A Parallel‐Computing Based Topology Optimization Method of Bi‐Modulus Material Structures With Large Property Difference

Abstract

Engineering materials frequently exhibit considerable disparities between their tensile and compressive moduli. However, there are some difficulties in existing topology optimization methods for material structures with large disparities between their tensile and compressive moduli. To address this issue, a parallel‐computing based topology optimization method for bi‐modulus material structures with large property differences and deformation control is proposed. The main challenges are twofold: (1) the large discrepancy between tensile and compressive moduli usually leads to convergence difficulties within finite element analysis (FEA); (2) the iterative finite element solution procedure imposes a heavy computational burden during the topology optimization process. For the first challenge, new four‐node membrane element formulas with rotational DOFs, which can generate a diagonally dominant stiffness matrix, and an FEA modified model algorithm are proposed, and the form of a smooth elastic modulus matrix related to principal strain states is introduced. These measures ensure the diagonal dominance of the element stiffness matrix, and importantly relieve the FEA difficulty of bi‐modulus material structures with large differences in tensile and compressive moduli, thereby overcoming convergence issues and improving the accuracy of iterative calculations for displacements and strains. To improve computational efficiency, an algorithm based on the Gershgorin circle theorem is proposed to estimate the largest eigenvalue of a two‐level preconditioner matrix integrating diagonal and Chebyshev preconditioners. Subsequently, a novel diagonal‐Chebyshev bi‐level preconditioned conjugate gradient iterative method based on Graphics Processing Units is developed, which significantly reduces the computation time of bi‐modulus material structural optimization. Finally, two numerical examples are presented. Results demonstrate that the proposed method can generate reasonable optimal topologies for the aforementioned bi‐modulus material structures, further verifying the feasibility and superior computational efficiency of the proposed optimization methodology.