Three-dimensional finite-element analysis including elastic-plastic material response

Abstract

The development of a linear finite-element program using an isoparametric 60-DOF hexahedron is presented. As a special feature dictated by programming considerations, the enforcement of boundary conditions and the modification of the stiffness matrix due to a rotated coordinate system for selected nodal points is carried out on the element level. Numerical integration is performed with the aid of a 14-point integration rule.

The nonlinear program is capable of modelling elastic-plastic material behavior. It is based on the constant stiffness iteration employing the initial stress concept.

The iterative procedure is accelerated by a new scheme termed uniform acceleration.

Three practical applications are presented. The thick-walled cylinder under internal pressure and the transversely loaded thin plate on simple supports are analyzed under the assumption of ideal plasticity. Comparisons with existing solutions are also made. For the third example, an aluminum-epoxy fiber composite is subjected to a uniform temperature difference. Both materials are characterized by strain hardening. The effect of a free surface perpendicular to the fiber direction is shown.