An Immersed Boundary Framework for Topology Optimization of Nonlinear Thermoelastic Structures with Internal Radiation

Thermoelastic structures poses a critical challenge to designers due to the inherent proportionality of the thermal loading on the structural thickness. This is further exacerbated by structural nonlinearity where any out-of-plane deformation further increases the effective loading on the structure. As a result of this, conventional design optimization procedures, which are typically based on linear thermoelastic analysis, have been shown to result in infeasible designs. The density-based approach does not provide a crisp definition of the topology and its boundary, which limits its utility for applications requiring modeling of boundary physics, such as radiation heat-transfer. The proposed research will create a topology optimization framework using a level-set formulation on a predefined computational mesh. The nonlinear thermoelastic system-of-equations will be solved on the implicit geometry using an extended finite element method (X-FEM) approach. This will be implemented inside the computational framework, MAST, that has been used extensively for design of nonlinear thermoelastic structures. Computational efficiency of the procedure will be enhanced using adjoint-sensitivity of the coupled problem and the optimization framework will be demonstrated using topology optimization of representative three-dimensional structures. Finally, the internal (cavity) radiation solvers, developed by the co-PI Bhatia, will be integrated as a module inside MAST.