Application Of Mesh-free Method In Thermo-elasticity

In the field of engineering which pursues precision simplification and high precision,the contact heat transfer research of structural interface has always been a hot direction.With the research of structural heat transfer,the research is gradually from simple to complex,from macro to micro,from appearance to mechanism,from qualitative to quantitative.The rough characteristics(convex peak and concave Valley on the surface)on the structure surface are becoming the key factors which influence thermal coupling on the interface.Searching for the appropriate calculation method to calculate the thermal coupling phenomenon on the interface are the key to solve the heat transfer in the structure interface.The mesh free method is free from the constraints of the mesh,and the node distribution is used in the computing domain to replace the mesh function.The shape function of the calculation point changes with the change of the calculation point,so it can fully describe the distribution of various field variables.Because the node generation is more convenient,the adaptive performance is superior.By introducing the posterior error control node effectively,the adaptive function is improved The combination of technology and mesh free method can ensure that the nodes can be effectively added to ensure the shape of the boundary while processing the convex convex boundary,and the accuracy of the calculation can be guaranteed.The work of this paper is as follows(1)The basic theory of mesh free Galerkin method(EFG)is introduced systematically.Taking the control equation of two-dimensional transient heat conduction as an example,the derivation process and one-dimensional application example of MLS are given in detail.MLS is applied to the weak formula of Galerkin,and the temperature control equation is discretized and assembled.The Lagrangian multiplier method is used to solve the problem of the essential boundary conditions.Based on the analysis,the difference between the finite element method and the mesh free method is compared in detail.The results show that the accuracy of the method is slightly higher than that of the finite element method.(2)In order to solve the heat conduction problem with convex convex boundary,the adaptive method is introduced into mesh free method,and the node regular increase is controlled by adaptive method,so as to ensure the calculation accuracy of heat conduction problem.(3)The control equations of temperature field and displacement field are discretized by the method of weighted residual value and the variational principle.The two cases of sequential coupling and complete coupling are calculated respectively.In the calculation of smooth boundary,the finite element method is used as a reference to characterize the accuracy and convergence of the mesh free method.(4)In order to solve the problem of fully coupled thermoelastic with convex convex boundary,the adaptive method is introduced into mesh free method.The node is increased regularly by adaptive method,which ensures the calculation accuracy of coupled thermoelastic problem,and provides a new way for the calculation of coupled thermoelastic problems in complex situations.