The effect of residual stress on the stability of a circular cylindrical tube

Abstract Residual stresses in an unloaded configuration of elastic material have a significant influence on the response from that configuration, but effect residual stress stability material, whether loaded or unloaded, has only been addressed to limited extent. In this paper we consider level can be supported thick-walled circular cylindrical tube non-linearly without loss when subjected fixed axial stretch and either internal external pressure. particular, radial circumferential stresses, with simple form constitutive law accommodates stress, incremental deformations restricted cross section tube. Results are described for subject (internal external) pressure characterized by azimuthal stretch. Subject restrictions imposed strong ellipticity condition, emergence bifurcated solutions is detailed their dependence mode number.