Integración Numérica de Elementos Finitos Cuadriláteros

Abstract

One-point quadrature provides great benefits in nonlinear algorithms because the number of evaluations of gradient
operators and constitutive equations is reduced substantially. The major drawback of one-point quadrature in quadrilateral elements is a mesh instability often known as hourglassing.
The technique presented here gives the explicit expression of finite element matrices of quadrilateral elements without the use of Gauss integration and without knowledge of the spurious modes. It is based in the Taylor series expansion of
the integrands and the resulting elements have no spurious modes and pass the patch test.