Topological Derivativem based Optimization of Fiber reinforced Structures Coupled Thermoelastic Structures and Compliant Mechanisms

Abstract

The topological derivative of a functional quantifies the sensitivity with respect to an infinitesimal domain perturbations such as a hole, an inclusion, a source term, a crack, etc. In this thesis, topological derivatives are used in conjunction with level-set methods to optimize stiff structures and compliant mechanisms. In the first part of the thesis, we use topological derivatives in polar form to obtain fiber-reinforced structural designs with non-periodic continuous fibers that are optimally arranged in specific patterns. The distribution of anisotropic fiber material within isotropic matrix material is determined for given volume fractions of void and material as well as fiber and matrix simultaneously, for maximum stiffness. In this three-phase material distribution approach, we generate a Pareto surface of stiffness and two volume fractions by adjusting the level-set plane in the topological sensitivity field. The next part of the thesis deals with the topology optimization of thermally coupled elastic structures. .. newline