Hybrid equilibrium elements for accurate stress analysis

Abstract

It is widely recognized that displacement elements produce poor stress fields, which do not satisfy strong equilibrium conditions. In several fields of computational mechanics, such as cohesive crack propagation and cohesive delamination, stress fields drive all the nonlinear phenomena and very fine meshes have to be employed in order to avoid numerical instabilities. In fact, inter-element equilibrium condition is generally not satisfied and stress fields can abruptly change between adjacent elements, producing strong inconvenient in crack propagation analysis. In the present paper hybrid stress elements are proposed as alternative to standard finite element for linear and non linear analysis. Hybrid stress formulation is developed in a rigorous mathematical setting and some methods for elimination of spurious kinematic modes are presented. The proposed approach is qualitatively compared to displacement and mixed methods by linear elastic analysis of some structural examples, well known in literature.