Nonlinear analytical modelling of flat and hyperbolic paraboloidal panels under shear

The hyperbolic paraboloid (hypar) form has been widely used in long-span roof structures and is the subject of much research under out-of-plane loading. However, the behaviour of hypars under in-plane loading has been less keenly studied, and there is no suitable guidance for their design in current codes of practice. A nonlinear analytical model treating the hypar as a deliberate imperfection applied to a flat plate is presented. A Rayleigh–Ritz formulation using appropriate shape functions is developed and the resulting equations are solved using numerical continuation techniques. The results are verified with nonlinear finite-element models, showing good correlation across a range of thicknesses and degrees of initial curvature. Key modal contributions that influence the behaviour of the hypar are identified, providing insight into the nonlinear behaviour of hypars subject to in-plane shear. The main differences in behaviour between the flat plate and the hypar panel are shown to be most prevalent in the early stages of loading, where the influence of the initial geometry is at its greatest.