Stress Analysis of Thin Elasto-Plastic Shells

The stress analysis of thin shells with large deflections loaded into the strain hardening range is presented. Plastic strain incompressibility is assumed. The two governing differential equations in terms of the stress function and the normal displacement are derived in a form where the corresponding equations of the elastic problem are modified only by the addition of the integrals of the plastic strains. The equations can be utilized in conjunction with any yield criterion, flow rule, and hardening law. The theory is applied to the problem of stress concentration around a circular opening in a pressurized spherical shell. A numerical solution is obtained by an iterative procedure using the finite difference technique for the special case of small displacements, bilinear stress strain curve, and deformation theory of plasticity. The speed of convergence for plastic stress and strain concentration factors was found to decrease with increasing pressure.