Level-set topology optimization considering nonlinear thermoelasticity

At elevated temperature environments, elastic structures experience a change of the stress-free state of the body that can strongly influence the optimal topology of the structure. This work presents level-set based topology optimization of structures undergoing large deformations due to thermal and mechanical loads. The nonlinear analysis model is constructed by multiplicatively decomposing thermal and mechanical effects and introducing an intermediate stress-free state between the undeformed and deformed coordinates. By incorporating the thermoelastic nonlinearity into the level-set topology optimization scheme, wider design spaces can be explored with the consideration of both mechanical and thermal loads. Four numerical examples are presented that demonstrate how temperature changes affect the optimal design of large-deforming structures. In particular, we show how optimization can manipulate the material layout in order to create a counteracting effect between thermal and mechanical loads, even up to a degree that buckling and snap-through are suppressed. Hence the consideration of large deformations in conjunction with thermoelasticity opens many new possibilities for controlling and manipulating the thermo-mechanical response via topology optimization.