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A quasi-3D hyperbolic shear deformation theory for functionally graded plates

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Abstract

A quasi-3D hyperbolic shear deformation theory for functionally graded plates is developed. The theory accounts for both shear deformation and thickness-stretching effects by a hyperbolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the top and bottom surfaces of the plate without requiring any shear correction factor. The benefit of the present theory is that it contains a smaller number of unknowns and governing equations than the existing quasi-3D theories, but its solutions compare well with 3D and quasi-3D solutions. Equations of motion are derived from the Hamilton principle. Analytical solutions for bending and free vibration problems are obtained for simply supported plates. Numerical examples are presented to verify the accuracy of the present theory.

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Authors and Affiliations

  1. School of Civil and Environmental Engineering, The University of New South Wales, Sydney, Australia

    Huu-Tai Thai

  2. Faculty of Engineering and Environment, Northumbria University, Newcastle upon Tyne, NE1 8ST, UK

    Thuc P. Vo

  3. Department of Civil Engineering, University of Siegen, Paul-Bonatz-Str. 9-11, 57076, Siegen, Germany

    Tinh Q. Bui

  4. Faculty of Civil Engineering and Applied Mechanics, University of Technical Education Ho Chi Minh City, 1 Vo Van Ngan Street, Thu Duc District, Ho Chi Minh City, Vietnam

    Trung-Kien Nguyen

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  1. Huu-Tai Thai
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  2. Thuc P. Vo
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  3. Tinh Q. Bui
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  4. Trung-Kien Nguyen
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Correspondence to Huu-Tai Thai.

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Thai, HT., Vo, T.P., Bui, T.Q. et al. A quasi-3D hyperbolic shear deformation theory for functionally graded plates. Acta Mech 225, 951–964 (2014). https://doi.org/10.1007/s00707-013-0994-z

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  • DOI: https://doi.org/10.1007/s00707-013-0994-z

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