On topology optimization of plates with prestress. (English) Zbl 0983.74051

Pedersen, Niels L.

Int. J. Numer. Methods Eng. 51, No. 2, 225-239 (2001).

Summary: We use the topology optimization to optimize the compliance or eigenvalues of prestressed plates. The prestress is accounted for by including a force equivalent to the prestressing, and by adding the initial stress stiffness matrix to the original stiffness matrix. The calculation of sensitivities is complicated because of the initial stress stiffness matrix, but the computational cost can be kept low by using the adjoint method. The topology optimization problem is solved using a method for solid isotropic material with penalization in combination with the method of moving asymptotes. Finally, we give numerical examples of minimizing compliance or maximizing the first eigenvalue of plates (one example is a micro-electro-mechanical system with a backplate used in microphone in hearing aid).

MSC:

74P15	Topological methods for optimization problems in solid mechanics
74K20	Plates

Keywords:

eigenvalue optimization; topology optimization; prestressed plate; initial stress stiffness matrix; adjoint method; solid isotropic material with penalization; method of moving asymptotes; micro-electro-mechanical system