A dipole method of fundamental solutions applied to Reissner’s plate bending theory

Mohareb, Sherif; Rashed, Youssef F.

doi:10.1016/j.mechrescom.2009.08.005

Cited by 8 publications

(1 citation statement)

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“…The stationary condition (that corresponds to the equilibrium condition) for such a functional represents an approximate integral equation of the problems to approximate the domain terms ( ( ) ( ) ( )) in the first four integrals in equation (25). As in the indirect boundary element or the super-position formulation for Ressiner's plate bending problems (Mohareb and Rashed [10]),the rotation and the displacement components vector at any point (y) inside the domain could be approximated via a collection series. This series contains the product of fundamental solution ( ( )) and an unknown set of fictitious concentrated tractions ( ( )) located at a set of arbitrary source points ( ), as follows:…”

Section: The Proposed Bem Hybrid Displacement Formulationmentioning

confidence: 99%

A Hybrid Displacement Boundary Element Formulation for Reissner Plate With Quadratic Elements

Naga¹,

Rashed²

2014

Proceedings of the 3rd South-East European Conference on Computational Mechanics (SEECCM III)

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Abstract. 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, 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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Section: The Proposed Bem Hybrid Displacement Formulationmentioning

confidence: 99%