Multi-material topology optimization for maximizing structural stability under thermo-mechanical loading

Mechanical structures are often simultaneously subjected to thermal and mechanical loading, both of which can lead to buckling failure. Developing efficient structural forms with better capacity for stability is important to keep structures safe. This study aims to optimize structural buckling capacity by using a density-based topology optimization scheme. Instead of treating the mechanical and thermal loadings as a single coupled part in the linearized buckling analysis, the effects of mechanical and thermal loadings are decoupled, which allows to separately analyze and optimize buckling aspects induced by mechanical or thermal loading. Two optimization models based on the decoupled analysis models are developed to respectively maximize the critical load factor of buckling induced by mechanical loading under a specified thermal loading and buckling induced by thermal loading under a specified mechanical loading. Further, based on a three-phase material model, a multi-material topology optimization scheme is employed to optimize the buckling capacity of active structures made of structural and actuating materials and prestressed structures containing prestressed components. The actuation effects are mimicked by the thermal loading of active material. The sensitivities of the objective functions and constraints are derived through the adjoint technique, and the method of moving asymptotes (MMA) is employed to solve the topology optimization problems. Numerical examples are adopted to verify the effectiveness of the proposed approach.