Research On Local Basic Solutions For Some Mechanical Problems Of Composite Materials

The localized method of fundamental solutions(LMFS)is a relatively new domaintype meshless collocation method.This paper makes the first attempt to apply the LMFS,in conjunction with a domain-decomposition technique,for the numerical solution of 2D anisotropic heat conduction problems and the 2D/3D transient convection-diffusionreaction equations.In the LMFS method,the entire computational domain should be divided into a set of local subdomains,and in each of the local subdomain,the classical MFS approximation is applied to construct the local systems of linear equations.The LMFS method will finally yield a banded and sparse matrix system,which can be solved very quickly by various sparse matrix solvers.Compared with the traditional mesh-based numerical methods,such as the finite element(FEM)and boundary element(BEM)methods,the LMFS avoids the time-consuming mesh generation process as well as the tedious numerical quadrature,and thus,highly improves the computational efficiency and saves the cost of numerical computation in the simulation process.Prior to this study,the LMFS method has been successfully applied to 2D Laplace and biharmonic equations,3D heat conduction equations,and 2D and 3D elasticity problems.In the present study,we document the first attempt to apply the LMFS method for large-scale simulations of layered materials.The main attention is focused on the numerical simulations of anisotropic heat conduction and the transient convection-diffusion problems.As the numerical examples illustrated,the LMFS method still keeps the advantage of simplicity of the traditional MFS and yet be able to solve the large-scale and complex problems effectively.In short,the proposed numerical algorithm can be used to solve engineering applications studied here very accurately,stably and effectively.