Development of a novel non-positive definite correspondence modified optimality criteria method for multi-objective density-based topology optimization

Abstract

The aim of this study is to propose a new modified optimality criteria method for non-positive definiteness in multi-objective density-based topology optimization problems. Our proposed modified optimality criteria method is a density update method that was developed by incorporating the concept of Newton's method into the conventional optimality criteria method. Topology optimization for strain energy minimization and von Mises stress minimization problems were performed separately, and actual experiments revealed the characteristics of each. Each optimization problem setting has its individual advantages: strain energy minimization is computationally stable, whereas von Mises stress minimization obtains a higher-strength structure. Therefore, in this study, to take advantage of both, we performed multi-objective optimization using the modified optimality criteria method. Since updating was not possible with the previously proposed modified optimality criteria method in multi-objective optimization problems, we propose incorporating mapping to enable it to be updated. As a numerical example problem, topology optimization was performed on the MBB beam model and gripper model for a robotic arm using the conventional optimality criteria method and our proposed mapping-based modified optimality criteria method to compare the update methods. Numerical example of the MBB beam model demonstrate that the mapping-based modified optimality criteria method is independent of the move-limit and can be updated. The mapping-based modified optimality criteria method also has a small number of arbitrary parameter settings that can cause problems for engineers because the weighting factor in the optimality criteria method is set in each element. Numerical example of the gripper model are used here to investigate the speed of updating the mapping-based modified optimality criteria method and guidelines for setting the appropriate weight coefficients of performance function to create a design.