5. Conclusions
Nonlinear dynamic response topology optimization is performed using ESLSO with the transformation variables and the newly defined objective function. In ESLSO, nonlinear analysis is performed, ESLs are generated at each time step, linear static response topology optimization is carried out the ESLs and the process cyclically proceeds until the convergence criteria are satisfied. The transformation variables which correspond to the design variables are defined to overcome the mesh distortion problem that is a typical obstacle in nonlinear response topology optimization. After linear static response topology optimization, if the value of a design variable is smaller than a certain value, the corresponding transformation variable is 0. Otherwise, the corresponding transformation variable is 1. The elements for the transformation variables with zeros are eliminated in the FE model for nonlinear dynamic response analysis. The proposed objective function is to minimize the weighted summation compliance near the peak points to prevent a large deformation at a certain time. The newly proposed ESLSO is applied to two examples that are a simple plate structure and the crash box for the crashworthiness design. The results show that the proposed method provides quite an excellent solution. It is well known that nonlinear dynamic response optimization is quite expensive for a large scale structure. The results of the examples show that the process terminates in a few cycles with ESLSO. It means that only a few nonlinear dynamic analyses are required. Additional research is needed as well. For example, a technique to determine the separation parameter for the transformation variable should be established, or various responses such as the stresses and eigenvalues should be considered in the objective function or constraints.
