Research On Structural Topology Optimization Methods Based On Topological Sensitivity

Structural topology optimization is to find the optimal design of material distribution in a given conditions under load.Generally speaking,the structural stiffness is selected as the optimization goal,and the essence is to use the energy principle to reduce the strain energy of the structure as much as possible under the constraint conditions of the structure.In this paper,topological sensitivity is introduced to structural topology optimization,and a method of structural topology optimization based on topological sensitivity is proposed.It is applied to structural topology optimization of compliance minimization and structural topology optimization of stress minimization.Main work is as follows.Firstly,the optimal structural judgement criterion based on topological sensitivity is established.Shape derivative has been adopted to infer the mathematical expression of topological sensitivity.And a judgment criterion based on the topological sensitivity is established.The topology sensitivity is used to drive the structure boundary evolution,and the optimal structure is judged on the basis of the criterion.The validity of the optimal structural judgment criterion is verified by comparative analysis.Secondly,a structural topology optimization method based on topological sensitivity for compliance minimization is proposed.The structural topology optimization model of the compliance minimization is constructed,and the sensitivity analysis of the compliance target function is carried out based on the topological sensitivity,and the compliance topological sensitivity field of the structure is established.The Gauss filtering technique is used to filter the sensitivity,and a linear and smooth high dimensional function field is obtained.Taking the volume step size decreasing,the topological structure under the current volume constraint is obtained.The optimal structural judgement criterion based on topological sensitivity is used to screen out the optimal topology.Through an exact example,we get the clear and smooth boundary of structure.Thirdly,this thesis propose a structural topology optimization method based on topological sensitivity for stress minimization.The global stress is used to measure the overall stress level of the structure.The structural topology optimization model of the stress minimization structure is constructed.The sensitivity analysis of the global stress objective function is carried out based on the topological sensitivity,and the stress topological sensitivity field of the structure is established.Taking the volume step size decreasing,we obtain the topology structure under the current volume constraint,and select the optimal topology by using the optimal structural judgement criterion based on topological sensitivity.Combined with an example,the maximum stress can be obtained as small as possible.Finally,the paper is summarized and the future research directions are prospected.