Boundary Element Methods in Dynamic Analysis: Part II (1986-1996)
01 Mar 1997-Applied Mechanics Reviews (American Society of Mechanical Engineers)-Vol. 50, Iss: 3, pp 149-197
About: This article is published in Applied Mechanics Reviews.The article was published on 1997-03-01. It has received 509 citations till now. The article focuses on the topics: Boundary knot method & Boundary element method.
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TL;DR: In this paper, a methodology for solving numerically, for engineering purposes, boundary and initial boundary value problems by a peculiar approach characterized by the following features: the continuous formulation is centered on integral equations based on the combined use of single-layer and double-layer sources, so that the integral operator turns out to be symmetric with respect to a suitable bilinear form.
Abstract: This review article concerns a methodology for solving numerically, for engineering purposes, boundary and initial-boundary value problems by a peculiar approach characterized by the following features: the continuous formulation is centered on integral equations based on the combined use of single-layer and double-layer sources, so that the integral operator turns out to be symmetric with respect to a suitable bilinear form. The discretization is performed either on a variational basis or by a Galerkin weighted residual procedure, the interpolation and weight functions being chosen so that the variables in the approximate formulation are generalized variables in Prager’s sense. As main consequences of the above provisions, symmetry is exhibited by matrices with a key role in the algebraized versions; some quadratic forms have a clear energy meaning; variational properties characterize the solutions and other results, invalid in traditional boundary element methods enrich the theory underlying the computational applications. The present survey outlines recent theoretical and computational developments of the title methodology with particular reference to linear elasticity, elastoplasticity, fracture mechanics, time-dependent problems, variational approaches, singular integrals, approximation issues, sensitivity analysis, coupling of boundary and finite elements, and computer implementations. Areas and aspects which at present require further research are identified, and comparative assessments are attempted with respect to traditional boundary integral-elements. This article includes 176 references.
292 citations
TL;DR: In this paper, a 2.5D finite/infinite element procedure for dealing with ground vibrations induced by moving loads is proposed, where the profile of the half-space is divided into a near field and a semi-infinite far field, and the near field containing loads and irregular structures is simulated by finite elements, while the far field covering the soils extending to infinity by the infinite elements with due account taken of the radiation effects for moving loads.
Abstract: The objective of this study is to propose a 2.5D finite/infinite element procedure for dealing with the ground vibrations induced by moving loads. Besides the two in-plane degrees of freedom (DOFs) per node conventionally used for plane strain elements, an extra DOF is introduced to account for the out-of-plane wave transmission. The profile of the half-space is divided into a near field and a semi-infinite far field. The near field containing loads and irregular structures is simulated by the finite elements, while the far field covering the soils extending to infinity by the infinite elements with due account taken of the radiation effects for moving loads. Enhanced by the automated mesh expansion procedure proposed previously by the writers, the far field impedances for all the lower frequencies are generated repetitively from the mesh created for the highest frequency considered. Finally, the accuracy of the proposed method is verified through comparison with a number of analytical solutions. Copyright © 2001 John Wiley & Sons, Ltd.
254 citations
Cites methods from "Boundary Element Methods in Dynamic..."
...Previously, a number of methods have been employed for modelling the far $eld with in$nite domain, including the boundary element method [7–9], consistent boundary [10; 11], various transmitting boundaries [12; 13], consistent in$nitesimal $nite-element cell method [14], and in$nite elements [15–29]....
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TL;DR: The scaled boundary finite element method as mentioned in this paper is a semi-analytical fundamental-solutionless boundary-element method based solely on finite elements, which is used to solve the wave propagation problem.
240 citations
Proceedings Article•
01 Jan 1998TL;DR: In this paper, the LCH-CONF-1998-009 Record created on 2007-04-24, modified on 2016-08-08, was used as a reference.
Abstract: Note: [255] Reference LCH-CONF-1998-009 Record created on 2007-04-24, modified on 2016-08-08
238 citations
TL;DR: In this paper, a general and fully three dimensional multi-body-finite element-boundary element model, formulated in the time domain to predict vibrations due to train passage at the vehicle, the track and the free field, is presented.
234 citations