A Nodal Averaged Formulation for Axisymmetric Solids Using Bilinear Quadrilaterals

Abstract

In this work we present a finite element formulation for the stress analysis of axisymmetric solids based on the nodal recovering of stresses and deformations. This procedure is based on a truncated Taylor series expansion of the gradient matrices. For constant constitutive properties the resultant stiffness matrices have polynomial integrands and can be integrated analytically without using numerical integration. If the constitutive properties are variable over the bilinear quadrilateral element, it is shown that we can use an equivalent constant constitutive matrix made by nodal averaged properties for computing the stiffness matrices. Also, the procedure is convergent for any type of material nonlinearity, including plasticity.