Micro-frame structure design method using shape and topology optimization based on H¹ gradient method

Abstract

In this study, we propose a non-parametric shape-topology optimization method for tailoring the static deformation of micro-frame structures. The design objective is to minimize the sum of squared error norms for achieving the desired displacements on specified members. The shape gradient function, the topology gradient function, and the optimality conditions for this problem are theoretically derived with the Lagrange multiplier method, the material derivative method, adjoint variable method, SIMP and GSIMP method. The sensitivity functions for this problem are applied for the H¹ gradient method for frame structures. With the proposed method, the optimal arbitrarily formed frame structures will be obtained without any shape and topology parameterization while maintaining their smoothness. Optimum design examples are demonstrated and the results are discussed.