Topological Optimization Of Stress Constraints Based On Reaction-diffusion Equation

Topology optimization design is the process of establishing an objective function based on the design requirements of the structure such as strength,stiffness,and stability,and finding the optimal solution under various constraints.Among them,the continuum topology optimization method considering the design of the maximum rigidity of the structure is relatively mature.However,there are still some problems that need to be solved for topology optimization under stress constraints.The main reason is that the topology optimization problem under stress constraints has such difficulties as stress singularity,excessive number of constraint functions and highly nonlinear problems about design variables.The research work of this paper is to use the phase field function to deal with the stress-constrained topology optimization problem.At the same time,a combination of BESO and phase field method is also proposed to deal with the stress topology optimization problem.In this paper,a topology optimization method based on phase field description is used to find the optimal layout of a continuum structure that exhibits asymmetric strength behavior in tension and compression.According to the Drucker-Prager yield criterion and power rate interpolation scheme,the optimization problem can be described as minimizing the volume of the structure under local stress constraints.The pq relaxation method is used to solve the singularity problem of local stress constraints,and the aggregation method based on p-norm function is used to condense the stress constraints.This method reduces the number of constraints and introduces STM method to deal with a large number of stress constraints and highly nonlinear stress behavior to correct stress and improve stability of optimization convergence.When solving optimization problems,the Lagrange multiplier method is used to deal with the stress constraints.The adjoint variable method is used for sensitivity analysis,and the phase field function design variables are updated by solving the Allen-Cahn equation.Numerical examples demonstrate the effectiveness of this optimization model and the effectiveness of corresponding numerical techniques.At the same time,it was also found that the optimal design of the structure with stress-dependent materials may exhibit a different topology results compared to the stress-independent material model.Because the topology optimization result of the phase field function depends on the initial layout of the structure,Therefore,this paper uses the advantages of the BESO method that does not rely on the initial layout to combine with the phase field method,uses the BESOto generate holes,and then uses the phase field method to update the variables.At the same time,the results of topology optimization are combined with mature commercial software hypermesh to deal with the post-processing problems of topology optimization.