Stresses around a square tunnel using a meshless scaled boundary method

Deeks, A.J.; Augarde, C.E.

Abstract

The scaled boundary finite element method (SBFEM) combines advantages of the conventional displacement finite element method (FE) and the boundary element method for problems in solid mechanics. In the SBFEM, a “scaling centre” is defined for a domain which becomes the origin of a polar coordinate system. From this origin, conventional FE type approximation is used in the circumferential direction, combined with an analytical solution in the radial direction. The SBFEM has many advantages over more popular methods, including accurate solutions at singularity points and exact solutions for unbounded (i.e. infinite) domains. Another area of current interest in numerical modelling is “meshless methods” where no elements are required, thus removing the need for mesh generation, a major overhead in many conventional FE calculations. In this paper we outline a recent development of the SBFEM where shape functions from a “meshless method”, rather than a conventional Galerkin approach, are used for the circumferential approximation. This consists of a moving least squares approximation with spline functions as interpolants. Incorporation of these shape functions requires relatively small changes to the SBFEM to a Petrov-Galerkin formulation. Issues arise such as the numbers of nodes required at boundary edges as discussed in the paper. As an example of the new method, the stresses around a square tunnel in a linear elastic soil, with insitu prestress, are studied. It is shown that the new method is both more economical (in terms of degrees of freedom) and accurate than other (currently) more popular approaches.

Citation

Deeks, A., & Augarde, C. (2004, April). Stresses around a square tunnel using a meshless scaled boundary method. Presented at 12th ACME Conference, Cardiff

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 12th ACME Conference
• Publication Date: 2004-04
• Public URL: https://durham-repository.worktribe.com/output/1679560