A Meshless Generalized Finite Difference Method For Stress Analysis Of Composite Materials

In recent years,with the rapid development of industrial technology,more and more new high-performance materials have been synthesized.Among them,composite materials composed of single or multi-domain materials have been widely used in engineering.For example,the coating domain of the coating material can protect the substrate material from corrosion and reduce wear,which greatly enhances mechanical properties of the overall material.In view of the important industrial uses of composite materials,many scholars have used finite element,finite difference,boundary element and other numerical calculation methods to study and predict the mechanical properties of composite materials.The main work of this paper is using the generalized finite difference method to study the mechanical properties of composite materials.The generalized finite difference method is a kind of regional meshless method,which has just been developed in recent years.This method combines the multivariate function Taylor series expansion with the weighted least squares theory,and the partial derivative of the unknown function of the governing equation is expressed as a linear combination of its nearby function values.This method largely overcomes the dependence of grid-based numerical methods on the grid,such as traditional finite element.Involving large deformations,thin body and coating structures,and crack propagation problems,this method shows significant advantagesFor the first time,the generalized finite difference method is extended to the stress analysis of multi-domain composites.First,the domain decomposition technique is used to decompose the composite material into multiple sub-domains along the common interface.Then,in each sub-domain,its corresponding elastic mechanics generalized finite difference method discrete format is established.Finally,the algebraic equations,in each sub-domain,are coupled to solve by using the displacement and surface force continuous conditions of the composite interface.It should be pointed out that the use of the region decomposition method can form a sparse block matrix,which is very convenient for the computer to solve quickly.Numerical examples show that the proposed algorithm is accurate and stable,which provides a new idea for the accurate numerical simulation of the mechanical properties of composite materials.