A novel robust stress-based multimaterial topology optimization model for structural stability framework using refined adaptive continuation method

Considering both stress and stability factors in topology optimization is of great importance from both theoretical and practical perspectives. This work proposes an efficient stress-based structural stability approach to the topology optimization framework using multiple materials. Specifically, descriptions of the multimaterial structure’s layout defining interpolated material tensors are performed using the generalized solid isotropic material with the penalization (SIMP) method. To achieve this, a rule for determining the difference between solid and empty regions is used to keep the buckling constraint active while avoiding the appearance of pseudo modes. Also, an extendedly refined adaptive continuation method (RACM) is developed for the first time for multimaterial problems under stability constraints to determine the penalization parameter values so that the buckling constraints are appropriately considered throughout the optimization process. This automatic scheme for adjusting the penalization parameter is introduced to deal with the conflict between structural stiffness and stability requirements, thus achieving better designs. In addition, the von Mises stresses of the elements are aggregated using a P-norm function to measure the global stress level. The density filter is then utilized to suppress the checkerboard formation in each topological phase of the current approach’s material distribution. The method of moving asymptotes (MMA) is used as an optimizer to update density design variables in the optimization process. The mathematical expressions of the proposed method are delivered in detail. Several numerical examples are presented to illustrate the effectiveness of the proposed method. Overall, the proposed approach considers both stress and stability factors rigorously and systematically, and the results demonstrate its effectiveness in producing better designs in topology optimization problems involving multiple materials.