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Finite Element Method with Applications in Engineering by T. L. Eldho, Y. M. Desai

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Appendix D

Review of Gauss Quadrature Procedure for Numerical Integration

D.1 GENERAL

It was shown in Chapter 7 that integrals, which may need to be evaluated numerically, are of the form

 

images

 

In finite element analysis, ‘Gauss Quadrature’ procedure is used extensively for numerical integration.

D.2 FUNDAMENTAL CONCEPT

Consider a simple curve shown in Figure D.1. Application of trapezoidal rule is shown in Part (a) of the figure to evaluate area under the curve between the limits of a and b. The area of the trapezoid is given by

 

images

 

where ...

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