Semi-analytical far field model for three-dimensional finite-element analysis

摘要

A challenging computational problem arises when a discrete structure (e.g. foundation) interacts with an unbounded medium (e.g. deep soil deposit), particularly if general loading conditions and non-linear material behaviour is assumed. In this paper, a novel method for dealing with such a problem is formulated by combining conventional three-dimensional finite-elements with the recently developed scaled boundary finite-element method. The scaled boundary finite-element method is a semi-analytical technique based on finite-elements that obtains a symmetric stiffness matrix with respect to degrees of freedom on a discretized boundary. The method is particularly well suited to modelling unbounded domains as analytical solutions are found in a radial co-ordinate direction, but, unlike the boundary-element method, no complex fundamental solution is required. A technique for coupling the stiffness matrix of bounded three-dimensional finite-element domain with the stiffness matrix of the unbounded scaled boundary finite-element domain, which uses a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co-ordinate system, is described. The accuracy and computational efficiency of the new formulation is demonstrated through the linear elastic analysis of rigid circular and square footings. Copyright