Topology optimization of geometrically nonlinear structures including thermo-mechanical coupling
The goal of this research is to develop an efficient and robust methodology for the topology optimization of geometrically nonlinear structures actuated by thermal expansion. The corotational finite element method is used to model the geometric nonlinearity because its element independent nature and linear elastic element core provide a flexibility to introduce thermal loads and formulate analytical sensitivities for any element type. To create thermal expansion, this work uses both prescribed temperature changes and localized heat generation via Joule heating, where electrical and thermal conduction are additionally considered. In this coupled multi-physics problem, emphasis is put on material models and coupling to maintain accuracy and efficiency. One-way coupling is shown to be equivalent to a small strain assumption, and the proper modeling of convection properties in topology optimization is addressed. To model the thermal and electrical conduction in planar layered materials, an averaged (smeared) model based on the smoothed properties of the individual layers is introduced. Large displacement structures are prone to exhibit buckling and limit point behavior. To include instabilities in topology optimization, specialized techniques are introduced to overcome inherent numerical difficulties. A nodal density transformation is introduced to isolate structurally relevant eigenmodes, and a homotopy between linear and nonlinear finite elements is provided to limit the effects of mesh distortion. The proposed methodology is successfully applied to micro-mechanism applications capable of a three-dimensional range of motion, including novel designs reflective of the manufacturing technology used in the micro-electro-mechanical (MEMS) community.