Nonlinear dynamic response topology optimization using the equivalent static loads method

A novel method for nonlinear dynamic response topology optimization is proposed using the equivalent static loads (ESLs) method. The ESLs are the loads that generate the same response field of linear static analysis as that of nonlinear dynamic analysis at each time step. In the proposed procedure, nonlinear dynamic analysis is performed, ESLs are made and linear static topology optimization is carried out with the ESLs. The process cyclically proceeds until the convergence criterion, which is specifically defined for this problem, is satisfied. Since the density method for topology optimization is utilized, the low-density finite elements can cause mesh distortion in nonlinear dynamic analysis. Transformation variables are introduced for a new update method for the incorporating process of the topology results into nonlinear dynamic analysis. Also, a new objective function is proposed to minimize the peaks of the time dependent transient responses. A couple of standard problems and a practical problem are solved to validate the proposed method.