‘Infinite domain’ elements

Abstract

A parametric element is formulated which enables the economic modelling of 'infinite domain' type problems. A typical problem is an opening in a stress field in an infinite medium, either in two or three dimensions. The strategy is to model around the opening with two or three layers of conventional isoparametric finite elements and surround these with a single layer of 'infinite domain' elements.Several sample problems have been analysed for circular, square and spherical openings in infinite media, and the results compared with either theoretical or boundary element solutions which include the 'infinite' boundary in their solution technique.

Finite element modeling of the three-dimensional tectonic flow and stress field beneath the Kyushu island, Japan.

“…6A, by using a hexahedral isoparametric finite element with 8 nodes (ZIENKIEWICZ, 1977), together with an infinite domain element with 4 nodes and 4 reference points (BEER and MEEK, 1981). We assume a viscous incompressible fluid with a negligible Reynold's number in the present finite element model.…”

Interaction of faults under slip‐dependent friction. Non‐linear eigenvalue analysis

“…The ÿrst one ( 0 ) is a square containing , and is covered by a classical triangulation. The second part ( ∞ ) is covered by inÿnite elements (see Reference [20] for a precise description). Inÿnite elements have two nodes on the exterior boundary of 0 and a third one at inÿnity.…”

The weighted Ritz‐Galerkin method for elliptic boundary value problems on unbounded domains

“…Several numerical methods for these problems were suggested. The following approaches are the most typical: truncating the unbounded part of the domain and introducing an artificial boundary condition on the resulting artificial boundary; coupling boundary element method with FEM [10]; and using infinite elements [11][12][13][14] The basic idea of these approaches is to divide the given unbounded domain ⍀ into two parts: the bounded part ⍀ c ϭ { x ʦ ⍀ : ͉x͉ Յ c} and the unbounded part ⍀ ϱ ϭ ⍀/⍀ c . In [8,[15][16][17], under the assumption that f(x) ϭ 0 on ⍀ ϱ , artificial boundary conditions were set up for the artificial boundaries of the remaining bounded domain ⍀ c .…”

“…Moreover, they are impractical if the support of f(x) is very large. In [11][12][13][14], ⍀ ϱ is partitioned into a finite number of infinite elements incorporated with the meshes on ⍀ c . Then the special decay shape functions are constructed for those infinite elements.…”