Efficient stress topology optimization based on multigrid preconditioned conjugate gradient method
GAO Dawei
CAI Shenli
SHI Guijie
ZHANG Lunping
Abstract：[Objective]Large calculation scale and slow convergence speed exist in structural stress topology optimization.Considering the computational requirements of large-scale finite element analysis,the multigrid preconditioned conjugate gradient(MGCG)method was adopted to reduce the solution cost and improve the computational efficiency of stress-constrained topology optimization.[Methods]Firstly,based on the framework of the solid isotropic material with penalization method,a topology optimization model with dual constraints of stress and compliance was constructed with structure volume minimization as the optimization objective.The P-mean function was used to relax local stress constraints into global stress constraints,providing mathematical support for the optimization solution.Secondly,starting from the adjoint sensitivity of the global stress measurement,the element-level sensitivity calculation formula was derived to improve the efficiency of sensitivity analysis.Then,the MGCG method was applied to accelerate the solution of finite element linear equations.The approximate inverse preconditioner of the stiffness matrix was constructed using the V-cycle strategy and damped Jacobi smoother to accelerate the convergence of the iterative solver.Finally,combined with density filtering and Heaviside projection to eliminate gray elements and checkerboard effect,the method of moving asymptotes was used to update design variables,forming a complete optimization process.[Results]The results show that the MGCG method can significantly accelerate the iterative convergence process of topology optimization.On the premise that the optimized structure meets the constraints of stress and compliance,the total calculation time is reduced by 11.1％-18.2％compared with the traditional variable density method.When the penalty coefficient of the P-mean function is set to 50,the stress concentration can be effectively alleviated,and the stress concentration factor is reduced by 41.87％.Meanwhile,a 0-1 binary topology configuration with clear boundaries can be obtained,which provides reference for the efficient solution of similar stress topology optimization problems.
Keywords：Structural topology optimizationStress constraintMultigrid preconditioned conjugate gradient methodSolid isotropic material with penalization method
Publication Date：2026-08-15
Online Publishing Date：2026-09-12(First online date of this platform, not the publication date of the document)
Pages：8( 37-44 )