A Computationally Efficient Model for Three-dimensional Stress Analysis of Stiffened Curved Panels

Lightweight, thin-walled structures stiffened by a set of stringers or ribs are widely used in many engineering applications. Thus, the need for the structural capability assessment of such structures has increased and development of accurate, yet computationally efficient, models has become a major interest to industry. We present a novel approach for the static analysis of stiffened structures using a one-dimensional (1D) refined beam model. The approach is based on Carrera Unified Formulation (CUF), and can recover complex, three-dimensional (3D) stress fields in a computationally efficient manner. As a novelty, recently developed hierarchical set of expansion functions, based on Lagrange polynomials, namely Serendipity Lagrange expansions (SLE), are used to define cross-sectional displacements. In this scheme, the beam’s cross-section is discretised using four-node Lagrange elements, which allows local stress-concentrations to be modelled. Further, the hierarchical nature of Serendipity Lagrange expansions within each cross-sectional element make it suitable for predicting higher-order effects. The higher-order expansion functions also improve the geometrical approximation of curved sections by employing a local mapping technique based on a blending function method. In the present work, the so-called 1D CUF-SLE model is used to analyse flat and curved panels stiffened with transverse ribs and longitudinal stringers. The performance of the proposed approach in terms of computational cost and precision is assessed in comparison to reference solutions obtained by employing 3D finite element (FE) analysis in ANSYS. Our results show the capability of the present formulation to model complex structures which otherwise could only be done with computationally expensive 3D FE analysis.