Topology optimization of nonlinear elastic structures and compliant mechanisms

The overall objective is to construct a computer-aided design environment in which solid structures and compliant mechanisms are synthesized. The design tool is based upon the rapidly growing research area of topology optimization which combines structural finite element analysis with nonlinear programming and design sensitivity analysis. The goal of the structural topology problem is to determine the optimal distribution of material within a design domain that minimizes a given cost function and satisfies a series of design constraints. A common topology problem is to find the least compliant structure by optimally distributing a limited amount of material. A well-posed topology optimization problem is formulated by the introduction of a density measure which is embedded in the structural analysis. Designs due to linear and nonlinear elastic analyses are compared, and the necessity of including the nonlinear analysis is demonstrated, e.g. to design compliant mechanisms that undergo large overall deformations. Low material density elements can cause convergence problems in the nonlinear finite element analysis, so a systematic strategy to remove and reintroduce these elements from and into the mesh is described. The arc length method is incorporated to accommodate more complex nonlinear behavior, e.g. to design structures that exhibit snap-through behavior. Structure and compliant mechanism design problems are presented throughout the discussion.