Design sensitivity analysis and optimization of nonlinear structures

Methods of design sensitivity analysis with linear response under static and dynamic loads have been developed and documented over the last fifteen years [1–5]. However, they are just beginning to be developed with nonlinear response [6–8]. Purpose of this paper is to describe a method of design sensitivity analysis of static nonlinear response using incremental finite element procedures. To accomplish this objective, nonlinear analysis of the structure must be performed which is usually quite tedious. The most effective procedure is to use load incrementation coupled with an iteration. With such a procedure, geometric as well as material nonlinearities (different material models) can be consistently and uniformly treated. However, the structure can collapse before the full load level is reached. In that case, design must be improved to have a stable structure. Thus procedures for calculation of collapse load and its sensitivity to design changes must be included in structural optimization problem with nonlinear response.