Research On Static And Dynamic Multi-Objective Topology Optimization Based On Variable Density Method

Topology optimization is an efficient algorithm to optimize the structure distribution in a given region according to the given load and boundary conditions,constraints and material parameters.The main research of topology optimization includes continuum topology optimization and geometric element topology optimization.Continuum topology optimization is to divide the material in the design area into a finite number of elements(shell element or volume element)with fixed characteristics,and complete the optimization design with the help of the continuous change of element density;Topology optimization of geometric elements is to establish a base structure composed of a limited number of elements with fixed characteristics in the design area,and then determine the movement and deformation of elements in the design space according to the given conditions.The remaining elements constitute the final topology scheme,so as to realize topology optimization.Stress constrained topology optimization is a kind of structural optimization algorithm to alleviate the phenomenon of structural stress concentration.In this paper,the topology optimization based on stress constraint is carried out by combining p-norm rule.The derivation and verification are carried out from theoretical and numerical simulation examples,and an efficient algorithm for solving the topology optimization of continuum structure under stress constraint is given.The proposed algorithm combines density filter for length and size control,solid isotropic material(SIMP)for black and white design,stress definition for stress singularity and normalization scheme for local stress control.At the same time,the static and dynamic multi-objective algorithm is used to further improve the local optimal solution phenomenon of stress constrained topology optimization.Although the topology optimization of continuum structure based on variable density method has achieved rapid development,the inefficiency of traditional design methods also appears with the increasing scale of structure and more complex objectives and constraints.In this paper,an explicit topology optimization method based on element density is introduced.The final optimal structure is described by discrete geometry.Numerical examples show that this method has the advantages of high efficiency and clarity,and is an effective means to break through the shortage of computing resources in the future.At the same time,due to the limited design space of the geometric projection explicit topology optimization method,it is easy to fall into the local optimal solution.In this paper,the static and dynamic multi-objective method is used for reference.By reducing the dynamic frequency eigenvalue of the structure in the design process,and considering the multi-order natural frequency at the same time,the design optimization method is further improved,Several examples show that this method is efficient and practical,the specific research contents are as follows:(1)The basic principle of topology optimization is introduced systematically,and the finite element method is described in detail.(2)The basic principle and method of continuum stress constrained topology optimization are described in detail,and an example is given to illustrate.At the same time,the algorithm combined with dynamic frequency optimization is used to optimize the topology optimization results.(3)The explicit topology optimization method based on geometric projection is described in detail.The geometric definition,distance calculation and projection formula of explicit topology optimization based on geometric projection are derived in detail.(4)In the explicit topology optimization method based on geometric projection,this paper innovatively adopts the method of reducing the multi-order natural frequency of the structure in the process of topology optimization,and verifies the correctness of the proposed method by combining with the classical examples.