A semianalytical formulation for the elastoplastic analysis of imperfect cylindrical shells
Abstract
A semianalytical formulation for the elastoplastic analysis of initially imperfect cylindrical shells under axial compression and lateral pressure was developed. The formulation is based on a small strain, moderate rotation shell theory and 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 quasilinearization 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. A comparison between the present results and the results from literature shows a good agreement.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 December 1991
 Bibcode:
 1991STIN...9316282D
 Keywords:

 Axial Loads;
 Compression Loads;
 Cylindrical Shells;
 Elastoplasticity;
 Stress Analysis;
 Algorithms;
 Buckling;
 Differential Equations;
 Galerkin Method;
 Linearization;
 Nonlinear Equations;
 Structural Mechanics