Generalized Finite Difference Method For Transient Heat Conduction Of Three-dimensional Composite Materials

In contrast to mesh-based numerical methods such as finite element method,the mesh-free method only needs to establish the interpolation basis function through the node information,thus getting rid of the dependence on the mesh to a great extent.It shows obvious superiority when it involves the problems of large deformation,high-dimensional complex domain,dynamic crack propagation and moving boundary,and so on.Among them,the generalized finite difference method(GFDM)is a regional meshless method,which is based on Taylor series expansion and weighted moving least squares fitting.The partial derivatives of physical quantities at any point in the region are expressed as linear combinations of physical quantities at adjacent nodes,which are generally applicable to all kinds of scientific and engineering problems.Similar to the traditional finite difference method,the coefficient matrix generated by the meshless generalized finite difference method is sparse,which can be solved quickly by the standard sparse matrix solver.Composite material is a new kind of material which is made up of two or more kinds of compositional materials by artificial recombination.All kinds of materials take advantage of each other in their properties,so that the comprehensive properties of composite materials are better than that of original materials.In recent years,it has been widely used in the fields of mechanical processing and national defense cutting edge.In view of the important industrial applications of composite materials,many scholars have studied and predicted the mechanical properties of composites by using finite element method,finite difference method and boundary element method.In this paper,the meshless generalized finite difference method is applied to the transient heat conduction analysis of composites for the first time.Firstly,the composite is decomposed into several subdomains along the common interface by using the domain decomposition technique.Then,in each subdomain,the respective generalized finite difference scheme for transient heat conduction is established.Finally,the algebraic equations in each subdomain are solved by using the continuity conditions of temperature and temperature flux at the common interface of composite materials.It is worth noting that the sparse block matrix can be formed by using the domain decomposition method,which is very convenient for the fast solution of the computer.Numerical examples show that the proposed algorithm is accurate and stable,which provides a new idea for accurate numerical simulation of transient heat conduction of composites.