Two-material topology optimization for the design of passive thermal control structures

A sandwich-panel structure that exhibits effective variable thermal conductivity through its thickness would find applications in spacecraft thermal control. Topology optimization is considered as a means to guide the design of a compliant-cell core that deforms in response to a temperature gradient, alternately creating and breaking heat conduction paths. Topology optimization is a mathematical tool that generates a material distribution to achieve the best performance as defined by an objective function. This paper explores a topology optimization method for the design of two-material structures that must operate under mechanical and thermal loads. 2D compliant mechanisms that are simultaneously subjected to both prescribed temperature and heat flux boundary conditions are of particular interest. The isotropic materials considered may have different stiffnesses, thermal conductivity, and coefficients of thermal expansion. The design domain is filled by two isotropic material phases and a void phase. The presence of one phase in preference to another at each location in the domain is determined using a Solid Isotropic Material Penalization (SIMP) approach. Mechanical and thermal behavior is coupled via material coefficients of thermal expansion; finite element models are used to predict both uncoupled and coupled behavior. Optimization of the mechanical compliance under uncoupled conditions yields results that agree with those in the literature; the coupled results are novel. The volume fraction of individual materials is typically prescribed. However, coupled multi-physics analysis with multiple materials can yield interesting and useful designs when only the amount of void is constrained and the algorithm is free to choose which combination of materials to use. This design freedom is especially important in problems for which thermal conduction is critical, and it produces designs in which the best thermal properties are exploited. This topology optimization approach, when combined with appropriate contact models, should find application to the development of a passive thermal control interface for spacecraft thermal control.