Analysis of Concentrated Boundary Loads in the Scaled Boundary Finite Element Method

Abstract

The scaled boundary finite element method models linear elastostatics problems excellently and out-performs the finite element method (FEM) when solving problems involving unbounded domains or stress singularities. This paper introduces a technique for solving concentrated boundary load problems using the scaled boundary finite element method. By employing fundamental solutions for the displacements and the stresses, the solution is computed as summation of a fundamental solution part and a regular part. The singularity of the solution is modelled exactly by the fundamental solution, and only the regular part, which enforces the boundary conditions of the domain onto the fundamental solution, needs to be approximated in the solution space of the basic scaled boundary finite element method.