Analysis of doubly curved laminated composite shells using hybrid-Trefftz finite element model based on a high order shear deformation theory

Static analysis of doubly curved laminated composite shells with rectangular plan form has been carried out using a novel hybrid Trefftz finite element (HTFE) model. A typical higher order shear deformation theory (HSDT) has been used for describing the kinematics of deformations delineating both internal and auxiliary displacement fields. This HSDT allows to derive the system of governing partial differential equations of the single layer equivalent to the element domain. The characteristic functions forming the exact solutions of these homogenous governing equilibrium equations are used as the Trefftz functions. A key aspect of our HTFE strategy is its efficiency in bypassing the use of particular solution of the governing equations. Validation against the exact solutions reveals the precision of this novel HTFE model. The versatility of the Trefftz functions allows them to accommodate a spectrum of geometric configurations, ranging from standard to complex polygonal HTFE designs. The HTFE model for the doubly curved composite shells employing the HSDT marks a significant advancement in the analysis of doubly curved spherical, paraboloid and hyperboloid cross-ply and antisymmetric angle-ply shells.