Stress-constrained level set topology optimization method based on subregional P-norm measurement

In stress-dependent topology optimization (TO), the design structure is highly dependent on stress constraints, and significant stress concentration is prone to occur near structural discontinuities and rigid constraints. Therefore, this paper proposes a TO method for level-set structures, incorporating a subregional P-norm stress constraint. The level set method is independent of the physical model and may delineate the border with greater clarity while precisely defining the stress of the boundary element, so circumventing the ambiguity associated with the variable density method’s boundary representation. Firstly, the structural topology optimization (STO) model with stress penalty is established by employing P-norm stress as a constraint and volume fraction as the objective function, integrated with the parametric level set approach. Secondly, a sensitivity analysis utilizing shape derivatives is conducted, and the TO problem is addressed using the moving asymptote approach, achieving STO with volume minimization under a stress constraint. The P-norm subregional stress-constrained topology optimization method exhibits enhanced stability and a more uniform structure in areas of stress concentration, as evidenced by two engineering cases.