Stress Topology Optimisation for Architected Material Using the Level Set Method

This paper presents a stress-based level set topology optimisation method applied to microstructural design of architected material. Microscopic architected material systems are of interest due to the rise of additive manufacturing. Multiscale topology optimization leads to small members that may be more prone to high stress. The main contribution herein will be the combination of microstructural optimization with a von Mises stress p-norm functional. This type of function has been used to address the local nature issue of stress in macroscale design, approximating the maximum stress in the structure with a single function. The p-norm stress shape sensitivities will be presented using the material derivative method. The proposed level set method formulates a sub-optimization problem in each iteration and uses mathematical programming to obtain the optimal boundary velocities. The Ersatz material approach is used to link the level set method with the finite element structural analysis. First, numerical results for the macroscale are presented to show that stress concentrations are removed. Finally, a microstructural stress analysis based on the homogenization method is devised to reduce stress levels in microstructural topology optimization.

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