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Elastodynamic boundary element method for piecewise homogeneous media
Author(s) -
Birgisson B.,
Crouch S. L.
Publication year - 1998
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19980730)42:6<1045::aid-nme398>3.0.co;2-d
Subject(s) - boundary element method , bounded function , mathematics , boundary (topology) , interpolation (computer graphics) , element (criminal law) , quadratic equation , displacement (psychology) , domain (mathematical analysis) , mathematical analysis , piecewise linear function , piecewise , traction (geology) , finite element method , time domain , computer science , geometry , structural engineering , engineering , animation , psychology , mechanical engineering , computer graphics (images) , law , political science , computer vision , psychotherapist
A general higher‐order formulation for the time domain elastodynamic direct boundary element method is presented for computing the transient displacements and stresses in multiply connected two‐dimensional solids. The displacement and traction interpolation functions are linear in time and quadratic in space. All integrations are analytical, and are expressed in terms of twelve basic recurring integrals. Causality is ensured by integrating only over the dynamically active parts of each element, and the algorithm presented is time‐marching and implicit. The use of analytical integrations allows both unbounded and bounded domain problems to be solved without having to introduce special enclosing elements. All of these improved features allow for a formulation that is very efficient and accurate. The stability and accuracy of the elastodynamic boundary element algorithm is demonstrated by solving several example problems and comparing the results with available analytical and numerical solutions. © 1998 John Wiley & Sons, Ltd.