and 61.8%.
If the currency pair bounces strongly off the 38.2% level, traders might expect that level to act as support in the future. Similarly, if the currency pair encounters strong resistance at the 61.8% level, traders might expect that level to act as resistance in the future.
Overall, using Fibonacci numbers to identify support and resistance levels can be a useful tool in forex trading. By paying attention to these levels and the price action surrounding them, traders can gain valuable insights into potential future price movements and make more informed trading decisions.
Fibonacci and Elliot Wave Theory in Forex Trading
Fibonacci retracements are a widely-used technical analysis tool in forex trading. They are based on the sequence of numbers known as the Fibonacci sequence, which is derived from the mathematical discoveries of Leonardo Fibonacci in the 13th century. Elliot Wave Theory, on the other hand, is a technical analysis approach developed by Ralph Nelson Elliot in the 1930s that identifies waves in financial markets.
Using Fibonacci Numbers in Forex Trading
- Fibonacci retracements are used to identify potential levels of support and resistance in a market. Traders use Fibonacci retracements to identify potential entry and exit points for their trades.
- The most common retracement levels are 23.6%, 38.2%, 50%, 61.8%, and 78.6%. These levels are calculated by taking the high and low points of a price movement and applying Fibonacci ratios to determine where the price is likely to retrace to.
- Fibonacci retracements are often used in conjunction with other technical indicators, such as moving averages, to confirm potential entry and exit points.
The Relationship between Fibonacci and Elliot Wave Theory
Elliot Wave Theory identifies trends in the market as a series of impulsive and corrective waves. Fibonacci retracements are often used by Elliot Wave analysts to identify potential levels of support and resistance within these waves.
For example, an Elliot Wave analyst may identify a wave as being in an impulsive phase, and use Fibonacci retracements to identify potential levels of support for buying opportunities.
Fibonacci Retracement Levels
Overall, the use of Fibonacci retracements in forex trading can be a useful tool for identifying potential entry and exit points for traders. When used in conjunction with other technical indicators, such as Elliot Wave Theory, Fibonacci retracements can help traders gain a better understanding of market trends and make more informed trading decisions.
Combining Fibonacci with other technical analysis indicators
Fibonacci retracement is just one of several technical analysis tools used in trading. However, it is commonly used alongside other indicators to confirm a trend, support or resistance level, or possible reversal points. Below are ways on how to combine Fibonacci with other technical analysis indicators:
- Moving Averages: Moving averages can help validate potential Fibonacci retracement levels. For instance, traders may be more inclined to look for retracements near key moving averages; the 50, 100, and 200 SMA. Similarly, if a retracement level coincides with a moving average, this may provide more emphasis on the level.
- Relative Strength Index (RSI): RSI is a momentum indicator used to determine if a currency is overbought or oversold. If the RSI is over 70, the currency may be overbought, and if the RSI is below 30, the currency may be oversold. Fibonacci levels can confirm RSI signals. For example, if the RSI becomes oversold at a Fibonacci retracement level, it may indicate a possible reversal of the downtrend.
- MACD: Moving Average Convergence Divergence (MACD) is a trend-following momentum indicator. This indicator is used to show the relationship between two moving averages. Similar to the RSI, traders combine it with Fibonacci retracements to confirm trend or reversal. If prices pull back to a Fibonacci level and the MACD is showing a bullish crossover, that could signal a potential bullish trend reversal.
Retracement Trading Strategies
There are different trading strategies that traders use to apply Fibonacci retracements alongside other indicators. One strategy is the “Fibonacci Fan” strategy. This involves drawing diagonal trend lines to connect significant price points and form a fan-like pattern.
Another popular Fibonacci strategy is known as the “Fibonacci extension” strategy. This technique uses Fibonacci retracements and extensions to determine price targets. Extensions are calculated by projecting the price level of a retracement from the previous trend wave. A trader can enter a position near a key Fibonacci retracement level and place a stop loss underneath. Then, they can use a Fibonacci extension level as a profit-taking target to exit the trade.
Fibonacci Retracement Levels Table
In conclusion, combining Fibonacci retracements with technical indicators can provide traders with additional confirmation of trend, support and resistance levels, or potential reversals. It is essential to have a solid understanding of both the tools and the market before applying any strategy to ensure positive trading outcomes.
Pros and cons of using Fibonacci in forex trading
Using Fibonacci in forex trading is a popular technique among traders. Fibonacci numbers are a mathematical sequence that appears in many natural phenomena. In forex trading, these numbers are used to identify potential price movements and support/resistance levels.
- The Fibonacci sequence can help traders identify possible price movements based on past trends and patterns.
- It can serve as a guideline for where to enter or exit the market.
- Fibonacci retracements can provide support and resistance levels that traders can use to set stop-loss or take-profit orders.
- It can help traders manage risk by identifying potential entry and exit points.
- The use of Fibonacci requires a certain level of technical analysis knowledge and expertise.
- The accuracy of Fibonacci levels is not guaranteed, and they should not be used as the sole basis for trading decisions.
- The strategy can be subjective and open to interpretation, leading to different outcomes.
- It can be easy to get caught up in the patterns and forget about other important factors that may affect the market.
Despite its advantages and disadvantages, the Fibonacci sequence is still a widely used tool in forex trading. Traders should always exercise caution and use it as part of a comprehensive trading plan that takes into account various factors, such as market conditions, news events and economic data.
One of the key Fibonacci numbers used in forex trading is 9. This number is often used in conjunction with the 38.2% and 61.8% retracement levels to identify potential support and resistance zones. The table below illustrates how the 9 Fibonacci number can be used in trading:
Traders can use the above table to determine potential levels for entry, stop loss and take profit orders based on the 9 Fibonacci number and the corresponding retracement and extension levels. However, it is important to keep in mind that this is not a foolproof method and should be used in conjunction with other strategies and analysis.
Real-life examples of successful Fibonacci trading strategies
There are many trading strategies that incorporate Fibonacci retracements and extensions. Here, we will explore some real-life examples of successful Fibonacci trading strategies.
- Retracement Strategy: This strategy involves identifying a trend, drawing a Fibonacci retracement from swing low to swing high (in an uptrend) or swing high to swing low (in a downtrend), and entering a trade at a retracement level. For example, if the retracement level is 50%, the trader would enter a buy (in an uptrend) or sell (in a downtrend) order at that level. If price bounces off the retracement level and continues in the direction of the trend, the trade is successful.
- Extension Strategy: This strategy involves identifying a trend, drawing a Fibonacci extension from swing low to swing high (in an uptrend) or swing high to swing low (in a downtrend), and placing buy (in an uptrend) or sell (in a downtrend) orders at the extension levels. For example, if the extension levels are 127.2%, 161.8%, and 261.8%, the trader would place buy (in an uptrend) or sell (in a downtrend) orders at these levels. If price reaches these levels and bounces, the trade is successful.
- Fibonacci Fan Strategy: This strategy involves drawing a Fibonacci fan from a swing low to swing high (in an uptrend) or swing high to swing low (in a downtrend). The fan creates diagonal support and resistance levels. Traders can use these levels to enter trades or take profit. For example, if price is in an uptrend and approaching a fan level, traders can enter a buy order at that level. If price bounces off the level and continues in the direction of the trend, the trade is successful.
Overall, Fibonacci retracements and extensions can be powerful tools when used in conjunction with other technical analysis tools and market knowledge. However, traders should always use proper risk management and consider the possibility of false signals or market manipulation.
Below is a table of common Fibonacci retracement and extension levels:
Remember that Fibonacci levels are not always foolproof, and it’s essential to use other technical analysis indicators and market knowledge in combination with Fibonacci tools. When used properly, Fibonacci retracements and extensions can give traders an edge in analyzing market movements and making informed trading decisions.
FAQs about How to Use Fibonacci Numbers in Forex Trading
1. What are Fibonacci numbers in forex trading?
Fibonacci numbers are a series of numbers used by traders in financial markets to predict future price movements.
2. How are Fibonacci numbers used in forex trading?
Fibonacci retracement levels are used by forex traders to identify potential levels of support and resistance in the market. Traders plot these levels on their charts to help them identify potential buy and sell points.
3. What is Fibonacci retracement level?
Fibonacci retracement level is the percentage of a price move that retraces before continuing in the original direction. These levels are drawn from the highest point to the lowest point, or vice versa, in a given price move.
4. Can Fibonacci numbers be used to predict future forex market trends?
Fibonacci numbers and retracement levels cannot predict future market trends with certainty. In fact, traders should always consider other technical and fundamental indicators before they make trading decisions.
5. How do I add a Fibonacci retracement level to my chart?
Most forex trading platforms have built-in Fibonacci tools that you can use to add retracement levels to your chart. Look for the Fibonacci Retracement option in your platform’s charting tools.
6. How do I interpret the Fibonacci retracement levels on my chart?
The retracement levels help traders identify areas of support and resistance in the market. These levels can be used to determine potential entry and exit points, as well as stop-loss and take-profit levels.
7. Are there any downsides to using Fibonacci numbers in forex trading?
Some critics argue that Fibonacci numbers and retracement levels are not based on any sound mathematical or statistical principles. However, many traders have found success using these tools in their trading.
Closing Title: Thanks for Reading Our Guide on How to Use Fibonacci Numbers in Forex Trading
We hope this guide has been helpful in gaining a better understanding of how to use Fibonacci numbers and retracement levels in forex trading. Remember that Fibonacci numbers are just one tool in your trading arsenal, and it should always complement your trading strategy. Thanks for reading and be sure to visit us again for more useful trading tips and information.


The Chief Executive of Northern Ireland’s awarding organisation, the Council for the Curriculum, Examinations and Assessment (CCEA) has welcomed this year’s improved GCSE results.
Commenting on this year’s GCSE results, Justin Edwards said: “We’re pleased to see that learners here continue to perform well in GCSE examinations. There is steady improvement across the grades, reflecting the continuing focus and hard work in our schools and colleges. Overall, the proportion of entries awarded A* - C grades in Northern Ireland has risen by 0.4 percentage points this year to 79.1 per cent. Northern Ireland’s performance remains higher than the full UK A*-C performance, which was 66.9 per cent this year.
“The strong performance in English and the individual sciences is of particular note, building on the improvements seen in recent years.
“A* - C performance in mathematics has fallen by 1.7 percentage points to 64.9 per cent. Analysis of the data shows that, for 16 year olds, performance in mathematics was stable, with a small decline of 0.2 percentage points from 2015. It also worth noting that, despite the fall this year, Northern Ireland is almost 4 percentage points ahead of the full UK A* - C performance in mathematics.
“Females continue to outperform males at GCSE in Northern Ireland and the gap, for A*-C grades achieved, has widened this year by half a percentage point to 7.6 percentage points. Whilst A*-C performance for both males and females has continued to rise since 2006, females have improved their performance at a faster and more consistent rate.
“This year we’ve seen continued growth in entries for STEM subjects (Science, Technology, Computing, Engineering and Mathematics). STEM subjects here now account for close to one third (31.9 per cent) of all GCSE entries.”


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The quant. section includes many important topics like- percentage, average, simple and compound interest, time and work, time and distance, algebra etc. We provide you with a guide on how to solve percentage and average related problems.
A percentage is a number or ratio expressed as a fraction of 100.Percentage is considered a very important chapter.
When we say 100 percent in mathematical notation we write 100% so 35 % means 35 per 100 and 65% means 65 per 100 it is a proportion per hundred and it is used to find marks, profit percent or loss percent of a particular product.
Here are some different percent related problems given with shortcut tricks below.
Percentage is a fraction whose denominator is always 100. x percentage is represented by x%.
We know that x/y = (x/y× 100 )
[ R/(100+R)×100 ] %
[ R/(100-R)×100 ] %
Let the present value of a machine be P. Suppose depreciates at the rate of R% per annum Then :
1. Value of the machine after n Years
[ R/(100+R)×100 ]%
Example 1: The average mark of 70 students in a class is 80. Out of these 70 students, if the average mark of 40 students is 75, what is the average mark of the remaining 30 students?
Average of 70 students = 80.
Hence total marks of all the 70 students = 70×80 = 5600
Out of these 70, average of 40 students = 75
Hence total marks of these 40 students = 40×75 = 3000.
So the total marks of the remaining 30 students = 5600-3000 = 2600
Hence the average of the remaining 30 students = 2600/30 = 86.66
Now there will be a serious difference in the time taken if the numbers given here are not multiples of 10. Just look at example 2 below:
Example 2: “Average of 75 students is 82, out of which average of 42 students is 79. What is the average of the remaining 33 students?
Let’s go back to Example 1
Given that average of 70 students is 80. This class is split into two groups of 40 and 30. I am sure you will agree with me that if the average of each of these groups is 80, then the average of the total group i.e. 70 students will also be 80.
But the first group of 40 students, instead of 80 they had an average of only 75. So definitely the average of the remaining 40 students must be greater than 80.
The loss incurred because of the first group must be compensated by the second group.
Let us look at the loss incurred because of the first group
We want them to have an average of 80, but they managed only 75. So we lost an average of 5 upon 40 students. So the loss in the sum = 40×5.
Now this loss of 40×5 must be compensated by our second group i.e. 30 students.
So their average must be not only the initial 80, but also the average meant to compensate the loss incurred because of the first group.
Hence the average of the remaining 30 students = 80 + (40×5)/30 = 80 + 20/3 = 86.66
Now let us look at Example 2 where the numbers are not comfortable.
Example 3: Average of 75 students is 82, out of which average of 42 students is 79.
What is the average of the remaining 33 students?
Average of 75 members = 82.
Two groups of 42 and 33 and we want each group to have an average of 82.
But the first group i.e. 42 students they had an average of 79.
We fell short by 3 in the average.
So the loss in the sum= 3×42.
So the average of the second group i.e. 33 students must be 82 + (3×42)/33 = 82+ 42/11 = 85.82
So folks it’s time to get into some more different situations that arise when we calculate averages.
Let’s look at one more sum similar to the one discussed above.
The average height of 74 students in a class is 168 cm out of which 42 students had an average height of 170 cm. Find the average height of the remaining 32 students.
Average of 74 students = 168.
Here we can observe that, in the case of the first group we had a gain.
Since the average of 42 students is 170 cm, the gain is 2 cm in the average upon 42 students.
So the gain in the sum = 42×2
Hence average of the remaining 32 students = 168 – (42×2)/32= 168-(21/8) = 165.37
The average height of 40 students in a class is 172 cm. 30 students whose average height is 172.5 cm left the class and 40 students whose average height is 170.5 cm joined the class. Find the average height of the present class.
Going back to the ideal situation, we want the average of the students leaving the class as well as joining the class to be 172 so that the average remains the same.
But it is given that the average of the 40 students leaving the class is 172.5 (more than 172).
So we will incur a loss of 0.5 cm in the average upon 30 students.
Hence the loss in the sum = 0.5x 30 = 15 cm
Also, since the average of the 40 students joining the class is 170.5 (less than 172) we will incur a loss in this case as well. The loss in the average is 1.5 cm upon 40 students.
Hence the loss in the sum = 1.5×40 = 60 cm
Thus the total loss in the sum = 75 cm. This loss will be shared by 50 students which is the present strength of the class.
Hence the average of the present class = 172 – 75/50 = 170.5 cm.
Important Concepts and Formulas – Permutations and Combinations 1. Multiplication Theorem (Fundamental Principles of Counting) If an operation can be performed in m different ways and following which a second operation can be performed in n different ways, then the two operations in succession can be performed in m×n different ways.
If an operation can be performed in m different ways and a second independent operation can be performed in n different ways, either of the two operations can be performed in (m+n) ways.
3. Factorial Let n
be a positive integer. Then n factorial can be defined as
Examples 5!=5×4×3×2×1=120 3!=3×2×1=6
Special Cases 0!=1 1!=1
Suppose we want to select three out of three girls P, Q, R. Then, only possible combination is PQR
Sometimes, it will be clearly stated in the problem itself whether permutation or combination is to be used. However if it is not mentioned in the problem, we have to find out whether the question is related to permutation or combination.
Consider a situation where we need to find out the total number of possible samples of two objects which can be taken from three objects P, Q, R. To understand if the question is related to permutation or combination, we need to find out if the order is important or not.
If order is important, PQ will be different from QP, PR will be different from RP and QR will be different from RQ .If order is not important, PQ will be same as QP, PR will be same as RP and QR will be same as RQ. Hence,If the order is important, problem will be related to permutations. If the order is not important, problem will be related to combinations.
For permutations, the problems can be like “What is the number of permutations the can be made”, “What is the number of arrangements that can be made”, “What are the different number of ways in which something can be arranged”, etc.
For combinations, the problems can be like “What is the number of combinations the can be made”, “What is the number of selections the can be made”, “What are the different number of ways in which something can be selected”, etc. pq and qp are two different permutations, but they represent the same combination.
Mostly problems related to word formation, number formation etc will be related to permutations. Similarly most problems related to selection of persons, formation of geometrical figures, distribution of items (there are exceptions for this) etc will be related to combinations.
The term repetition is very important in permutations and combinations. Consider the same situation described above where we need to find out the total number of possible samples of two objects which can be taken from three objects P, Q, R.
If repetition is allowed, the same object can be taken more than once to make a sample. i.e., PP, QQ, RR can also be considered as possible samples.
If repetition is not allowed, then PP, QQ, RR cannot be considered as possible samples.
Normally repetition is not allowed unless mentioned specifically.
8. Number of permutations of n distinct things taking r at a time : Number of permutations of n distinct things taking r at a time can be given by
nPr = n!(n−r)!
=n(n−1)(n−2)...(n−r+1) where 0≤r≤n
Special Cases nP0 = 1 nPr = 0 for r>n
nPr is also denoted by P(n,r). nPr has importance outside combinatorics as well where it is known as the falling factorial and denoted by (n)r or nr
Examples 8P2 = 8 × 7 = 56
5P4= 5 × 4 × 3 × 2 = 120
9. Number of permutations of n distinct things taking all at a time
Number of permutations of n distinct things taking them all at a time
= nPn = n!
Number of combinations of n distinct things taking r at a time ( nCr) can be given by
nCr = n!(r!)(n−r)!
=n(n−1)(n−2)⋯(n−r+1)r! where 0≤r≤n
Special Cases nC0 = 1, nCr = 0 for r>n
nCr is also denoted by C(n,r). nCr occurs in many other mathematical contexts as well where it is known as binomial coefficient and denoted by (nr)
Examples 8C2 = 8×7/2×1= 28, 5C4= 5×4×3×2/4×3×2×1= 5
Here’s an easy way to remember: permutation sounds complicated, doesn’t it? And it is. With permutations, every little detail matters. Alice, Bob and Charlie is different from Charlie, Bob and Alice (insert your friends’ names here).
Combinations, on the other hand, are pretty easy going. The details don’t matter. Alice, Bob and Charlie is the same as Charlie, Bob and Alice.
Permutations are for lists (order matters) and combinations are for groups (order doesn’t matter).
A joke: A “combination lock” should really be called a “permutation lock”. The order you put the numbers in matters. (A true “combination lock” would accept both 10-17-23 and 23-17-10 as correct.)
Let’s start with permutations, or all possible ways of doing something. We’re using the fancy-pants term “permutation”, so we’re going to care about every last detail, including the order of each item. Let’s say we have 8 people:
1: Alice 2: Bob 3: Charlie 4: David 5: Eve 6: Frank 7: George 8: Horatio
How many ways can we award a 1st, 2nd and 3rd place prize among eight contestants? (Gold / Silver / Bronze)
We’re going to use permutations since the order we hand out these medals matters. Here’s how it breaks down:
We picked certain people to win, but the details don’t matter: we had 8 choices at first, then 7, then 6. The total number of options was 8 · 7 · 6 = 336.
Let’s look at the details. We had to order 3 people out of 8. To do this, we started with all options (8) then took them away one at a time (7, then 6) until we ran out of medals.
We know the factorial is:
Unfortunately, that does too much! We only want 8 · 7 · 6. How can we “stop” the factorial at 5?
This is where permutations get cool: notice how we want to get rid of 5 · 4 · 3 · 2 · 1. What’s another name for this? 5 factorial!
So, if we do 8!/5! we get:
And why did we use the number 5? Because it was left over after we picked 3 medals from 8. So, a better way to write this would be:
where 8!/(8-3)! is just a fancy way of saying “Use the first 3 numbers of 8!”. If we have n items total and want to pick k in a certain order, we get:
And this is the fancy permutation formula: You have n items and want to find the number of ways k items can be ordered:
Combinations are easy going. Order doesn’t matter. You can mix it up and it looks the same. Let’s say I’m a cheapskate and can’t afford separate Gold, Silver and Bronze medals. In fact, I can only afford empty tin cans.
How many ways can I give 3 tin cans to 8 people?
Well, in this case, the order we pick people doesn’t matter. If I give a can to Alice, Bob and then Charlie, it’s the same as giving to Charlie, Alice and then Bob. Either way, they’re equally disappointed.
This raises an interesting point — we’ve got some redundancies here. Alice Bob Charlie = Charlie Bob Alice. For a moment, let’s just figure out how many ways we can rearrange 3 people.
Well, we have 3 choices for the first person, 2 for the second, and only 1 for the last. So we have 3 · 2 · 1 ways to re-arrange 3 people.
Wait a minute… this is looking a bit like a permutation! You tricked me!
Indeed I did. If you have N people and you want to know how many arrangements there are for all of them, it’s just N factorial or N!
So, if we have 3 tin cans to give away, there are 3! or 6 variations for every choice we pick. If we want to figure out how many combinations we have, we just create all the permutations and divide by all the redundancies. In our case, we get 336 permutations (from above), and we divide by the 6 redundancies for each permutation and get 336/6 = 56.
The general formula is
which means “Find all the ways to pick k people from n, and divide by the k! variants”. Writing this out, we get our combination formula, or the number of ways to combine k items from a set of n:
Here’s a few examples of combinations (order doesn’t matter) from permutations (order matters).
Permutation: Picking a President, VP and Waterboy from a group of 10. P(10,3) = 10!/7! = 10 · 9 · 8 = 720.
Permutation: Listing your 3 favorite desserts, in order, from a menu of 10. P(10,3) = 720.
Don’t memorize the formulas, understand why they work. Combinations sound simpler than permutations, and they are. You have fewer combinations than permutations.
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Caesar cipher The transformation can be represented by aligning two alphabets, the cipher alphabet is the plain alphabet rotated left or right by some number of positions. When encrypting, a person looks up each letter of the message in the 'plain' line and writes down the corresponding letter in the 'cipher' line. About Sudoku. Sudoku is a logic-based, combinatorial number-placement puzzle. The objective is to fill a 9x9 grid with digits so that each column, each row, and each of the nine 3x3 subgrids that compose the grid (also called "boxes", "blocks", or "regions") contains all of the digits from 1 to 9.If you are looking for Free Printable Sudoku Puzzles then visit this site.. ok so im checking a 9x9 soduku game and i need help checking the part where the 3x3 boxes are all cheked. i cant seem to output the errors for the 3x3. Jun 28, 2011 · The Personal Paper Cipher employs two “Phases” for the encryption of a domain name into a secure domain-specific password: The first phase determines the starting point for the second phase by tracing the domain name's characters through the Grid, as shown to the left and (larger) above. Once the first phase has determined the starting .... Caesar cipher The transformation can be represented by aligning two alphabets, the cipher alphabet is the plain alphabet rotated left or right by some number of positions. When encrypting, a person looks up each letter of the message in the 'plain' line and writes down the corresponding letter in the 'cipher' line. Your result will be the number they circled To see how the unscrambled puzzle looks, set this number to 0 The 9x9 is filled with digits 1 through 9 so that each column, row, and 3x3 subgrid contains each number only once (3,4,5,6,7,8) Step-by-step method of solving magic squares is provided in a hidden link Step-by-step method of solving magic. In the digrafid cipher, a mixed alphabet is written into a 3x9 grid, and a second mixed alphabet is written into a 9x3 grid. A 3x3 grid of numbers is written to the right of the first mixed alphabet grid, and the second mixed alphabet grid is written below the 3x3 grid. The first mixed alphabet grid has the numbers 1-9 written at the heads of. All grilles are simply transposition ciphers. The reason for using the grille is to make the task of encoding and decoding easier for the human operator. Without the grille, encoding and decoding instructions become a list of characters: row 1 column 8, row 2 column 12, etc., which are tedious for a human to use. . If anyone could solve this cipher, that would be great. A big THANKS in advance . Oct 31, 2010 #2 jiggy Member. Joined Oct 21, 2009 Messages 454 Location ... The top/bottom, left/right, and four corners in your 3x3 grid are the same too. Oct 31, 2010 #4 Stefan Member. Joined May 7, 2006 Messages 7,284 WCA 2003POCH01. Easy Ciphers - most popular ciphers: caesar cipher, atbash, polybius square , affine cipher, baconian cipher, bifid cipher, rot13, permutation cipher Affine Cipher In the affine cipher the letters of an alphabet of size m are first mapped to the integers in the range 0..m - 1. Grid Cipher (sometimes also called a grid code) is very simple transposition block symmetric encryption algorithm. the ever popular ROT13, which can be accomplished with a grid, but is so much cooler with a wheel like this). ... Cipher is a 3x3 rectangle (with open outer borders, think #) with 3 letters in each block, left to right in. The number 15 is called the magic number of the 3x3 square We will now look at magic squares that are of even order where the order is not a multiple of 4 Also note that the 6x6 magic square of the Sun has now swapped positions ... (5X5 grid)which are the number of letters in the Shema / the Jewish proclamation of faith It has twenty-five boxes. Playfair cipher - encoder / decoder. The Playfair cipher, Wheatstone-Playfair cipher, or Playfair square is a polygraphic substitution cipher. It was invented in 1854 by the English inventor Charles Wheatstone. It was popularized by the Scottish scientist and parliamentarian Lord Lyon Playfair. Playfair has been trying for many years to use .... To encipher with a one-time pad each successive letter of the plain text is combined with each successive letter of the key (one-time pad) to produce each successive letter of the cipher text. To combine a pair letters using Table 1, you look at the row, column and cell position of both letters. If both letters are in the same column of the.
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NCERT Solutions for Class 10 Maths Chapter 2 ( Polynomials)
NCERT Solutions for Class 10 Maths Chapter 2 Polynomials of exercise 2.1 for all boards. We have updated all the contents for the new academic session 2020-2021.
In this chapter, you have studied the following points:
- Polynomials of degrees 1, 2, and 3 are called linear, quadratic, and cubic polynomials respectively.
- A quadratic polynomial in x with real coefficients is of the form ax²+ bx + c, where a, b, c are real numbers with a ≠ 0.
- The zeroes of a polynomial p(x) are precisely the x-coordinates of the points, where the graph of y = p(x) intersects the x-axis.
- A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most 3 zeroes.
- If α and β are the zeroes of the quadratic polynomial ax²+ bx + c, then α +β= −b/a ; αβ= c/a
- If α, β, γ are the zeroes of the cubic polynomial ax³ + bx² + cx + d, then α + β + γ=−b/a; αβ+ β γ + γ α=c/a ; αβ γ=−b/a
- The division algorithm states that given any polynomial p(x) and any non-zero polynomial g(x), there are polynomials q(x) and r(x) such that
- p(x) = g(x) q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).


Some of the highest salaries in IT right now are in data science. Data scientists are also at the top of the demand list. And one of the highest earnings increases in the last six months — surprise-surprise — is also there.
So if you’re not already interested in data science, maybe it’s time to start? And if you’re already familiar with the topic, you can always go deeper. This selection includes the best books on Data Science for professionals of all levels. If you are a mature data scientist, come to one of our FP or AI projects, or keep reading.
One of them might be precisely what you are looking for. Nee
Head First Statistics: A Brain-Friendly Guide
As with other Head First books, the tone of this book is friendly and conversational, and it’s the best book to get started on data science. The book covers a lot of statistical data, starting with descriptive statistics – mean, median, modus, standard deviation – and then moves on to probabilistic and logical statistics such as correlation, regression, etc. If you studied natural sciences or commerce in school, you might have studied all this, and this book is a great start for a detailed update of everything you’ve already learned.
Practical Statistics for Data Scientists
The book is intended for Data Science professionals who have experience with the R programming language and have a preliminary understanding of mathematical statistics. It presents key concepts from statistics that relate to data science in a convenient and easily accessible form. It also explains which concepts are important and valuable in terms of data science, which are less critical, and why. Topics covered in detail include exploratory data analysis, data and sample distributions, statistical experiments and significance testing, regression and prediction, classification, statistical machine learning, and teacherless learning.
Introduction to Probability
This book by William Feller introduces probability theory with the right balance between mathematical precision, probabilistic intuition, and specific applications. An Introduction to Probability describes the material accurately while avoiding unnecessary technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text invites the reader to familiarize themselves with the main theorems of the subject: the law of large numbers and the central limit theorem.
Introduction to Machine Learning with Python
This book by Sarah Guido and Andreas K. Mueller is perfect for people who want to learn more about building machine learning models with Python. Everything is explained in an accessible way for beginners, and there are lots of examples, so you won’t get lost while reading. After finishing the book, you’ll be able to create your own models quickly. What’s more, you don’t need any prior knowledge of math or programming languages to read this book.
Python Machine Learning By Example
As the name suggests, this book is the easiest way to get acquainted with machine learning. The book will introduce you in detail and interestingly to Python and machine learning with the help of some examples, such as spam detection using Bayes and predictions using regression and tree algorithms. The author shares his experience in different areas of machine learning, such as advertising optimization, conversion rate prediction, click fraud detection, etc., which perfectly complements the reading experience.
Pattern recognition and machine learning
This textbook from Christopher M. Bishop covers the latest developments, providing a thorough introduction to the field of machine learning and pattern recognition. It is intended for students as well as researchers and practitioners. No prior knowledge of the concepts described is assumed. However, knowledge of multivariate calculus and linear algebra is required, and some experience in the probabilistic theory implementation. The latter may not be necessary since the book includes a separate introduction to basic principles.
Python for data analysis
Get complete instructions on manipulating, processing, cleaning, and analyzing datasets in Python. Updated for Python 3.6, this practical guide is filled with practical examples that will show you how to solve a range of data analysis problems. While reading, you will learn the latest versions of pandas, NumPy, Python, and Jupyter. Wes McKinney writes this book, creator of the Python pandas project, this book is a practical, modern introduction to Python data science tools.
This book reveals the beauty of statistics and enlivens statistics. The tone is witty and conversational. You won’t be bored reading this book or feeling the weight of mathematics! The author explains all the concepts of statistics – basic and advanced – using real-life examples. The book starts with straightforward things, such as the normal distribution and the central theorem, and moves on to complex real-world problems, correlation data analysis, and machine learning.
Data Science and big data analytics
This book from EMC Education Services provides you with all the information: the process and how you can use Python to make it all work for you. Even if you have no idea how to code or know what to do with all the data you have collected, this book will give you all the tools you need. There are many different components in data science, and the ability to put them together can really help better understand customers, find new products, and more.
R for data science
Last but not least. R for data science explains the concepts of statistics and the type of data you will see in real life, how to transform it using concepts like median, mean, standard deviation, etc., AND how to create data, filter, and clean it up. The book will help you understand how confusing and raw data is and how it is processed. Converting data is one of the most time-consuming tasks. This book will help you learn about the different methods of converting data for processing to extract meaningful information from it.
If you are interested in data science, then these books are for you. Pick one that seems to be more on your level of knowledge and start learning! AI is among the most progressive and perspective areas, these blog collects more IT-related items about the most progressive topics. To gain knowledge of machine learning modeling, neural network principles, and artificial intelligence opportunities will be useful for both personal and business development.


3 edition of Elastic-plastic mixed-iterative finite element analysis found in the catalog.
Elastic-plastic mixed-iterative finite element analysis
1993 by National Aeronautics and Space Administration, National Technical Information Service, distributor in [Washington, DC, Springfield, Va .
Written in English
|Statement||Edhi Sutjahjo and Christos C. Chamis.|
|Series||NASA technical memorandum -- 106164.|
|Contributions||Chamis, C. C., United States. National Aeronautics and Space Administration.|
|The Physical Object|
Finite Element Method for Elastic Plastic Plates. A finite element method is developed for the analysis of elastic, perfectly plastic sandwich plates. The method is formulated by means of Greenberg's complementary energy rate theorem using constant moment elements. This formulation results in a quadratic programming by: 9. Reference: UEDA, Y. and YAMAKAWA, T. (). Analysis of Thermal Elastic-Plastic Stress and Strain during Welding by Finite Element Method. Trans. JWS. 2(2). (). 0 10 20 30 40 50 0 Thermal expansion coefficient x(oC) Yield stress/Yield stress at room temperature Young's modules x (kgf/mm2) Young's. James C. Newman is an American engineer and materials scientist known for his work on fracture and fatigue for aerospace vehicles. and pioneered the finite element studies of planar cracks in three-dimensional finite bodies, and are used as benchmarks for new crack stress analysis . Daryl L. Logan has written: 'A First Course in the Finite Element Method/Book and Disk (The Pws Series in Engineering)' 'A first course in the finite element method' -- subject(s): Finite element.
A NASTRAN elastic-plastic finite element analysis of a notched fatigue specimen was performed and the results compared with experimental notch root strain. The calculated notch stress and strain were used in a cumulative damage procedure for determining specimen life which was compared to experimentAuthor: G. E. Barron.
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Of the mixed-iterative method, however, it must be understood that the discontinuities to be smoothed are those originating from finite element discretizations, not from the physics of the problem. Elastic-Plastic Mixed-Iterative Analysis The accuracy of stress and strain solutions has a direct effect on the quality of elastic-plastic analysis.
I recommend this book to anybody interested in Finite Element Method. Read more. One person found this helpful. Helpful. Comment Report abuse. ELMA. out of 5 stars MODERN. Reviewed in the United States on Ma HELLO,THIS IS A GREAT BOOK, ESPECIALLY FOR THOSE WHO FEEL LOST IN COMMERCIAL FEA-SOFTWARE TUTORIALS/5(4).
Elastic-plastic mixed-iterative finite element analysis: Implementation and performance assessment. [Edhi Sutjahjo; C C Chamis; United States.
National Aeronautics and Space Administration.]. An elastic-plastic algorithm based on Von Mises and associative flow criteria is implemented in MHOST-a mixed iterative finite element analysis computer program developed by NASA Lewis Research Center. The performance of the resulting elastic-plastic mixed-iterative analysis is examined through a set of convergence : Edhi Sutjahjo and Christos C.
Chamis. Finite Element Analysis by Mike Fagan (Author) out of 5 stars 4 ratings. ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book.
The digit and digit formats both work. Cited by: 4. The Elastic-Plastic Finite-Element Method. Abstract. The rigid-plastic and viscoplastic finite-element techniques described in the previous chapters are useful approaches to the modelling of metal deformation when the elastic component of strain may reasonably be ignored.
This is often the case, for example, for hot working by: 4. Material nonlinear analysis via mixed-iterative finite element method. Nonlinear thermo-elastic-plastic and creep analysis by the finite element method.
SHARIFI and. An elastic-plastic constitutive equation can be probabilistically integrated at each material integration (Gauss) point using the strain from the finite element level by. In the analysis by Shivpuri et al.  the influence of roll speed mismatch on the curvature of the plate was analysed using an explicit time-integration elastic-plastic finite-element method.
The asymmetric hot rolling process with rolls of the same diameter but different roll speed at the upper and lower roll was analysed by Cao et al.
[10 Cited by: l~t. Mech. Sci. Pergamon Press Ltd. Vol. 9, pp. Printed in Great Britain ELASTIC-PLASTIC ANALYSIS OF TWO-DIMENSIONAL STRESS SYSTEMS BY THE FINITE ELEMENT METHOD P. M~RCAL* and I. KI~CG~ (Received 11 August ) Summary--A method is described for the incremental elastic-plastic analysis of two- dimensional stress Cited by: Computers i Structures Vol.
43, No. Printed in Great Britain. /+ 3 Pcrgamon Press Ltd CONSISTENT STIFFNESS ITERATION METHOD FOR ELASTIC-PLASTIC ANALYSIS CHIH-CHAO CHANG Department of Civil Engineering, Feng Chia University, Taichung, Taiwan, R.O.C. (Received 20 March ) Abstractn this paper, a new Cited by: 1. Elastic plastic material model and updated-Lagrangian formulation are used in the analysis.
The simulation uses a special method of computation, called the ‘Iterative Convergence Method (ICM)’ in order to obtain solutions for steady state cutting and for quickening the convergence of computations compared with the real transient process.
Yung-Li Lee, Mark E. Barkey, in Metal Fatigue Analysis Handbook, Constant Amplitude Pseudo Stress-Life Curve. The synthetic constant amplitude pseudo stress-life curve for a notched component is preferable if the local stress is determined by a linear elastic finite element section presents the method to convert the nominal stress-life curve mentioned.
In ten chapters, Advanced Topics in Finite Element Analysis of Structures: with Mathematica® and MATLAB® Computations covers: Essential background.
Analysis of elastic solids. Solids of revolution. Multifield formulations for beam elements. Multifield formulations for analysis of elastic solids. Plates and shells. Introduction to nonlinear by: A thorough guide to the fundamentals--and how to use them--of finite element analysis for elastic structures For elastic structures, the finite element method is an invaluable tool which is used most effectively only when one understands completely each of its by: Introduction to Nonlinear Analysis Slide Slide R ~ in.
h ~ 1in. E =x10' Ib/in2 II = O'y~xlO'lb/in2 E1 =x10slb/in 2 f = xlO-2 lb/in3 Initial imperfection: Wj(¢) =ShPll C05¢ Analysis of spherical shell under uniform pressure loading p I I I I L Twenty 8-node aXlsymmetnc els.
p deformation dependent Finite element. Non-linear Finite Element Analysis of Solids and Structures, 2nd Edition is an essential reference for practising engineers and researchers that can also be used as a text for undergraduate and Author: Khaled Megahed.
Abstract: The welded joint is the critical area in the structure integrity investigation. To understand the influence of the mechanical heterogeneous on the fracture parameters in welded joint, the represented way of the welded mechanical heterogeneity and its effect on the mechanical parameters at the crack tip are analyzed by using an elastic-plastic finite element analysis.
The finite element method (FEM) is a computational technique for solving problems which are described by partial differential equations or which can be formulated as functional minimization.
The FEM is commonly used in the design and development of products, especially where structural analysis is by: Thermal Contact Elastic-Plastic Finite Element Analysis of Hole-Structure Abstract: Finite element models of hole-structure are built for analyzing hole-edge contact problems under thermal loads.
In order to obtain accurate and reasonable numerical results, elastic model and elastic-plastic model are built in gradual improvement.
Finite element analysis of the ramberg-osgood bar. nonlinear two point boundary value problem is established an d used as a foundation for th e finite element analysis. Numerical analysis, in the form of the finite element, finite difference or boundary element method, has become a preferred calculation tool in the design of complex geotechnical structures.
Finite Element Method The major steps in carrying out a finite element analysis are reviewed and their relations to elements of elasticity are pointed out. Stress Concentrations and Singularities Two major pitfalls in finite element analysis – stress concentrations and singularities – are Size: KB.
Finite element solutions are presented for the subsurface stress and deformation fields in a layered elastic-plastic half-space subjected to repeated frictionless indentation by a rigid sphere.
A perfectly adhering layer is modeled using two different thicknesses and elastic modulus and yield stress two and four times greater than those of the Cited by: See Section in Crisfrield book  e: Strain vector in the current iteration.
Output: Material_State2: A history variable containing material state variables at current iteration. D_ep: Tangent constitutive matrix. References:  Crisfield, Michael A.
Non-linear finite element analysis of solids and structures. Vol. Wiley, Reviews: 2. Finite element analysis is now widely used for solving complex static and dynamic problems encountered in engineering and the sciences.
In these two video courses, Professor K. Bathe, a researcher of world renown in the field of finite element analysis, teaches the basic principles used for effective finite element analysis, describes the general assumptions, and discusses.
Hybrid-stress models for elastic-plastic analysis by the initial-stress approach International Journal for Numerical Methods in Engineering, Vol. 14, No. 3 Large deflection static analysis of typical tail-wheel structure of light aircraft by finite element methodCited by: Books shelved as finite-elements: Practical Stress Analysis with Finite Elements by Bryan J.
MacDonald, Modeling of Metal Forming and Machining Processes. elasto-plastic problems by the finite element method (FEM). References 1 provides an excellent review of the techniques of elasto-plastic modelling in the framework of the finite element method.
Almost all research work on elasto-plastic finite element analysis was based on the traditional h-version of the finite element method. The finite element iterative method (FEIM), for the analysis of the eigenvalue problem arising at singularities, has been applied to elastic and inelastic, homogenous and dissimilar media [1–5].
In this paper, we will discuss the convergence and accuracy of the method in evaluating singularities at interfaces of dissimilar by: 2.
ELASTIC-PLASTIC INDENTATION DEFORMATION IN HOMOGENEOUS AND LAYERED MATERIALS: FINITE ELEMENT ANALYSIS The complex phenomenon of indentation deformation is studied using finite element analysis for both homogeneous and layered materials.
For the homogeneous materials, the elastic-plastic deformation at large indentation Cited by: 4. "A pseudo-coupled numerical approach for stability analysis of frozen soil slopes based on finite element limit analysis method." Sciences in Cold and Arid Regions 5, no. 4 (): • Yuan Feng, Kaveh Zamani and Boris Jeremić.
Procedure to Build Trust in Nonlinear Elastoplastic Integration Algorithm: Solution and Code Verification. Key features: Presents fundamental theory in an accessible and logical way. - Explains finite element analysis using simple, understandable mathematics.
- Emphasizes the practical approach to the study, teaching through worked examples. - Describes commercially-available finite element packages. - Introduces more advanced non-linear, eigenvalue and transient 5/5(2).
finite element program, for small strain elastic-plastic analysis, to be simply and rigourously adapted to problems involving arbitrary amounts of deflection and arbitrary levels of stress in comparison to large plastic deformation. Naylor^ has analysed a number of problems by finite element File Size: 4MB.
Moreover, the performed elastic-plastic finite element analyses (FEA) indicate that the crack growth in the specimens begins by significant yielding around the crack tip. Elastic-Plastic Finite Element Analysis of Vehicle Structural Components This paper examines how two practical finite elements, a beam element and a triangular plate bending element, can be applied to vehicle design analysis with acceptable accuracy, yet without expensive computer time by: 6.
In this review the use of the finite element method (FEM) and the extended finite element method (XFEM) to model fatigue crack propagation is discussed.
The basic techniques are presented, together with some of the recent by: 7. In the finite element method, when structural elements are used in an analysis, the total stress distribution is obtained. Therefore, to produce membrane and bending stresses, the total stress distribution shall be linearized on a stress component basis and used to calculate the equivalent stresses.
If shell elements (shell theory) are used, then the membrane. 4/5 Wed 1D contact analysis Chap5 4/7 Fri Constraint methods for contact analysis 4/10 Mon 2D contact variational inequality 4/12 Wed Finite element formulation for contact Exam 2 4/14 Fri Contact modeling issues 4/17 Mon Contact analysis File Size: 43KB.
Stochastic Elastic-Plastic Finite Element Method Boris Jeremi´c In collaboration with Kallol Sett, You-Chen Chao and Levent Kavvas CEE Dept., University of California, Davis and ESD, Lawrence Berkeley National Laboratory Intel Corporation Webinar Series, October Jeremi´cComputational Geomechanics Group Stochastic Elastic-Plastic Finite File Size: 4MB.
Large Strain Elastic-Plastic Analysis. Pages procedures for the stress integration of inelastic constitutive relations within the incremental-iterative finite element analysis and general strain-driven problems of solids and structures.
The book gives the physical and theoretical foundations of inelastic material models commonly. The objective of this paper is to develop a finite element model for 3D elastic–plastic frictional contact problem of Cosserat materials.
Because 3D elastic–plastic frictional contact problems belong to the unspecified boundary problems with nonlinearities in both material and geometric forms, a large number of calculations are needed to obtain numerical Cited by: 4.Download.
finite element source codes, tutorials and examples, course documents. Download the test data and finite element model of square concrete filled steel tubes (36 Specimens) Finite element analysis source codes Finite element analysis for reinforced concrete. 0.


Introduction to the Subject
Maths is one of Bolingbroke Academy’s specialisms. Maths is an essential subject for many careers – from Engineering, Medicine and the Sciences, to Finance, Programming and Architecture. Our vision is not only to enable our pupils to choose maths for further study or their career if they wish, but also to ensure that all pupils, regardless of their future choices, can have a positive experience of mathematics at school. At the root of Mathematics, at Bolingbroke Academy, is a belief that all pupils can be successful mathematicians, if they are given the tools and the confidence to access the material.
We follow the Mathematics Mastery programme, which is a new approach to Mathematics that has been developed by teachers at ARK schools. We cover fewer topics in more depth, so that pupils are able to master topics thoroughly when they learn a new concept. We also use physical manipulatives and pictures to aid pupils’ understanding of abstract concepts.
Problem solving and communication are at the heart of our mathematics curriculum. Every lesson contains a ‘talk task’, where pupils discuss their mathematical ideas. We have high expectations of the language that our pupils use in the maths classroom and challenge our pupils through rich tasks and open ended questions.
Each department has a 'DNA', that is to say our vision for that department.
The DNA of the Maths Department can be viewed here:
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If you have any queries please contact the Head of Maths Ms Tibbetts


Elliptic curves are relatively obscure mathematical objects: you can get a PhD in maths without ever having come across them. Yet these objects play an important role in modern cryptography and as such are found in most HTTPS connections, in Bitcoin, and in a large number of other places.
To really understand elliptic curve cryptography (ECC) to the point that you can implement algorithms, you'd have to study the maths behind it. This talk assumes that you haven't studied the maths, but just want to understand what ECC is about, how is works and how it is implemented.
It will discuss how 'point addition' works and how the Elliptic Curve Diffie-Hellman algorithm is used, for example in HTTPS - and how you can find it using Wireshark. It will explain how to use elliptic curve for digital signatures and why you don't want to be like Sony when it comes to implementing them. It will discuss how ECC was used in an infamous random number generator and, finally, will take a brief look at the use of elliptic curves in post-quantum algorithms.
The goal of this talk is to keep things simple and understandable and no knowledge of maths is assumed. The talk won't make you an expert on ECC -- that would take years of studying. But it might help you understand the context a bit better when you come across them in your research. And hopefully it will also be a little bit fun.


Our familiar approach to regression requires nearly normal residuals. However, there are circumstances when this is impossible. An important example is when the response variable is categorical with two levels. This video accompanies OpenIntro Statistics’ discussion of “Logistic Regression”, which is a helpful tool when the response variable is binary. First we will be introduced to the ’email’ data set, for which our goal will be to build a spam filter. Then we will learn about the fundamentals of logistic regression and modeling the probability of an event. Finally, we will discuss diagnostics for the
email classifier. Throughout this video we will focus on the email data set. These data represent incoming emails for the first three months of two thousand and twelve from a single email account, and our goal
will be to develop a basic spam filter using these data. The response variable, *spam*, has been encoded to take value one when the message is spam and zero when it is not. The data set also includes additional variables such as “cc”, which indicates if someone was copied or cc’ed on the email, and “dollar”,
which indicates whether a dollar symbol appeared in the email. Remember, regular multiple regression requires the residuals to be approximately normally distributed. This is impossible in our current example,
because the response variable is binary. Therefore, we will explore our new tool: logistic regression. Logistic regression is a type of generalized linear model for response variables where regular multiple regression doesn’t work very well. The outcome Y_i takes the value one (in our application, this represents a spam message) with probability p_i and the value zero with probability one minus p_i. It is the probability p_i that we model in relation to the predictor variables. Fundamentally, the logistic model relates the probability an email is spam to the predictors through a framework much like that of multiple regression. The key is to transform the response variable, and a common transformation for p_i is the logit transformation. You may be wondering why we picked this particular transformation. Well, let’s start with the right hand side
of the equation. Notice the coefficients beta one, beta two,
and all the rest of them, could be any number positive, negative, or zero. Therefore, when the right-hand side is summed up, it can also take any of these values. In addition to other useful properties, the logit transformation makes it possible for the left side to take values along the same interval that is possible on the right side. There are two key conditions for fitting a logistic regression model. First, the model relating the parameters to the predictors must closely resemble the true relationship between the parameter and the predictors. Here, x_1i, x_2i, and so on represent the values of the predictors corresponding to the i-th observation. And secondly, the outcome for each case must be independent of the outcome for other cases. In other words, it must be reasonable to model the emails as approximately independent from each other once we account for the influence of the predictors. Let’s consider how we might check the condition regarding the structure of the model. Among emails modeled as having a 10% chance of being spam, are about 10% of them actually spam? To help us out, we’ve borrowed an advanced statistical method called *natural splines* that estimates the local probability, smoothly from zero to one. For this video, all we need to know about natural splines is that they fit flexible lines rather than straight lines. The curve fit using natural splines is shown as a solid black line. If the logistic model fits well, the curve should closely follow the dashed line. We have added shading to represent the confidence bound for the curved line to clarify what fluctuations might plausibly be due to chance. Even with this confidence bound, there are weaknesses in the first model assumption. The solid curve and its confidence bound dip below the dashed line from about 0.1 to 0.3, and then it drifts above the dashed line from about 0.35 to 0.55. These deviations indicate the model relating the parameter to the predictors does not closely resemble the true relationship. Continuing with our investigation, We might evaluate the independence assumption using the model residuals. We can use the same approach as in regression, where each residual equals observed outcome minus the expected outcome. As we saw earlier in this video, for logistic regression, the expected value of the outcome is the fitted probability for the observation. We could plot our residuals against a variety of variables or in their order of collection, as we did with the residuals in multiple regression. Our goal in this video was to think about a model for determining whether an email was spam or not. Along the way, we were introduced to logistic regression, which is a helpful tool when the outcome variable is binary. We also reviewed the necessary assumptions for logistic regression and discussed possible diagnostic approaches. If you learned something you found interesting, share this video with a friend and visit openintro.org for more resources.


Andy Sun a learner in grade 11 at Edgemead High School can be described by his teachers and peers as a dedicated and hardworking learner with a passion for Mathematics and Physical Sciences.
At the UCT Mathematics Competition, which took place on Thursday, 25 April 2019, Andy did Edgemead High proud by achieving gold. He was also one of the top learners in grade 11 after competing against many learners from other schools in the Western Cape.
Andy was then invited by UCT to take part in the UCT mathematics challenge, which took place on Saturday, 18 May 2019, where he competed against the top grade 11 learners in the Western Cape.
Ms S Saunders, organiser of the UCT Mathematics Competition, from Edgemead High School comments: “Andy has truly done the school proud, we are immensely proud of his contribution to Edgemead High School. It is the first time in years that we have achieved such outstanding results in the UCT Mathematics competition.”
We look forward to seeing Andy at the UCT mathematics competition prize giving which will take place on the 7 June 2019 where his achievements will be celebrated.


By Yuan Y.
Read or Download A Bernstein problem for special Lagrangian equations PDF
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Extra resources for A Bernstein problem for special Lagrangian equations
Likewise, always when the matrix A−1 occurs as an operator acting on some vector or some other matrix, then the expression can be numerically evaluated as we have demonstrated for y. 38 H. van der Vorst For sparse matrices, computational differences may be even much more dramatic. In relevant cases, A−1 may be dense, while L and U are sparse. For instance, if A is a positive deﬁnite tridiagonal matrix, then solving Ax = b via LU decomposition requires only in the order of n arithmetic computations.
Bur. Stand, 49:33–53, 1952. Linear Systems, Eigenvalues, and Projection 45 6. B. N. Parlett. The Symmetric Eigenvalue Problem. , 1980. 7. Y. Saad. Numerical methods for large eigenvalue problems. Manchester University Press, Manchester, UK, 1992. 8. Y. Saad and M. H. Schultz. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. , 7:856–869, 1986. 9. G. W. Stewart. Matrix Algorithms, Vol. II: Eigensystems. SIAM, Philadelphia, 2001. 10. L.
These equations are normally solved by ﬁrst calculating a Schur decomposition for the matrix A. Therefore, ﬁnding the solution of the Lyapunov is quite expensive, the number of operations is at least O(n3 ), where n is the size of the original model. Hence, it is only feasible for small systems. Furthermore, because we arrived at this point using the inverse of an ill-conditioned matrix we have to be careful. B can have very large entries, which will introduce tremendous errors in solving the Lyapunov equation.


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Many students ask whether a university is far better than a college. No matter what kind of class you’re taking, while it is social psychology or human sexuality, you are going to be spending a good deal of time learning about research. Of course it’s possible to play with many topics besides numbers.
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Understanding how betting odds work is critical when it comes to sports betting since they help you understand how likely something is to occur and what your winning potential is.
Step One: Defining Probability
For any given event, be it an MMA fight, an F1 Grand Prix, a Horse Race, an NRL game, or a Basketball match, there are a set number of possible outcomes. Betting odds give you a number which represents these, in various formats, including decimal and fractional.
When you see two numbers separated by a trailing slash, you are looking at fractional Odds. A quick calculation using these integers will tell you how likely X is to occur, Probability, or %, = B / (A+B). So, if you’re looking at 9/1, the sum will become 1 / (9 + 1) = 0.1, so there is a 10% chance that X will occur.
Now that you know how to work out the probability that something will happen, you can move on to figuring out how much money you can win with the given betting odds.
Step Two: Calculating Wins via Betting Odds
To put it simply, let’s once again turn 9/1 into A/B. For every value of B that you wager, you will win A, along with the amount you staked in fractional odds. So, for every $1 you bet, in this example, you will win $9 back.
Step Three: Bringing Decimals In To Your Calculations
Decimal odds are more commonly used than fractional odds, so it’s important that you become familiar with them too. You will be glad to hear that they’re easier to work out!
The calculation here is winnings = (odds X stake) – stake, so, in our example, 9.0 works out to (9.0 X $10 stake) – $10 stake = $80 winnings.
But don’t stress out too much if this is taking a little time for you to get the hang of since there are many bet calculators available online that will work out the numbers for you if you need them to. And you can be sure that you’ll find yourself understanding them more and more easily as you gain experience wagering.
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While neither format is really better than the other, there is definitely a trend emerging which sees decimal odds being favoured. Historically, fractional odds were the top pick for bookmakers in the United Kingdom but because decimal odds are so much easier to understand, online sportsbooks tend to provide them almost unanimously nowadays.
The major difference between the two formats is that fractional odds only represent winnings, they don’t include the return of your stake, and decimals do, so the latter group gives bettors a much more accurate idea of what they can expect to see in their pockets at the end of the day.
The enormous popularity of betting exchanges can also be linked to the increased use of decimal odds just as NRL premiership odds has to offer. When odds change just slightly it’s tough to alter probabilities marginally without creating huge fractions which can boggle bettors’ brains!


Marvellous Mathematics: Patterns, Relationships & Creation
In our maths lessons at the beginning of the year, our new Year 7 students have been discovering what maths is really about.
The famous scientist Galileo Galilei (1564-1642) said, “Mathematics is the language in which God has written the universe”. This language is often expressed in patterns, and much of mathematics is about finding, explaining, modelling and linking these patterns. We find astonishing patterns everywhere, especially in Creation, but also in human systems and behaviour, even in love!
Having celebrated Valentine’s Day at the secondary school last week, this video is a fascinating look at a mathematical pattern found in marriage relationships. The patterns in relationships confirm the biblical advice found in Proverbs 15:1, “a kind answer soothes angry feelings, but harsh words stir them up”.
Finding patterns is increasingly important as technological advancement enables us to collect enormous amounts of data. What are the secrets in all this data, the patterns? Mathematical analysis can help us find them. Mathematics is one of the tools God has given us to help us better understand his Creation, himself and ourselves.
Look about you this week. What patterns do you notice in Creation or in yourself? Thank God for all the different ways he provides for us to see him.