Recent progress in nonlinear FEM-based sensitivity analysis

Abstract

This paper reviews the recent progress in sensitivity analysis applied to the nonlinear finite element method (FEM). The sensitivity analysis method has been successfully developed over the years as a convenient tool for use in linear FEM, and it is reasonable to say that today the framework of the methodology is nearly completed. Nonlinear FEM-based sensitivity analysis, however, has only received considerable research attention since the mid 80's. Regarding static nonlinear problems, path-dependent problems such as elastic-plastic problems have been investigated by a number of research groups, and several competitive methods exist. Sensitivity analysis is also practically important in nonlinear buckling and postbuckling problems, for which several methods have been proposed. The performance of the proposed methods in static and buckling/postbuckling problems are compared, and some numerical examples are introduced to clarify the characteristics of the sensitivity which are peculiar to nonlinear problems.