Topology optimization of laminated plates with prestress

Laminated plates with different prestress in the layers are topology optimized. The objectives are to minimize the deflection due to the prestress or to minimize ordinary compliance. The prestress is accounted for by including the force equivalent to the prestressing and adding the initial stress stiffness matrix to the structural stiffness. The calculations of sensitivities are complicated not only by the prestress but also because we are dealing with laminates. The topology optimization problem is solved using a new penalization scheme as an alternative to the SIMP (power law) approach. In the examples we are optimizing a practical micro-electro-mechanical systems (MEMS) application involving a backplate used in a microphone for hearing aids. In this MEMS application the prestress level is very high.