Research On Multi-level Method For The Optimization Of Fiber Reinforced Composite Structure Based On Parametric Divergence-free Vector Field

Because of its excellent mechanical properties,fiber reinforced composites are more and more used in practical engineering,and its optimal design has also been widely concerned.Aiming at the problem that the efficiency of optimization solution decreases with the increase of optimization scale,this paper integrates the multi-level optimization idea into the optimization method based on parametric divergence-free vector field to optimize the fiber layout of fiber-reinforced composite structure,and explores the influence of the configuration mode of each level on the multi-level optimization results.First,In this paper,the parametric divergence-free vector field is used to describe the fiber layout,which ensures that the fiber path is not intersected and meets the necessary conditions of the manufacturing process for the fiber layout.Taking the expansion coefficient of the parametric divergence-free vector field as the design variable,The method of moving asymptotes algorithm is used to optimize the design.Secondly,In order to solve the problem that the optimization efficiency decreases when the design variables increase,a multi-level optimization method is proposed.The optimization problem is divided into rough to fine levels,and the fiber layout is optimized in a progressive way.In the first layer,large step size and relaxed convergence condition are adopted to obtain the general trend of fiber layout with minimum computational cost;In the last level of optimization,small steps and strict convergence conditions are used to ensure the quality of optimization results.Numerical examples show that multi-level optimization can effectively improve the optimization efficiency.Finally,in multi-level optimization,different levels can have different configurations,so the influence of the configuration mode of multi-level optimization method on the optimization results is studied.Several numerical examples are compared from the optimization results of the objective function,the total number of iterations and the calculation time.It is found that the layout of sample points and the density of the finite element mesh in multiple levels have a significant impact on the optimization efficiency and effect,and the reasonable configuration method is summarized.