The scaled boundary finite-element method - a fundamental solution-less boundary-element method

In this boundary-element method based on finite elements only the boundary is discretized with surface finite elements yielding a reduction of the spa tial dimension by one. No fundamental solution is necessary and thus no sin gular integrals must be evaluated and general anisotropic material can be a nalysed. For an unbounded (semi-infinite or infinite) medium the radiation condition at infinity is satisfied exactly. No discretization of free and f ixed boundaries and interfaces between different materials is required. The semi-analytical solution inside the domain leads to an efficient procedure to calculate the stress intensity factors accurately without any discretiz ation in the vicinity of the crack tip. Body loads are included without dis cretization of the domain. Thus, the scaled boundary finite-element method not only combines the advantages of the finite-element and boundary-element methods but also presents appealing features of its own. After discretizin g the boundary with finite elements the governing partial differential equa tions of linear elastodynamics are transformed to the scaled boundary finit e-element equation in displacement, a system of linear second-order ordinar y differential equations with the radial coordinate as independent variable , which can be solved analytically. Introducing the definition of the dynam ic stiffness, a system of nonlinear first-order ordinary differential equat ions in dynamic stiffness with the frequency as independent variable is obt ained. Besides the displacements in the interior the static-stiffness and m ass matrices of a bounded medium and the dynamic-stiffness and unit-impulse response matrices of an unbounded medium are calculated. (C) 2001 Elsevier Science B.V. All rights reserved.