Topology Optimization For The Design Of Heat Conduction Structures Based On The Variable Density Method

In the area of aerospace,automotive industry,integrated circuits and other manufacturing industries,the thermal protection of equipment structure has been a hot topic for scholars to discuss.The traditional experience-based design methods has been unable to meet the needs of the practical engineering.The development of the topology optimization technology has opened up a new way for the design of the heat insulation and heat dissipation structures.This paper studies the topology optimization design of the thermal conduction structures based on the variable density method.Starting from both macro and micro scales,the topology optimization design of the macro thermal structure and thermal conduction microstructure is carried out respectively.On this basis,the porous structure with thermal conductivity is studied in detail,and the multi-scale topology optimization design of the heat conduction structure is realized finally.The main work is as follows:Firstly,for the problem of the gray scale elements appearing frequently in the variable density method,this paper puts forward a new filtering method and applies it to the topology optimization design of macroscopic heat dissipation structure.By introducing a combination of sensitivity filtering and grayscale filtering into the new filtering method,it can effectively suppress the generation of gray-scale elements in the optimization process.At the same time,the preconditioned conjugate gradient method has been introduced into the designing of the 3-D heat dissipation structure,which greatly improves the efficiency of optimization.Ultimately,the 2-D and 3-D examples have verified the effectiveness of the proposed method.Secondly,for the design-ability of the porous composite material,this article researches the topology optimization design of the microstructure of heat conduction under the microscopic scale,based on the homogenization theory.An optimization model with the weighted combination of the equivalent heat conduction coefficients as the optimization target has been proposed,which is solved by the improved OC method.The gray-scale element is also suppressed by the filtering method above.In the end,the validity and rationality of the proposed model and method are verified by four typical examples.Finally,for the macrostructure design and microstructure design mentioned above,this thesis studies the multi-scale topology optimization design of the heat conduction structure systematically,and comes up with a new multi-scale concurrent optimization design method based on the heat conduction structure.The two-scale optimization model is also solved by the improved OC method.The multi-scale topology optimization design of the thermal conductivity structure is realized by several examples,which provides important guiding significance for the heat dissipation problem in practical engineering application.