The scaled boundary finite-element method—alias consistent infinitesimal finite-element cell method—for elastodynamics

Abstract

The scaled boundary finite-element method, alias the consistent infinitesimal finite-element cell method, is developed starting from the governing equations of linear elastodynamics. 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 and fixed 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. For a bounded medium symmetric static-stiffness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption. A stress singularity is represented very accurately, as the condition on the boundary in the vicinity of the point of singularity is satisfied without spatial discretization.