This research presents a new adjoint sensitivity analysis for repeated eigenvalues and topology optimization scheme. Despite the vast researches regarding the eigenvalue optimization problems, there are few examples considering mode shapes in topology optimization. For the structural topology optimization with the eigenmodes especially with the repeated eigenmodes, we propose to use a general adjoint variable approach developed for structural topology optimization for the repeated eigenvalue problem. Furthermore, this research presents a new method to track repeated eigenmodes during optimization. To validate the present approach, we compare the sensitivity values from the finite difference method, the direct method (the Dailey's method), and the adjoint sensitivity analysis method. To show the validity of the present approach, some benchmark problems are considered and included.
This work was supported by the National Research Foundation of Korea (NRF) grant fundedby the Korea government (MSIT) (No.2018R1A5A7025522).