Topology optimization of multi-directional variable thickness thin plate with multiple materials

This study firstly presents a multi-material topology optimization approach for thin plates with variable thickness based on Kirchhoff plate theory. For this purpose, an alternating active-phase algorithm in conjunction with the block Gauss-Seidel method is utilized to transform a multiphase topology optimization problem with multiple volume fraction constraints to many binary phase topology optimization sub-problems with only one volume fraction constraint. Accordingly, the number of design variables depends only on one active phase in each of those sub-problems no matter how many phases the original problem are. In addition, moved and regularized Heaviside function (MRHF) that plays the role of a filter is also investigated in the framework of multiple materials field. The mathematical formulations of stiffness and complaint sensitivity with respect to multi-directional variable thickness linked to thin plate potential energy are derived in terms of multiphase design variables. Numerical examples demonstrate interactions of variables thickness and multiple materials to thin mid-plates with the same amount of volume fraction and total structural volume.