Free vibration analysis of variable stiffness composite laminated beams and plates by novel hierarchical differential quadrature finite elements

The present work deals with the free vibration behavior of the variable stiffness composite laminates (VSCLs) featured by spatially varying fibre orientation angles via novel quasi-three-dimensional solutions. The Carrera Unified Formulation (CUF) is employed to construct such novel models, where cross-section kinematics are described with the improved hierarchical Legendre expansion (IHLE) of primary mechanical variables. The proposed expansions not only maintain the hierarchical properties of the HLE model but also become less sensitive to the numbering sequence of expansion terms. As a result of these enhanced kinematics, Equivalent Single Layer (ESL) and Layer-Wise (LW) models can be formulated more robustly. The weak form differential quadrature finite element method (DQFEM) is employed to solve the governing equations derived by the principle of virtual displacements. Based on CUF-based DQFEM, even a single beam element is sufficient to tackle many complex issues with high accuracy. Compact VSCL beams and plates with various fibre paths, boundary conditions, lamination schemes, and thickness-to-width ratios have been studied in several numerical examples. The proposed method's accuracy and effectiveness are validated by comparing results to published data.