Triangular C⁰ continuous finite elements based on refined zigzag theory {2,2} for free and forced vibration analyses of laminated plates

This study presents a finite element formulation to perform vibration analysis of laminated composite plates based on the Refined Zigzag Theory of order {2,2}, namely RZT-{2,2}. This theory considers the transverse stretching by introducing quadratic through-thickness variations of both in-plane and transverse displacement components. Also, it eliminates the use of shear correction factors and is highly suitable for the analyses of thick and heterogeneous laminated plates. The governing equations of the RZT-{2,2} are derived based on Hamilton's principle. The stiffness matrix, consistent mass matrix, and load vector of the governing equations are constructed by adopting anisoparametric interpolation functions associated with a triangular element that involves three corner nodes and three mid-side nodes along its edges. The corner nodes consist of eleven kinematic variables while each mid-side node possesses only three deflection components. An adaptive time-stepping algorithm is employed with an optimum time increment determined automatically at each time step, thus, eliminating the stability concerns. The capability of the present approach is demonstrated by considering several benchmark cases regarding free vibration analysis. The effect of transverse stretching is revealed through the dynamic characteristics of the laminated composite plates. In the case of forced vibration analysis, the accuracy of the present approach is established through comparison with three-dimensional finite element models.