Nonlinear dynamic topology optimization with explicit and smooth geometric outline via moving morphable components method

For nonlinear dynamic topology optimization, explicit geometry information cannot be obtained with the currently density-based topology optimization methods. To directly obtain an explicit geometry structure in nonlinear dynamic topology optimization, the moving morphable components method is employed to find the optimal topology by changing geometrical parameters of a series of components. However, nonlinear dynamic topology optimization is extremely resourced-consuming, since the objective function and constraints should be evaluated by solving the dynamic equations in each optimization cycle. To solve this problem, the equivalent static loads method is introduced to convert a nonlinear dynamic problem into a linear static problem. The equivalent static loads are obtained by nonlinear dynamic analysis and used as linear static loading conditions. Then, the linear static optimization is carried out by using the moving morphable components method. The linear static system is continuously approaching the nonlinear dynamic systems. In this procedure, the key time steps are selected to calculate the equivalent static loads, and optimization is not coupled with nonlinear dynamic analysis. To avoid mesh distortion problems and make optimization more efficient, the transformation variable is introduced to transform the optimization results before nonlinear dynamic analysis. In this paper, the objective function is defined as the minimum strain energy, with the constraint of volume fraction. Three numerical examples are presented to verify the effectiveness of this method.