Calculation of an Elliptic Cylindrical Shell Outside Elastic Limits Based on the FEM with Various Forms of Defining Equations

Abstract

At the loading step when the shell is deformed outside the elastic limits, the relations between strain increments and stress increments are used in three forms. In the first two forms, the dependences of the strain increments were obtained by differentiating the relations of the deformation theory of plasticity both with the use of the hypothesis of the material incompressibility during plastic deformation and without it. In the third form, to obtain the governing equations, we proposed an algorithm based on the hypothesis that the deviator components of the strain increments are proportional to the deviator components of the stress increments without taking into account the hypothesis of the material incompressibility during elastoplastic deformation and without dividing the stress increments into elastic and plastic parts.