Semi-Analytical Formulation for the Elastoplastic Analysis of Imperfect Cylindrical Shells.

摘要

In the report, a semi-analytical formulation is developed for the elastoplastic analysis of initially imperfect cylindrical shells under axial compression and lateral pressure. The formulation is based on a small-strain, moderate-rotation shell theory and a small-strain incremental constitutive theory. The basic shell equations and the partially inverted constitutive relations in total form are reduced to a set of coupled nonlinear algebraic/ordinary differential equations by means of a Fourier decomposition of the state variables, imperfections and loads in circumferential direction of the shell, and application of Galerkin's method. The governing nonlinear equations are solved with an incremental-iterative technique. The method of quasi-linearization is used to generate the governing equations of the iterative procedure which consistently takes into account both geometrical and material nonlinearities. Plasticity effects are described using a layered approach. The classical flow theory based on the von Mises yield surface, associative flow rule and the isotropic hardening law is used to describe the evolution of the plastic strains in the integration points. In every iteration a set of linear ordinary differential equations is solved numerically with a shooting method and a return mapping algorithm is used to integrate the constitutive equations locally. A number of elastic and elastoplastic buckling problems are solved for which results are known from literature. It is shown that the quadratic rate of convergence, characteristic for a Newton-type iteration procedure, is retained even for large load steps.