FE Implementation of an Inverse-Cotangent HSDT for Laminated Composite Rectangular Plates

This study presents a finite-element (FE) implementation of a novel inverse-cotangent higher-order shear deformation theory (nICSDT) for the static bending analysis of laminated composite rectangular plates. The key innovation of the proposed formulation is the incorporation of a non-polynomial inverse-cotangent shear function that naturally satisfies traction-free transverse shear conditions at the plate surfaces, thereby eliminating the need for empirical shear correction factors. In addition, symbolic through-thickness integration is employed to derive closed-form laminate stiffness matrices, resulting in enhanced numerical stability and improved computational efficiency compared to conventional HSDTs.The theory is implemented using an eight-node C0-continuous quadrilateral finite element and validated against benchmark results for (0/90) and (0/90/0) cross-ply laminates subjected to sinusoidal (SDL) and uniformly distributed loads (UDL). The nICSDT demonstrates excellent agreement with three-dimensional elasticity solutions, superior prediction of transverse shear stresses, and rapid, monotonic mesh convergence. The present work introduces the FE-based realization of an inverse-cotangent shear deformation theory, offering a compact, accurate, and computationally efficient modelling framework suitable for advanced analysis of composite plate structures.