Efektywne Obliczanie Rur Grubościennych w Przypadku Liniowego Wzmocnienia Plastycznego - Ryś, J. (Engineering Transactions, 1969)
Making use of the integral equations of equilibrium for a thick-walled tube loaded by a pressure and an axial force, assuming incompressibility and linear strain hardening of the material, the strain regions of the tube are determined in a system of coordinates selected in a certain way, depending on the loaded. By approximating the limit curves by ellipses and knowing the loads, we can answer beforehand the question as to whether the tube is in the elastic, elastic-plastic of plastic state up to the moment of collapse. For the region of plastic strain a single equation of equilibrium is obtained, its solution being found for any load. Equations for the components of the stress and strain tensor are also given. For the region of elastic-plastic strain of the tube six equilibrium equations are obtained. Then, by approximation, the problem is reduced to a plane problem. Expressions of the stresses and strains are also derived for both regions: elastic and plastic. The examples given illustrate the way in which use is made of the equations obtained.