Research On Thermoelastics Analysis And Thermo-Mechanical Coupling Topology Optimization Of Orthotropic Material Based On Meshless Method

The thermo-elastic analysis and structural optimization design of composite structures are currently hot and challenging research topics.At present,the thermo-elastic analysis and structural optimization design of composite structures are mainly based on numerical methods based on the mesh.The pre-processing workload is huge for complex three-dimensional problems.The workload is often larger than the calculation and analysis itself,and the calculation accuracy is seriously restricted by the mesh.The mesh will be seriously distorted especially when solving the problems of moving boundary and optimization design problems.At this time,the computational domain must be reconstructed.The meshless method is a rapidly developing numerical method.It can get rid of mesh during the construction of shape function.Meanwhile,meshless method can efficiently avoid numerical instability problems such as checkerboard in topology optimization design since it does not require meshing.In this paper,the thermo-elastic analysis of anisotropic material is studied based on the element-free Galerkin(EFG)method.Based on this,a thermo-mechanical coupled topology optimization model is established to explore the thermo-mechanical coupling topology optimization problem of anisotropic material.The main research contents are summarized as follows:Firstly,combining EFG method with the thermo-elastic theory,the calculation model of steady thermo-elastic problem for anisotropic material under thermal and mechanical loads was established.The essential boundary condition was enforced by penalty method and the reasonable range of penalty factor was given.The correctness of the calculation model was verified through several engineering examples.Meanwhile,the effects of the off-angle and orthotropic material factors on thermal deformation and thermal stress were explored.Secondly,the calculation model of transient thermo-elastic problem for anisotropic material was established based on EFG method and the implicit backward difference scheme was used to discrete the time domain.Several engineering examples with complex geometry shape were calculated to verify the correctness of the calculation model and calculation programs.The influence of time step on the computational stability of EFG method was discussed,and the reasonable time step was given.Also,the influence of weight function on the accuracy of EFG method was discussed.What is more,the effects of the off-angle and orthotropic material factors on the EFG transient thermal deformation and thermal stress were studied.Meanwhile,the EFG calculation results were compared with FEM results at any time,which showed the advantages of EFG method in calculation accuracy and numerical stability.Thirdly,combining EFG method and the variable density method,the thermo-mechanical topology optimization model for anisotropic structures based on EFG method was established.The EFG topological results were compared with FEM to verify the correctness of the proposed model.Meanwhile,the effects of the weight factor,the orthotropic material factors,off-angle and volume fraction on the results of thermo-mechanical topology optimization were explored based on EFG method.Meanwhile,the EFG optimal structures were manufactured by 3D printing technology.The results showed that the boundaries of the EFG optimal structures were clear and easy to manufacture.Finally,the heat transfer and mechanical analysis of the structures before and after topology optimization was conducted using EFG method,and the results were compared to verify the effectiveness of the optimal structures.The thermo-elastic problem and thermo-mechanical coupling topology optimization for anisotropic material under the thermal and mechanical loads are studied based on meshless method.The results show that EFG method has high calculation accuracy,and is suitable for solving the thermal deformation and thermal stress of two-dimensional and three-dimensional complex engineering problems.Meanwhile,the outline and boundaries of the optimal structures obtained by EFG thermo-mechanical coupling topology optimization are clear and easy to manufacture.It can promote the application of topology optimization method in engineering.The research has good theory and engineering application value.