Scaled boundary finite element method with circular defining curve for geo-mechanics applications

Abstract

This paper presents an efficient and accurate numerical technique based upon the scaled boundary finite element method for the analysis of two-dimensional, linear, second-order, boundary value problems with the domain completely described by a circular defining curve. The scaled boundary finite element formulation is established in a general framework allowing single-field and multi-field problems, bounded and unbounded bodies, distributed body source, and general boundary conditions to be treated in a unified fashion. The conventional polar coordinates together with a properly selected scaling center are utilized to achieve the exact description of the circular defining curve, exact geometry of the domain, and exact spatial differential operators. A general solution of the resulting system of linear, second-order, nonhomogeneous, ordinary differential equations is constructed via standard procedures and then used together with the boundary conditions to form a system of linear algebraic equations governing nodal degrees of freedom. The computational performance of the implemented procedure is then fully investigated for various scenarios within the context of geo-mechanics applications.

Keywords:

exact geometry; geo-mechanics; multi-field problems; SBFEM; scaled boundary coordinates.