Topology Optimization Method And Its Application Under Thermal-Mechanical Loads Based On Element Differential Method

Topology optimization is an important auxiliary design method for structural design of engineering products,which can effectively reduce the design cycle and cost,improve the design efficiency and the performance of product structure.The problem of the interaction of thermal and mechanical loads exists in the research and manufacturing fields of engine,internal combustion engine,thermal machinery and so on.Therefore,the topology optimization design considering thermal and mechanical loads has important theoretical research significance and practical application value.Finite element method is a commonly used analysis method of thermal-mechanical problems,which has the advantages of strong adaptability and easy to understand.However,finite element method can not directly analyze the thermal load,and it needs to carry out the equivalent integral treatment,which leads to the tedious and lengthy calculation process.In this thesis,the element differential method is studied.Taking the continuum structure as the research object,the topology optimization method of continuum structure under the thermal-mechanical load based on the element differential method is proposed.The main research work includes:Firstly,the theory of topological optimization method of continuum structure based on variable density is studied.Aiming at the problem that the boundary of topological structure is not clear due to the existence of gray-scale elements,an improved gray-scale element suppression method and boundary processing algorithm are proposed.The former mainly applies penalty function to the update operator of design variable in optimization criterion method.By increasing the penalty factor step by step in optimization,the density value of elements in the optimization result is oriented to the set density value of solid material.The second one is a quadratic optimization algorithm,which sharpens the boundary of the structure by redistributing the density gradient of the elements to enhance the filtering of the gray elements.Test cases show that the proposed algorithm can obtain a clear boundary topology.Secondly,the theoretical model of the element differential method is studied.According to the algorithm characteristics of the element differential method,the adaptive configuration processing method of the element differential method is studied,simplified the configuration process of the node equation to speeds up the solution efficiency.This paper discusses and analyzes the influence of different element models on the accuracy and efficiency of the results in the thermal-mechanical application scenario,and explores the specific performance of the element differential method in dealing with different problems.The validity and convergence of the element differential method are verified by an experimental case.At last,aiming at the topology optimization of continuum structure under thermalmechanical load,two kinds of topology optimization objective models based on element differential method are proposed.The topology optimization model is analyzed,according to the algorithm characteristics of the optimization objective model,the solution process of the optimization model is analyzed,and the specific implementation and optimization process of the optimization algorithm are discussed and analyzed.Based on the test cases of sandwich panel and bridge etc,the results of topology optimization under different working conditions are analyzed and discussed,and compared with the results of traditional topology optimization model to verify the effectiveness and superiority of topology optimization model.The experimental results show that the proposed topology optimization model can improve the performance of the structure and improve the topology.