| Meshless method is an emerging numerical calculation method,which only requires a series of flexible arrangement nodes to construct shape function.Compared with finite element method,finite volume method,finite difference method and other numerical calculation methods based on mesh technique,meshless method can alleviate the mesh constraint of node and mades the preprocess simplify.Besides,meshless method can efficiently solve the problem of mesh dependence and checkerboard in topology optimization.As a potential method ? Element-free Galerkin(EFG)method,EFG method is used to analyze the two dimensional steady and transient heat transfer problems of anisotropic materials in this paper.In addition,the paper has also utilized EFG method to study the topology optimization of thermal structures from isotropic materials to anisotropic materials.Meanwhile,some computing programs have been developed based on MATLAB platform.The main research contents are summarized as follows:Firstly,the transform model of thermal conductivity for anisotropic materials was established using matrix transform method.The calculation model of steady heat transfer under mixed boundary conditions was established using EFG method,and the essential boundary condition was enforced by the penalty method.The correctness of the heat transfer calculation model was verified through some numerical examples.The calculation model was also introduced into engineering problem in practices,and the effects of the orientation angle of anisotropic materials and orthotropic factors on temperature field were explored.It was verified that the calculation accuracy of EFG method was not affected by the distribution patterns of nodes.The effects of scaling factors,penalty factors and weight functions on the calculation accuracy of temperature using EFG method for different orthotropic factors were evaluated,and the rational suggestions were provided,respectively.Secondly,according to the numerical heat transfer theory and EFG method,the calculation model of transient heat transfer under mixed boundary conditions was established,and the feasibility of the present model was verified.Based on the discrete Galerkin scheme of time domain,the transient heat transfer analysis of practical engineering problem for different anisotropic materials were performed by using MATLAB programs.The relationship between the thermal property parameters of the anisotropic materials and transient temperature were analyzed.It was indicated that EFG method has a higher accuracy and better stability than finite element method,and the rational time steps were provided.Thirdly,the mathematical model of topological optimization for thermal structure was established by integrating EFG method with rational approximation of material properties(RAMP)model,and the node density and minimum heat dissipation were selected as the design variable and the objective function,respectively.A series of typical examples were solved and the correctness of the proposed model was verified.Moreover,the topological optimization of thermal structure for anisotropic materials was studied based on the transform model of thermal conductivity for anisotropic materials.The effects of the orientation angle of anisotropic materials and orthotropic factors on the optimal topological structure were also studied.The temperature field of optimal topological structure was analyzed by EFG method.The significant references for the topology optimization design of thermal structures in future were provided.The EFG method has been introduced into the two dimensional heat transfer problems and topological optimization of anisotropic materials successfully in the paper,and the application field of EFG method has been extended.Complex engineering problem in practices have been analyzed by the established models,and the numerical solutions have good stability,convergence and calculation accuracy.It not only has high academic theories,but also has important values in engineering application. |
PDF Full Text Request