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Research Papers

A Variational Boundary Element Formulation for Shear-Deformable Plate Bending Problems

[+] Author and Article Information
Taha H. A. Naga

Assistant Lecturer
Faculty of Engineering (Shoubra),
Department of Engineering Mathematics and Physics,
Benha University,
Benha, Egypt

Youssef F. Rashed

Professor
Deputy Secretary General,
Supreme Council of Universities in Egypt;
Department of Structural Engineering,
Cairo University,
Giza, Egypt
e-mail: youssef@eng.cu.edu.eg

1Corresponding author.

Manuscript received December 12, 2011; final manuscript received January 31, 2013; accepted manuscript posted February 11, 2013; published online July 12, 2013. Assoc. Editor: Glaucio H. Paulino.

J. Appl. Mech 80(5), 051004 (Jul 12, 2013) (11 pages) Paper No: JAM-11-1469; doi: 10.1115/1.4023623 History: Received December 12, 2011; Revised January 31, 2013; Accepted February 11, 2013

This paper presents the derivation of a new boundary element formulation for plate bending problems. The Reissner's plate bending theory is employed. Unlike the conventional direct or indirect formulations, the proposed integral equation is based on minimizing the relevant energy functional. In doing so, variational methods are used. A collocation based series, similar to the one used in the indirect discrete boundary element method (BEM), is used to remove domain integrals. Hence, a fully boundary integral equation is formulated. The main advantage of the proposed formulation is production of a symmetric stiffness matrix similar to that obtained in the finite element method. Numerical examples are presented to demonstrate the accuracy and the validity of the proposed formulation.

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Figures

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Fig. 1

Cantilever plate subject to edge load

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Fig. 5

Effect of source point location on results

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Fig. 2

Annular plate under edge load

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Fig. 3

The cantilever plate divided into two parts

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Fig. 4

The considered degrees of freedom for each part

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