Boundary element method for vibration analysis of two-dimensional anisotropic elastic solids containing holes, cracks or interfaces

By using the anisotropic elastostatic fundamental solutions and employing the dual reciprocity method, a special boundary element method (BEM) was developed in this paper to perform elastodynamic analysis of anisotropic elastic plates containing holes, cracks or interfaces. The system of ordinary differential equations obtained for the vibration transient analysis was solved using the Houlboltʹs algorithm and modal superposition method. These equations were reduced to the standard eigenproblem for free vibration, and a purely algebraic system of equations for steady-state forced vibration. Since the fundamental solutions used in the present BEM satisfy the boundary conditions set on the holes, cracks, or interfaces, no meshes are needed along these boundaries. With this special feature, the numerical examples presented in this paper show that to get an accurate result much fewer elements were used in the present BEM comparing with those in the traditional BEM or finite element method.