ABSTRACT
This paper introduces a technique for computing the Green’s functions using the associated fundamental solutions. 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. Although the fundamental solutions are evaluated by different sets of formulae depending on the location of the concentrated load in the domain, the basic procedures for formulating and solving the boundary value problem for the regular part remain unchanged. The dual problem for obtaining the Green’s function associated with a displacement component or a stress component is formulated and solved with high accuracy using the concept of the fundamental solution. Examples provided illustrate that the new approach is simple to implement and accurate for solving the dual problem. The proposed technique is applied to 2D in this paper, but extension to any linear problem for which fundamental solutions exist is straightforward.
