Topology optimization of thermo-hyperelastic structures utilizing inverse motion based form finding

The inverse motion concept is used to optimize thermo-hyperelastic structures using an exact description of the deformed geometry. This method prescribes the shape of the structure in the deformed state, and the optimization yields the shape of the undeformed configuration, i.e. the manufactured state. The kinematics of the thermoelastic model is defined through the multiplicative decomposition of the deformation gradient in combination with neo-Hookean hyperelasticity. To regularize the optimization problem and obtain distinct boundaries, the mathematical design field is thresholded using a smoothed Heaviside function and smeared using a partial differential equation. The sensitivity analyses of the objective function and constraints are both based on the adjoint method. The capabilities of the proposed approach are shown by numerical examples wherein the weight is minimized and the performance of multi-material compliant mechanisms is optimized.