Layout of Linear and Nonlinear Structures by Shape and Topology Optimization

Abstract

Structural optimization of mechanical systems has evolved to provide powerful tools during all stages of structural design [1]. They are characterized by decisions on the structural layout, the shape, and the dimensions of the structure. Equivalent structural optimization problems deal with optimization of topology, shape, and cross sections, respectively. The result depends on interactions between these three different types of optimization problems, as well as on the underlying physical assumptions of the simulation of structural response. Even if linear static or dynamic structural response is assumed structural optimization problems are usually non-linear and in the case of topology optimization usually non-convex. Additionally, powerful optimization procedures have to combine methods of different disciplines: geometric modeling, computational mechanics, and mathematical programming [2]. Consequently, due to the inherent complexity, optimization problems tend to be formulated in a way that neither the full potential of the concerned methods are exploited nor the effects of interactions between the different types of optimization problems are considered. This is e.g. the case for the interactions of topology and shape optimization, and the shape optimization of imperfection sensitive structures with large deflections and instability response. The contribution focuses on these two distinct areas of structural optimization which are of actual importance.