The scaled boundary finite-element method — Alias consistent infinitesimal finite-element cell method — For unbounded media

Abstract

The scaled boundary finite-element method, alias the consistent infinitestimal finite-element cell method, is developed. The governing partial differential equations of linear elastodynamics are transformed to a system of linear second-order ordinary differential equations of displacements as functions of the radial coordinate. Introducing the definition of the dynamic stiffness a system of nonlinear first-order ordinary expansion for high frequency yeilds the boundary condition satisfying the radiation condition. In an application only the boundary of the medium is discretized with surface finite elements yielding a reduction of the spatial dimension by one. No fundamental solution is necessary, and thus no singular integrals must be evaluated. General anisotropic material is analysed without any increase in computational effort. Boundary conditions on free surfaces and on interfaces between different materials are enforced exactly without any discretization. This method is exact in the radial direction and converges to the exact solution in the finite-element sense in the circumferential directions.