SYMBOLIC INTEGRATION TECHNIQUE IN ELASTICITY WITH CONTOUR ELEMENT. CASE PLACEMENT POINT NOT BELONGING TO THE ELEMENT

Abstract

This paper is about a methodology to calculate all the components of the influence matrices of the curved boundary elements of three nodes in plane elasticity problems, using a semi- analytical formulae and coordinate transformations, with which it is possible to savings of CPU time of the numerical integration used in these cases (Gauss-Legendre), maintaining its accuracy. To make the comparison of CPU times and precision of the results obtained by both techniques, numerical and semi-analytical subroutines were created using MAPLE symbolic-manipulation software. Among the results achieved is the reduction of computation times by 76%, 61% and 35% compared to the Gaussian numerical integration with four, six and eight integration points, respectively. That this technique successfully was used by the authors in the integration of matrices in the Finite Element Method (FEM).