A new trigonometric zigzag theory for buckling and free vibration analysis of laminated composite and sandwich plates

In this work, a new trigonometric zigzag theory is proposed for the analysis of laminated composite and sandwich plates. The theory is based upon shear strain shape function assuming non-linear distribution of transverse shear stresses. It satisfies the necessary conditions of inter-laminar stress continuity at the layer interfaces as well as the condition of zero transverse shear stresses at the top and bottom surfaces of the plates. The theory has the same number of unknown field variables as that of FSDT and the number of unknowns is layer independent which makes the solution computationally more efficient. A C0 continuous isoparametric serendipity element is employed to solve the discrete eigenvalue equations arising in both the problems. The accuracy and the efficiency of the theory are thus demonstrated through numerical experiments on the free vibration and stability analysis of laminated composite and sandwich plates with different modular ratio, aspect ratio, span to thickness ratio, loading and boundary conditions, ply orientations, lay-up number, eigen modes, etc. Higher modes with corresponding mode shapes of vibration and buckling are also represented for laminated composite and sandwich plates. An elegant performance of the proposed theory is observed when it is validated with relevant numerical examples.

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