Nonlinear Kinematic Analysis of the Deformation of Plates for Ship Hull Fabrication

Curved plates in a ship's hull are fabricated by mechanical or thermal processes, such as roller bending and line heating methods. The formation of curved plates is a process in which, from the point of view of mechanics, permanent bending and/or in-plane strains are applied to flat plates. Only bending strains are applied to single curvature shells, while in-plane strains, in addition to bending strains, need to be applied in order to form double curvature shells. In-plane strains, however, are known to be small and, thus, can be neglected. The mechanics of plate bending is different from the production of plate bending. In the mechanics of plate bending, an initial configuration of a plate is given, along with boundary and loading conditions. The deformed shape can then be calculated. In the production of plate bending, however, only the final deformation shape is given and the initial configuration is unknown. Loading conditions must also be determined. This paper presents rigorous formulations of a kinematic problem for the production of plate bending. Nonlinear kinematic analysis with and without initial imperfections is employed in order to include in-plane strains. An algorithm is suggested to determine an initial configuration from given surface data. Numerical examples show that the in-plane strain must not be negligible and, rather, plays an important role in the determination of heating paths in the line heating method.