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A Galerkin symmetric and direct BIE method for Kirchhoff elastic plates: formulation and implementation
Author(s) -
Frangi Attilio,
Bonnet Marc
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(19980130)41:2<337::aid-nme287>3.0.co;2-g
Subject(s) - regularization (linguistics) , mathematics , galerkin method , mathematical analysis , displacement (psychology) , boundary element method , integration by parts , finite element method , weak formulation , bending of plates , boundary (topology) , boundary value problem , bending , structural engineering , computer science , engineering , psychology , artificial intelligence , psychotherapist
Abstract A variational Boundary Element formulation is proposed for the solution of the elastic Kirchhoff plate bending problem. The stationarity conditions of an augmented potential energy functional are first discussed. After addressing the topic of the choice of the test functions, a regularization process based on integrations by parts is developed, which allows to express the formulation in terms of double integrals, the inner being at most weakly singular and the outer regular. Standard integration procedures may then be applied for their numerical evaluation in the presence of both straight and curved boundaries. The normal slope and the vertical displacement must be C 0 and C 1 continuous, respectively. Numerical examples show, through comparisons with analytical solutions, that a high accuracy is achieved. © 1998 John Wiley & Sons, Ltd.