Polygonal topology optimization for Reissner-Mindlin plates

Polygonal finite elements have recently been widely implemented in topology optimization problems due to their great advantages such as highly accurate solutions and flexibility in mesh generation of arbitrary-shaped design domains. In this study, a polygonal topology optimization for Reissner-Mindlin (R-M) plate with minimizing the compliance under a volume constraint is proposed. In order to avoid the critical transverse shear locking phenomenon arising in the R-M plate theory, a simple and efficient locking-free polygonal R-M plate element (PRMn) based on the Timoshenko's beam assumptions is applied to solve the R-M plate topology optimization problems. In our proposed method, we use the solid isotropic material with penalization model, the standard optimality criteria methods and density filter.