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Isogeometric boundary integral formulation for Reissner’s plate problems

Ahmed K. Abdelmoety (Department of Structural Engineering Department, Cairo University, Giza, Egypt)
Taha H.A. Naga (Department of Engineering Mathematics and Physics Department, Faculty of Engineering – Shoubra, Benha University, Cairo, Egypt)
Youssef F. Rashed (Department of Structural Engineering Department, Cairo University, Giza, Egypt)

Engineering Computations

ISSN: 0264-4401

Article publication date: 30 July 2019

Issue publication date: 16 January 2020

Abstract

Purpose

This paper aims to develop a new isogeometric boundary element formulation based on non-uniform rational basis splines (NURBS) curves for solving Reissner’s shear-deformable plates.

Design/methodology/approach

The generalized displacements and tractions along the problem boundary are approximated as NURBS curves having the same rational B-spline basis functions used to describe the geometrical boundary of the problem. The source points positions are determined over the problem boundary by the well-known Greville abscissae definition. The singular integrals are accurately evaluated using the singularity subtraction technique.

Findings

Numerical examples are solved to demonstrate the validity and the accuracy of the developed formulation.

Originality/value

This formulation is considered to preserve the exact geometry of the problem and to reduce or cancel mesh generation time by using NURBS curves employed in computer aided designs as a tool for isogeometric analysis. The present formulation extends such curves to be implemented as a stress analysis tool.

Keywords

Citation

Abdelmoety, A.K., Naga, T.H.A. and Rashed, Y.F. (2020), "Isogeometric boundary integral formulation for Reissner’s plate problems", Engineering Computations, Vol. 37 No. 1, pp. 21-53. https://doi.org/10.1108/EC-11-2018-0507

Publisher

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Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited