Maximum stress minimization by vibration loads using topology optimization for transient response problems

Abstract

This study proposes a topology optimization method to minimize the maximum stress of a structure for transient external loads. To deal with external loads with arbitrary waveforms, the equations of motion are solved using the Newmark’s β method of the step-by-step integration. Also, a new objective function is defined to minimize the maximum von mises stress occurring at all times of interest in the analysis. We formulate the analytical sensitivity of the transient response problems by applying the adjoint variable method and the idea of the Discretize then differential approach, which provides sensitivity with high accuracy. The formulated sensitivities are validated by an accuracy verification using the finite difference method as a benchmark. Finally, the effectiveness of the proposed method is confirmed by presenting several optimization calculations.