Numerical Methodology for Predicting the Nonlinear Elastic Deflection of Curved Beams and Plates Using Nonlinear Integral Equations

Abstract

Ships, ship-shaped offshore structures, land-based structures and aerospace structures typically consist of various curved beam and plate components. An important issue is how to manufacture and construct systems correctly and accurately when their variously shaped curved beams and plates display structural nonlinear behaviour. Multi-point forming is a general process that can be used to form variously shaped curved plates and beams. It has been difficult to apply the integrated systems to thin and/or thick metal plates and beams that have the characteristic of non-linear structural mechanics, such as nonlinear behaviour when loading is applied to the plates. The aim of this study was to derive a simplified numerical calculation based on the formulation of a nonlinear integral equation and a mathematical solution, to predict the nonlinear elastic deflection, load profile and elastic foundation of curved plates or/and beams during the early stages of the advanced manufacturing process of plate and beam formation. The validity of the method is demonstrated through simulations of the proposed numerical approach with experimental results.