Abstract
Increasing applications of laminated composite structures necessitate the development of equivalent single layer (ESL) models that can achieve similar accuracy but are more computationally efficient than 3D or layer-wise models. Most ESL displacement-based models do not guarantee interfacial continuity of shear stresses within laminates. A possible remedy is the enforcement of interlaminar equilibrium in variational formulations, for example, in the framework of the Hellinger-Reissner variational principle, leading to a mixed force/displacement model. In this paper, the governing equations for bending and stretching of laminated beams, comprising only seven stress resultants and two displacement functionals, are obtained using global fifth-order and a local linear zigzag kinematics. As a strong-form solution technique, the differential quadrature method (DQM) is an efficient tool which can provide excellent convergence with relatively few number of grid points. However, in dealing with high-order differential equations, the conventional DQM can incur considerable errors due to the nature of numerical differentiation. Therefore, a mixed inverse differential quadrature method (iDQM) is proposed herein to solve the governing fourth-order differential equations for bending and stretching of laminated beams. This approach involves approximating the first derivatives of functional unknowns, thereby reducing the order of differentiation being performed. Using a non-uniform Chebychev-Gauss-Lobatto grid point profile, numerical results show that the accuracy of stress predictions is improved by using iDQM compared to DQM. In addition, the Cauchy’s equilibrium condition is satisfied more accurately by iDQM, especially in the vicinity of boundaries.
Original language | English |
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Pages (from-to) | 66-87 |
Number of pages | 22 |
Journal | International Journal of Solids and Structures |
Volume | 210–211 |
Issue number | 66–87 |
Early online date | 23 Nov 2020 |
DOIs | |
Publication status | Published - Feb 2021 |
Bibliographical note
Funding Information:L.C. Trinh, S.O. Ojo and P.M. Weaver would like to acknowledge funding from the Science Foundation Ireland (SFI) for the award of a Research Professor grant (Varicomp: 15/RP/2773). R.M.J. Groh would like to acknowledge the Royal Academy of Engineering under the Research Fellowship scheme [Grant No. RF\201718\17178].
Publisher Copyright:
© 2020 Elsevier Ltd
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Royal Academy of Engineering Research Fellow
Groh, R. (Recipient), 2018
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