Bending, vibration and buckling of simply supported thick multilayered orthotropic plates: An evaluation of a new displacement model

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Abstract

Based upon a piecewise linear displacement field which allows the contact conditions for the displacements and the transverse shearing stresses at the interfaces to be satisfied simultaneously, the non-linear (in the von Kármán sense) equations of motion for thick multilayered orthotropic plates are developed. Successively, the equations are specified to the linear boundary value problem of the bending and to the linear eigenvalue problems of the undamped vibration and buckling of rectangular plates. In order to assess the accuracy of the proposed theory, the sample problem of the bending, free undamped vibration and buckling of a three-layered, symmetric cross-ply, square plate simply supported on all edges is investigated. For purposes of comparison, numerical results from the exact elasticity theory, the classical lamination (Kirchhoff) theory and the shear deformation theory (Timoshenko and Mindlin) with three different values of the shear correction factor are also presented. It is found that the proposed approach is very efficient in predicting the global responses (deflection, natural frequencies and buckling loads) of thick multilayered plates and models effects, such as the distortion of the deformed normals, not attainable from the classical lamination theory, as well as the shear deformation theory.

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