On topology optimization of plates with prestress

In this work, topology optimization is used to optimize the compliance or eigenvalues of prestressed plates. The prestress is accounted for by including the force equivalent to the prestressing and adding the initial stress sti ness matrix to the original sti ness matrix. The calculation of the sensitivities is complicated because of the initial stress sti ness matrix, but the computational cost can be kept low by using the adjoint method. The topology optimization problem is solved using the solid isotropic material with penalization (SIMP) method in combination with method of moving asymptotes (MMA). Numerical examples of minimizing compliance or maximizing the rst eigenvalue of plates are given. One example is a micro electro mechanical systems (MEMS) application involving a backplate used in a microphone in a hearing aid