A Robust Multiscale Topology Optimization for Fracture Resistance Based on Phase Field Method and Interval Model

  • Zhao, Wang (Beihang University)
  • Fan, Jiang (Beihang University)

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Conventional multiscale topology optimization mainly focuses on objectives such as stiffness and strength, making it difficult to effectively deal with existing damage and crack path dependence problems. Concurrently, the impact of multiple sources of uncertainty on the service performance and safety of structures. Hence, we consider uncertain factors containing load and material properties, and establish a robust topology optimization framework based on the fracture phase field to reduce the disturbance caused by uncertain factors. The phase field model is employed to describe damage, without the need for pre-set crack paths or remeshing, making it easy to combine with topology optimization. The equivalent elastic modulus and equivalent critical energy release rate are calculated based on the homogenization method, and these equivalent physical quantities are used to calculate the robustness index of the structure for its macroscopic and microscopic sensitivities. The interval model is employed to describe uncertainty factors, characterize fracture resistance with external force response, and construct corresponding robustness indicators. In response to the strong nonlinear relationship between external force work response to uncertain parameters, we employ the interval collocation method to calculate the response boundary. The validity and effectiveness of the proposed method are substantiated by numerical examples. The results show that the proposed method can enhance the robustness against uncertainties compared to deterministic optimization. Furthermore, under the same volume constraint, it achieves superior fracture resistance through multiscale design over single-scale topology optimization.