Energy-based analytical model to predict the elastic critical behaviour of curved panels

• Accurate and simple analytically derived expressions for the elastic critical stress of curved panels
• Influence of boundary conditions in the elastic critical stress of curved panels
• Influence on the number of DOF necessary to obtain accurate results for the elastic critical stress of curved panels

This paper presents an analytical study on the elastic critical behaviour of cylindrically curved panels under pure compressive stresses, for which an energy formulation is developed. Firstly, this energy formulation is described, the general assumptions are stated, the degrees-of-freedom and the displacement functions are defined and, using strain-displacement relations, the strain energy and the potential energy are derived. Secondly, the resulting general energy formulation is used to obtain, whenever feasible, simple expressions or, otherwise, values of the elastic critical stress of simply supported cylindrically curved panels under pure compression. A discussion on the number of degrees-of-freedom necessary to obtain accurate results is also presented. The analytical results are compared to numerical (finite element) results obtained by the authors. Finally, a parametric study is made regarding the influence of constraining (or not) the panel longitudinal edges on the elastic critical stress.