Geometric Nonlinear Isoparametric Spline Finite Strip Analysis of Perforated Thin-Walled Structures (No. R880)

Abstract

In previous reports [1, 2], the isoparametric spline finite strip method was successfully applied to the in-plane stress and bending linear elastic analysis of perforated plates. The method has been successfully applied to the elastic linear analysis and buckling analysis of folded plate structures [3, 4]. In the present report the application of the isoparametric spline finite strip method is further extended to the geometric nonlinear analysis of perforated folded plate structures. The general theory of the isoparametric spline finite strip method is briefly introduced. Kinematics, strain-displacements and constitutive assumptions are described and applied to the spline finite strip method. The derivation of the tangential and secant stiffness matrices is presented by applying the equilibrium condition and its incremental form. A large part of report is reserved to a review of the available nonlinear solution techniques, notably the cylindrical arc-length method. Classical nonlinear complex plate and shell problems are analysed and compared with exact solutions or with well established numerical results in order to demonstrate the reliability of the method. Furthermore, examples of the geometric nonlinear analysis of perforated flat and stiffened plates are included to highlight the effect of perforations on the behaviour of thin plate elements.