Dynamic analysis of structural deformation and metal forming

Abstract

In the dynamic analysis of the deformation of bodies and structures it is often found that the duration of significant loads and high stresses is such that stress waves traverse the body and reflect from the surfaces many times in the period of interest for stress and deformation analysis. This circumstance can even apply in impact problems such as those arising in automobile collisions and hammer forging. In many problems, particularly when plastic flow occurs, numerical methods of solution must be utilized. The equations governing the dynamic deformation of a continuous medium are of wave type, but if dynamic elastic-plastic computer codes, such as those developed for ballistics problems which analyse wave propagation, are used for problems of the type considered here, excessive computing effort and round-off errors can be expected. Finite difference schemes for the wave equation are examined to select a scheme which is stable for long time steps and which adequately encompasses both wave analysis and long time solution, avoiding in the latter the complexity of the wave interactions. Economical computation is then achieved. This approach is applied to the study of dynamic deformation of a porous metal using the finite element method.