The scaled boundary finite element method: Analytical solution in frequency domain
type: Item
instance of: scholarly article
title: The scaled boundary finite element method: Analytical solution in frequency domain
zbMATH Open document ID: 0982.74072
DOI: 10.1016/S0045-7825(98)00058-9
author: Chongmin Song
author: John P. Wolf
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2000-06-07T00:00:00Z
review text: A new procedure derived from the boundary finite element method (BFEM) is presented. This procedure is called the scaled BFEM since the author introduces a scaling parameter \(\xi\). The idea is based on the fact that around a node supporting a shape function \(N(\xi,\eta)\), it is possible to define a new radial coordinate \(\xi\). For a domain with a boundary defined by the segmentation with \(\xi=1\), its interior is defined by a family of shapes with \(\xi< 1\), whereas its exterior is defined by the family of shapes with \(\xi> 1\). By this way, an optimization procedure (such as Galerkin one) provides a system of ordinary differential equations in the radial coordinate \(\xi\). Solving these equations, the authors obtain an analytical solution in frequency domain. Comparison of the proposed procedure with other known methods validate the approach.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74J99
zbMATH DE Number: 1421618
zbMATH Keywords: scaled boundary finite element method
zbMATH Keywords: shape function
zbMATH Keywords: radial coordinate
zbMATH Keywords: optimization procedure
zbMATH Keywords: system of ordinary differential equations
zbMATH Keywords: analytical solution
zbMATH Keywords: frequency domain
reviewed by: Dumitru Stanomir
MaRDI profile type: Publication
cites work: Q4339012
cites work: CONSISTENT INFINITESIMAL FINITE-ELEMENT CELL METHOD: THREE-DIMENSIONAL VECTOR WAVE EQUATION
cites work: The scaled boundary finite-element method - alias consistent infinitesimal finite-element cell method - for elastodynamics
cites work: Q3254327
cites work: Q5689624
cites work: A Schur method for solving algebraic Riccati equations
full work available at URL: s0045-7825(98)00058-9
OpenAlex ID: W2046168696
description: scientific article; zbMATH DE number 1421618