Peridynamics‐Based Topology Optimization for Fracture Resistance Structures Under Quasi‐Static Loading

ABSTRACT This paper presents a topology optimization method based on peridynamics, considering the entire fracture process under quasi‐static loadings. By simulating the complete crack propagation behavior under quasi‐static loadings and employing the unique “bond” concept from peridynamics, the fracture performance is effectively quantified through a damage factor. The improvement of fracture resistance is achieved by directly controlling the elongation rate of the bonds. However, under quasi‐static loading conditions, repeated sensitivity analysis is required which demands prohibitively high computational cost. To deal with the problem, a preset actual crack is introduced in each of the optimization iteration steps during the entire loading process. Consequently, the repeated sensitivity calculation of functionals whose values are dependent on displacement history become unnecessary. This approximation technique maintains computational efficiency while ensuring analytical accuracy. Numerical examples verify the effectiveness of the proposed method, and the results obtained demonstrate better fracture resistance performance than that from static analysis.