3. What is the significance of numerical integration ? Name various techniques for numerical integration. Evaluate the following definite integral using Simpson's 1/3rd rule by dividing the range into 10 equal parts : what is value of n?
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Numerical integration is always used: the first order elements use one point for volume strain and two points in each direction for deviatoric strain, while the second order elements allow three point or two point (reduced) integration of all components.
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Explanation:
The integration points and weights depend on the specific method used and the accuracy required from the approximation. An important part of the analysis of any numerical integration method is to study the behavior of the approximation error as a function of the number of integral evaluations.
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