Modeling of Curved Stiffened Panels Using Refined 2D Finite Elements

Curved, stiffened panels are primary load-carrying components in aerospace and marine structures, where accurate prediction of displacements, three-dimensional stress concentrations at skin stiffener junctions, and buckling response often demands costly 3D solid models or ad-hoc 2D+1D couplings. This work proposes a unified two-dimensional finite-element strategy for curved panels reinforced by both straight and curvilinear stiffeners, developed within the Carrera Unified Formulation (CUF). In the proposed approach, the skin and each stiffener are discretized with the same 2D element. The stiffener height is embedded in the element thickness direction and enriched through selectable higher-order Lagrange polynomial expansions, which enhance local kinematics and enforce skin stiffener continuity directly at Lagrange points, without auxiliary constraints, tie interfaces, or mixed-dimensional coupling. Element matrices are derived from CUF fundamental nuclei independent of the chosen thickness order, enabling systematic refinement for local 3D stress evaluation at bends, corners, and junctions while preserving a consistent element architecture. The formulation naturally accommodates curvature in both the panel midsurface and stiffener layout, allowing mixed reinforcement patterns within a single framework. Benchmark studies show that the proposed 2D-only model reproduces 3D reference and high-fidelity literature results for deflections, critical axial/shear stress components, and nondimensional buckling parameters, capturing stiffener-dominated modes with substantially fewer degrees of freedom than 3D meshes and offering an efficient tool for design loops and parametric analyses.