Abstract
Topology optimization is a systematic computational design tool that identifies the optimized distribution of materials for a variety of performance metrics within a specified domain without prior knowledge on internal connectivity. This approach can handle large-scale problems and high-resolution FE meshes and is an ideal design tool from a variety of perspectives. In this thesis, we propose a topology optimization framework for designing stiff and lightweight multimaterial structures in the form of compliance/cost minimization subject to volume/cost constraints. The proposed optimization framework controls the minimum size of topological features within each phase through adopting the Heaviside projection method along with a single smooth constraint on design variables, those identifying existence of each phase within each element of a discretized design domain. Owing to its implicit incorporation of minimum length-scale control, the proposed approach can meet manufacturability constraints and prevent numerical instabilities, such as checkerboard patterns and mesh dependency, with minimal computational cost. Furthermore, using smooth functions within the proposed framework allows for application of gradient-based optimizers proven to be highly efficient. The effectiveness and robustness of the proposed method are demonstrated through several numerical examples consisting up to four different phases (three material phases and void phase) where we also explore the effect of optimizer choice including the method of moving asymptote, the globally convergent version of method of moving asymptote and an interior-point method.