Summary
The frequency and buckling equations of rectangular plates with various boundary conditions are developed within the third-order and the first-order shear deformation plate theories. The third-order theories account for a quadratic distribution of the transverse shear strains through the thickness of the plate. In the first part of this paper, Levinson's third-order theory, derived as a special case from Reddy's third-order theory, is used to study a plate laminated of transversely isotropic layers. The relationship between the original form of the governing equations and the interior and the edge-zone equations of the plate is closely examined and the physical insights from the latter equations are established. In the second part of the paper, the first-order shear deformation theory and the third-order theory of Reddy are studied for vibration and buckling.
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Nosier, A., Reddy, J.N. On vibration and buckling of symmetric laminated plates according to shear deformation theories. Acta Mechanica 94, 123–144 (1992). https://doi.org/10.1007/BF01176647
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DOI: https://doi.org/10.1007/BF01176647