Integración Semi-Analitica De La Matriz De Rigidez De Un Elemento Finito Plano De Ocho Nodos Usando Computación Simbólica.

Abstract

The explicit (semi-analytical) integration of an 8-noded plane-finite-element
stiffness matrix is presented in this work. The element is superparametric having straight
sides. Before to carry out the integration, the integral expressions are grouped into several
groups, thus avoiding duplication of calculations. Symbolic manipulation and integration is
used to obtain the basic formulae to evaluate the stiffness matrix. Then, the resulting
expressions are manipulated, optimized and simplified in order to reduce the computation
time. Maple symbolic-manipulation software was used to generate the closed expressions
and to write down the corresponding Fortran code. Comparisons between analytical
integration and numerical integration were made. Regarding the CPU time, it was shown
that the semi-analytical integration required less CPU time than numerical integration to
obtain stiffness matrices. Regarding the accuracy, several tests were conducted on extremely
distorted finite elements. Results shown that the analytical expressions behave very well even
in these cases.