Structural topology optimization on dynamic compliance at resonance frequency in thermal environments

This paper [r] carries out topology optimization to minimize structural dynamic compliance at resonance frequencies in thermal environments. The resonance response is the main dynamic component, minimization of which could possibly change structural dynamic characteristics significantly. A bi‐material square plate subjected to uniform temperature rise and driven by harmonic load is investigated in pre‐buckling state. The compressive stress induced by thermal environment is considered as pre‐stress in dynamic analysis, which could reduce stiffness of the structure and alter the optimal topology. Sensitivity analysis is carried out through adjoint method efficiently. As natural frequencies are constantly changing during the optimization, the associated sensitivity should be calculated in which multiple‐frequency case is briefly discussed. Mode switching may occur during the optimization, and mode tracking technique is adopted. Numerical results show that the topology is mainly determined by the excited modes, and could be altered by the location of the applied load if different modes are excited. The natural frequencies become larger in optimal design and the dynamic compliance decreases in nearby frequency band. The critical buckling temperature increases as optimization proceeds, indicating the structure is always in pre‐buckling state.