University of Limerick
Trinh_Groh_Zucco_Weaver_Strain_Displacement_DQM_Compos_B.pdf (1.88 MB)

A strain-displacement mixed formulation based on the modified couple stress theory for the flexural behaviour of laminated beams

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journal contribution
posted on 2021-02-08, 14:12 authored by Luan C. Trinh, Rainer M.J. Groh, Giovanni ZuccoGiovanni Zucco, Paul M. Weaver
A novel strain-displacement variational formulation for the flexural behaviour of laminated composite beams is presented, which accurately predicts three-dimensional stresses, yet is computationally more efficient than 3D finite element models. A global third-order and layer-wise zigzag profile is assumed for the axial deformation field to account for the effect of both stress-channelling and stress localisation. The axial and couple stresses are evaluated from the displacement field, while the transverse shear and transverse normal stresses are computed by the interlaminar-continuous equilibrium conditions within the framework of the modified couple stress theory. Then, axial and transverse force equilibrium conditions are imposed via two Lagrange multipliers, which correspond to the axial and transverse displacements. Using this mixed variational approach, both displacements and strains are treated as unknown quantities, resulting in more functional freedom to minimise the total strain energy. The differential quadrature method is used to solve the resulting governing and boundary equations for simply-supported, clamped and cantilever laminated beams. The deflections and stresses from this variational formulation for simply supported beams agree well with those from a Hellinger-Reissner stress-displacement mixed model found in the literature and the 3D elasticity solution given by Pagano. These strain-displacement models also accurately predict the localised stresses near clamped and free boundaries, which is confirmed by the high-fidelity Abaqus models.



Composites Part B: Engineering;185, 107740





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SFI, Royal Academy of Engineering


This is the author’s version of a work that was accepted for publication in Composites Part B: Engineering Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Composites Part B: Engineering



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