Dynamic Response Topology Optimization in the Time Domain Using Equivalent Static Loads

Abstract

Most topology optimization techniques find the optimal layout of a structure under static loads. Some studies are focused on dynamic response topology optimization because dynamic forces act in the real world. Dynamic response topology optimization is solved in the time or frequency domain. A method for dynamic response topology optimization in the time domain is proposed using equivalent static loads. Equivalent static loads are static loads that generate the same displacement field as dynamic loads at each time step. The equivalent static loads are made by multiplying the linear stiffness matrix and the displacement field from dynamic analysis and used as multiple loading conditions for linear static topology optimization. The results of topology optimization are again used in dynamic analysis and a cyclic process is used until the convergence criterion is satisfied. The paradigm of the method was originally developed for size and shape optimizations. A new objective function is defined to minimize the peaks of the compliance in the time domain and a convergence criterion is newly defined considering that there are many design variables in topology optimization. The developed method is verified by solving some examples and the results are discussed.