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An exact GITT solution for static bending of clamped parallelogram plate resting on an elastic foundation

An exact GITT solution for static bending of clamped parallelogram plate resting on an elastic... The purpose of this study is to propose generalised integral transform technique (GITT) to obtain the exact solutions for bending of clamped parallelogram plate resting on elastic foundation.Design/methodology/approachThe GITT is used to solve the bending problem of the full clamped parallelogram plate under an elastic foundation. The auxiliary problem was developed and the corresponding eigenfunction and eigenvalue were calculated simultaneously. The original partial differential governed equation has been represented by the transformed ordinary differential equation system and solved by the subroutine DBVPFD from International Mathematics and Statistics Library.FindingsThe GITT has been proven to be an efficient approach to solve the bending problem of the plate with different loads, boundary conditions and elastic foundations. The parametric study indicates that the elastic foundation modulus has significant contribution in reducing the vertical deflections and moments for both rectangular and parallelogram plates. With the increasing of aspect ratio (a/b) and the elastic foundation modulus, the trends of the deflection and moment reduction decreased significantly.Originality/valueThe present hybrid analytical-numerical methodology was first used to solve the mechanics problem of the clamped parallelogram plate resting on elastic foundation. Excellent convergence and high accuracy was observed by comparing with the published results. It exhibits potential application to investigate the mechanics problem of the composite plate with different boundary conditions in the shipbuilding and civil engineering. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Engineering Computations: International Journal for Computer-Aided Engineering and Software Emerald Publishing

An exact GITT solution for static bending of clamped parallelogram plate resting on an elastic foundation

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References (27)

Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
0264-4401
DOI
10.1108/ec-12-2018-0582
Publisher site
See Article on Publisher Site

Abstract

The purpose of this study is to propose generalised integral transform technique (GITT) to obtain the exact solutions for bending of clamped parallelogram plate resting on elastic foundation.Design/methodology/approachThe GITT is used to solve the bending problem of the full clamped parallelogram plate under an elastic foundation. The auxiliary problem was developed and the corresponding eigenfunction and eigenvalue were calculated simultaneously. The original partial differential governed equation has been represented by the transformed ordinary differential equation system and solved by the subroutine DBVPFD from International Mathematics and Statistics Library.FindingsThe GITT has been proven to be an efficient approach to solve the bending problem of the plate with different loads, boundary conditions and elastic foundations. The parametric study indicates that the elastic foundation modulus has significant contribution in reducing the vertical deflections and moments for both rectangular and parallelogram plates. With the increasing of aspect ratio (a/b) and the elastic foundation modulus, the trends of the deflection and moment reduction decreased significantly.Originality/valueThe present hybrid analytical-numerical methodology was first used to solve the mechanics problem of the clamped parallelogram plate resting on elastic foundation. Excellent convergence and high accuracy was observed by comparing with the published results. It exhibits potential application to investigate the mechanics problem of the composite plate with different boundary conditions in the shipbuilding and civil engineering.

Journal

Engineering Computations: International Journal for Computer-Aided Engineering and SoftwareEmerald Publishing

Published: Aug 15, 2019

Keywords: GITT technique; Bending solution; Elastic foundation; Parallelogram plate

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