Isogeometric topology optimization method for design with local stress constraints

Engineering structures are required to meet strength conditions to ensure engineering safety, where the maximum stress level of the structure mainly characterizes the structural strength. This study proposes an isogeometric topology optimization method for the local stress-constrained design. This method establishes an optimization model with volume fraction as the objective function and maximum von Mises stress as the constraint condition. The augmented lagrangian approach is introduced to ensure that the design results satisfy stress constraints locally. To increase the convergence rate of stress-constrained topology optimization, we develop a new stress constraint function, and compare it with the other two stress constraint functions proposed by previous research. Sensitivity analysis of the local stress-constraint and volume objective based on an isogeometric topology optimization framework is systematically derived. The design result is compared with the traditional global stress minimization design through typical numerical examples. In addition, this method is extended to the three-dimensional stress-constrained topology optimization design problem that has rarely been studied in the isogeometric-analysis-based topology optimization framework. Several typical numerical examples are presented to demonstrate the method's effectiveness. It demonstrates that the proposed method inherits the merits of the exact geometry and high-order continuity between elements of isogeometric analysis and can effectively control the maximum von Mises stress level of structures, with a faster convergence rate.