Nonlinear analysis of corrugated plates using a FSDT and a meshfree method

Abstract

This paper presents a geometrically nonlinear analysis of stiffened and un-stiffened corrugated plates using a meshfree Galerkin method that is based on the first-order shear deformation theory (FSDT). The strains are assumed to be small, and the corrugated plates are modeled approximately as equivalent orthotropic plates. The large deflection theory of von Karman is adopted in the nonlinear analysis of the orthotropic plate, and the equivalent flexure properties of the orthotropic plate are derived. Both the equivalent flexure and extensional properties are employed in the nonlinear analysis. The stiffened corrugated plates are analyzed as stiffened orthotropic plates, in which the stiffeners are modeled as beams and fitted to the equivalent orthotropic plate by implementing displacement compatibility conditions between the plate and the stiffeners. Because no mesh is required in the proposed method, the stiffeners can be placed anywhere on the plate, and changes to the positions of the stiffeners do not entail the remeshing of the plate. To demonstrate the convergence and accuracy of the proposed method, several numerical examples are employed. The solutions that are computed by the proposed method are compared with precise solutions that are given by ANSYS using shell elements and with the results of other research work.