Local Radial Basis Function Collocation Method For Dynamically Coupled Thermoelastic Problems Of Functionally Graded Materials

Functionally graded materials(FGMs)can still maintain good mechanical properties under extreme high temperature environment,so they are widely used in aerospace,nuclear engineering and other high-tech fields.Functional gradient materials are often subjected to thermal impact loads in the process of use,so it is very important to study the dynamic response of functional gradient materials under the effect of thermal impact loads for their safe use and structural optimization design.At present,the dynamic coupled thermoelastic analysis of functionally graded material structures is mainly based on the numerical calculation method of grid class.For complex structures,the workload and time of pre-processing is often more than the computational solution process,and the calculation accuracy is also seriously restricted by the quality of the grid.In recent years,the Local Radial Basis Function Collocation Method(LRBFCM)has developed due to its simple and efficient development.In this paper,meshless local radial basis function collocation Method is applied to the study of thermal impact of functionally gradient materials.Using Backward Difference Method(BDM)for discrete time,the modified Franke formula is introduced to select the ideal shape parameters.By arranging the nodes reasonably,the numerical models of transient heat conduction,elastodynamics and dynamic coupling thermoelasticity of two-dimensional functionally gradient materials are gradually established,which provides a new research idea for dynamic coupling thermoelasticity analysis of functionally gradient materials.By comparing with the numerical results of finite element software COMSOL Multiphysics,the effectiveness of the proposed method was verified.Specific work contents are as follows:(1)Based on transient heat conduction theory,a meshless local radial basis function allocation method for solving two-dimensional transient heat conduction problems of functionally gradient materials is established by adopting the timediscretization scheme of backward difference method.A numerical example is given to verify the accuracy and effectiveness of the proposed method,and the influence of the number of points and time step on the calculation accuracy and stability is discussed.(2)Based on the elastic dynamics theory,the local radial basis function coordination method is used to discretize the two-dimensional elastic dynamics problem of functionally gradient materials in space,the modified Franke formula is used to find the ideal shape parameters,and the backward difference method is used to solve the second order ordinary differential equations after discretization in space to obtain the dynamic response of the structure.A meshless local radial basis function allocation method for elastodynamics problems of two dimensional functionally gradient materials is established.Numerical examples are given to verify the accuracy and effectiveness of the proposed method,and the effects of the number of configuration points and time step on the dynamic response of the structure are studied.(3)Based on the basic theory of linear elastic dynamic coupled thermoelastic problem,the local radial basis function collocation method for the dynamic coupled thermoelastic problem of two-dimensional functionally gradient materials is established.The effectiveness of the proposed method is verified by numerical examples,and the influence of the number of configuration points and time step is studied.Moreover,the coupling influence between temperature field and displacement field under the combined action of thermal load and mechanical load is discussed,which provides a theoretical basis for the simplified calculation of dynamic coupling thermoelastic problem.The numerical results show that the local radial basis function collocation method has the characteristics of simple operation,accurate calculation results and fast convergence when solving the dynamic coupled thermoelastic problem of functionally gradient materials.The methods and procedures in this paper are not only applicable to solving dynamic coupled thermoelasticity problems of functionally graded materials,but also applicable to various degradation situations,such as dynamic coupled thermoelasticity problems of homogeneous materials,pseudo-static thermoelasticity problems,elastodynamics problems of functionally graded materials and transient heat conduction problems of functionally graded materials.