An improved numerical process for solution of solid mechanics problems

Abstract

This paper gives an overview of the development and status of an improved numerical process for the solution of solid mechanics problems. The proposed process uses a mixed formulation with the fundamental unknowns consisting of both stress and displacement parameters. The problem is formulated either by means of first-order partial differential equations or in a variational form by using a Hellinger-Reissner-type mixed variational principle. For presentation purposes, the components of a numerical process are characterized and the criteria for an ideal process are outlined. Commonly used finite-difference and finite-element procedures arc examined in the light of these criteria and it is shown that they fall short in a number of ways. The proposed numerical process, on the other hand, satisfies most of the optimality criteria and appears to be particularly suited for use with the forthcoming generation computers (e.g. STAR-100 computer). The paper includes a number of examples showing application of the proposed process to a broad spectrum of solid mechanics problems. These examples demonstrate the versatility and high accuracy of the numerical process obtained by using mixed formulations in conjunction with improved discretization techniques.