Stress Intensity Factor Of Cracks In Plates Using Multiple Boundary Element Method

Currently, a variety of numerical methods have been widely used to solve the stressintensity factor problem, mainly including the finite element method, boundary elementmethod, mesh-less method and so on. These methods have their own advantages anddisadvantages. Among them, The boundary element method is a technique for solving widerange of solid mechanics problems, which can be originally solved by complex functions.Using Airy function to solve classic isotropic elasticity problems, employing Stroh orLekhnitskii formalism for anisotropic solids, and solving SIF using Muskhelishvili orWestergaard functions, are some of the typical examples in solid mechanics.Stroh formalism is considered as one of the milestones in the field of mechanics ofanisotropic solids. The numerical method based on Stroh formalism is quiet attractive,since analytic Stroh solutions can be found only in infinite or simple shaped solids. Forthis reason, some finite element method based on Stroh formalism has been developed. Inpresent, the boundary element method based on Stroh formalism is rare in literature.In this paper, we have founded a new kind of a form of boundary element methoddirectly based on Stroh formalism. It is called multiple boundary element method(MBEM).In this method, complex functions is adopted as general solutions to the solid mechanicsproblem, and the boundary conditions are represented by complex functions in matrix form,and two new approaches using symbolic or numerical calculations are proposed to split theboundary conditions into several decomposition domains. Finally, the original problem canbe equivalently modeled as multiple Laplace problems in the transformed decompositiondomains, which are solved by multiple boundary element method in convenient way. Atfirst, two mathematical examples are used to demonstrate the MBEM solving combinedcomplex analytic functions in unit cycle and rectangle domains, respectively. Thenumerical solutions of SIFs in cracked rectangle plates with or without hole are obtainedusing the proposed method, and both isotropic material and anisotropic material are considered in computations. It is found that the maximum relative error between the exactand numerical solution is less than5%. The results show that multiple boundary elementmethod is accurate and reliable. Therefore, the proposed method provides a new approachfor anisotropic fracture mechanics.