Topology optimization of structures under band harmonic excitation using improved adaptive quadrature method

Abstract

In structural topology optimization under band harmonic excitation, inaccurate integration values may lead to incorrect topology optimization results, such as the inclusion of a large number of gray elements or islands. To address this problem, this work proposes an improved adaptive quadrature method and its restart criterion. When the restart criterion is satisfied, the subintervals divided in the previous iteration step are rolled back and reused in the subsequent integral calculation, which ensures the accuracy of the integral and effectively reduces the number of error estimations in the integral calculation. At the same time, considering that the structure topology optimization under band harmonic excitation with a non-zero starting frequency and ending frequency exceeding the first resonance frequency cannot obtain a feasible engineering configuration, an optimization model with the static response of the structure as a weighted part of the objective function is introduced. The improved adaptive quadrature method is integrated into structural topology optimization under band harmonic excitation. Three examples are given to illustrate the practicality and effectiveness of the proposed method.