An Efficient and Robust Topology Optimization Method for Thermoelastically Damped Microresonators

Abstract

The challenges of computational cost and robustness are critical obstacles in topology optimization methods, particularly for the iterative process of optimizing large-scale multiphysical structures. This study proposes an efficient and robust topology optimization method for minimizing the thermoelastic damping of large-scale microresonators. An evolutionary structural optimization method is adopted to passively determine the search direction of optimizing large-scale thermoelastic structures. To efficiently reduce the computational cost of the iterative process of an optimizing process, a model reduction method is developed based on the projection-based model reduction method whose reduced basis is generated within the Neumann series subspace. However, the projection-based model reduction method may be unstable when topology modifications are made during an iteration optimization process. To ensure robustness, a modal validation technique is first implemented in the iterative process to stabilize the iteration and narrow down the search domain, and a posterior evaluation of the Neumann series expansion is then developed to retain the convergence of the projection-based model reduction method. Furthermore, the efficiency and accuracy of the proposed topology optimization method are validated through numerical examples. Two large-scale numerical models are also used to demonstrate the advantage of the proposed method. It is found that large-scale thermoelastic structures with a phase-lag heat conduction law can be designed passively, precisely, and efficiently by using the proposed topology optimization method.