Higher Order 2D Solid Elements. Shape Functions and Analytical Computation of Integrals

Part of the Lecture Notes on Numerical Methods in Engineering and Sciences book series (LNNMES)

This chapter extends the concepts studied in the previous one for the analysis of solids under the assumptions of 2D elasticity using higher order triangular and quadrilateral elements.

The chapter is organized as follows. In the first sections we detail the systematic derivation of the shape functions for rectangular and triangular elements of different order of approximation. Next, some rules for the analytical computation of the element integrals over rectangles and straight side triangles are given. Finally the performance of linear and quadratic triangular and rectangular elements is compared in some academic examples.


Shape Function Triangular Element Rectangular Element Corner Node Lagrange Element 
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© International Center for Numerical Methods in Engineering (CIMNE) 2009

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