Determining the Axisymmetric Thermoelastoplastic State of Thin Shells with Allowance for the Third Invariant of the Deviatoric Stress Tensor

Abstract

A technique for determining the axisymmetric thermoelastoplastic state of thin shells with allowance for the third invariant of the deviatoric stress tensor is developed. The technique is based on the theory of thin shells that incorporates transverse shear and torsional strains. The equations of thermoplasticity relating the stress components in Euler coordinates with the components of the linear part of the finite-strain tensor are used as constitutive equations. The nonlinear scalar functions in the constitutive equations are determined from reference tests on tubular specimens under proportional loading at different temperatures and stress mode angles. The boundary-value problem is solved by numerically integrating a system of ordinary differential equations using Godunov’s discrete orthogonalization. The thermoelastoplastic stress–strain state of a corrugated shell is analyzed as an example