Static and free vibration analysis of laminated composite hyperbolic paraboloidal shells using carrera unified formulation

Abstract

This study presents a comprehensive framework for analyzing the static and free vibration behavior of laminated composite hyperbolic paraboloidal shells (LCHPS) using the Carrera Unified Formulation (CUF) and hierarchical finite elements. The CUF approach is employed to model the displacement field of LCHPS, taking into account the effects of higher-order shear deformation and curvature. A two-dimensional modeling approach is used to simulate the behavior of orthotropic and anisotropic LCHPS, utilizing the Principle of Virtual Displacement (PVD) and an eight-noded isoparametric quadrilateral element (Q8). The study investigates the static and free vibration behavior of LCHPS under various loading conditions, including uniform loads, and sinusoidal loads with different edge constraints. Numerous distinct lamination schemes are considered, including multilayered configurations, as well as cross-ply (CP) and angle-ply (AP) arrangements. The results of the study provide valuable insights into the effects of aspect ratios ‘a/h’, rise ratios ‘c/a’, and laminate schemes on the static and free vibration behavior of LCHPS under various boundary conditions. The numerical solutions presented in this study are intended to serve as benchmark solutions for future comparisons and can be used to guide the design and optimization of LCHPS for various engineering applications. © The Author(s), under exclusive licence to Springer Nature B.V. 2025.