Complications of Nonlinear Structural Optimization

Abstract

This chapter focuses on some of the main issues relating to nonlinear optimization with an emphasis on topology optimization. This is specifically done by comparing and reviewing the equivalent static load method (ESLM) which is based on the VDM-SIMP approach presented in Chapter 4; ESLM was, however, explicitly developed for nonlinear topology optimization. ESLM has been successfully used for many topology optimization applications; the case studies of this chapter are, however, intended to expose the shortcomings of this approach, thereby also exposing many of the central issues relating to any finite element-based nonlinear topology optimization algorithm. These include, but are not limited to, parameter sensitivity, boundary condition modeling, scalability, as well as robustness and sensitivity studies in general. This chapter concludes with a direct comparison of linear static VDM-SIMP to ESLM, including further review of the case studies presented in Chapter 5 (Applications of Linear Optimization to Concept Vehicle Safety Structures).