Dynamic topology optimization of hyperelastic materials based on an adaptive total Lagrangian material point method
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An adaptive total Lagrangian material point method for topology optimization (Top-ATLMPM) is proposed for hyperelastic materials involving massive deformation within a dynamic framework. The optimization formulation aims to minimize the structural compliance using the solid isotropic material with penalization method under volume constraints. During the topology optimization process for structures subjected to massive deformation, solution strategies based on the finite element method have been reported to suffer from mesh distortion. In this paper, a mesh-free method, called the material point method (MPM), is extended for topology optimization involving massive deformation, which significantly enhances the robustness. The dynamic topology optimization is then developed by the total Lagrangian discrete formulation for MPM with explicit time integration. Sensitivities are computed using the adjoint method within the dynamic response, and the optimization problem is solved by the method of moving asymptotes. Furthermore, the background grid of MPM is adaptively refined in the design domain to capture the structural boundary delicately, which significantly reduces the degrees of freedom and improves the efficiency of the topology optimization problems. Several representative examples, both in two- and three dimensions, are presented to verify the effectiveness of the proposed Top-ATLMPM for dynamic topology optimization of hyperelastic materials, and the computational cost shows remarkable improvement.
