Structural topology optimization of frequency response problem by approximately logarithmic Heaviside function based on ICM Method

A topology optimization model for frequency response was established based on ICM (Independent Continuous and Mapping) Method, in which the minimization of structure weight subject to the response amplitude of a harmonic excitation with a continuous frequency band or a discrete frequency. The approximately logarithmic Heaviside function was introduced as a filter function and design sensitivity was analyzed. The dual-quadratic programming was used to solve this optimization problem. The sensitivity filtering method was applied to deal with the numerical instability problems of frequency response. The numerical examples show that the modified logarithmic function and the power exponent function have different effects on a topology structure. In addition, the optimal results by using the modified logarithmic function is better than that by using the power exponent function in iteration number and convergence precision.