ABSTRACT
The scaled boundary finite-element method (SBFEM) a novel semi-analytical method of computational mechanics combining advantage of finite-element method with advantages of the boundary element method, was originally developed by Wolf and Song (1996) for dynamic analysis of unbounded domains. Only the boundary is discretized as in the boundary element method. No fundamental solution is necessary as in the finite-element method. General anisotropic materials can be analyzed without additional efforts. The method proved far more versatile than initially envisaged and was extended successfully to static and bounded domains (Wolf & Song, 1996). It is extended to dynamic the analysis of non-homogeneous unbounded domains with the elasticity modulus and mass density varying as power functions of spatial coordinates (Bazyar & Song 2006). In this method, the analytical nature of the solution in the radial direction allows accurate stress intensity factors in fracture mechanics to be determined directly from the definition. In statics, an eigen-value problem is solved leading to displacement and stress amplitudes. In the frequency domain, the scaled boundary finiteelement equation is expressed in terms of dynamicstiffness matrix being a system of nonlinear first order ordinary differential equations in the independent excitation frequency. In the time domain, the scaled boundary finite-element equation in acceleration unitimpulse response including convolution integrals is obtained.
