Elastic Stiffness Of Straight-sided Triangular Finite Elements By Analytical And Numerical Integration

摘要

Most finite element (FE) software uses numerical integration to compute FE stiffness matrices. In the case of straight-sided isoparametric triangular elements, numerical integration is exact, provided a sufficient number of integration points are used. In this paper, the same integrations are performed analytically in closed form with the help of computer algebra software for 3-, 6-, 10- and 15-noded triangles. The resulting analytical expressions have been converted into Fortran 95 subroutines and compared with the conventional numerical integration methods. The analytical routines produce exactly the same results as their numerical counterparts, but run significantly faster. All Fortran 95 code developed in this study is available on the first author's Web site.