Development and Application of a Finite Volume Method for Static and Transient Stress Analysis

This paper on "Development and Application of a Finite Volume Method for Static and Transient Stress Analysis" was presented at the NAFEMS World Congress on Effective Engineering Analysis - 25-28 April 1999, Newport, Rhode Island, USA.

Summary

A wide variety of physical problems in continuum mechanics are commonly treated by numerical methods and, among these, the Finite Element Method (FEM) has found widespread scope for application.
On the other hand, Finite Volume Methods (FVM) were initially developed in connection with computational fluid dynamics applications but can, in principle, be extended for the solution of solid stress analysis problems.
In this paper, a finite volume method is presented for the solution of static and transient problems in the field of structural mechanics. This paper is thus aimed at introducing finite volume techniques, with their possible advantages, in a field traditionally dominated by finite element methods.
A detailed description of the FV method developed will be given in the paper, with emphasis on the treatment of the general discretisation procedure, both in space and in time. The method is valid for curvilinear computational meshes that may be fitted to complex geometries such as those likely to be found in stress analysis. The possibilities of this method will then be assessed from results of application to some test problems, both in static and in dynamic structural situations. Particular attention will be paid to discretisation in time with view to accurately model transient dynamic situations.