Thin-Walled Circular Cylinders Under Internal and/or External Pressure and Stressed in the Linear Elastic Range
Circular cylinders are generally divided into two families, according to the equations governing their stress state. If the wall thickness is small compared to the inside diameter, within the limits indicated below, it is assumed that the stresses are uni
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Thin-Walled Circular Cylinders Under Internal and/or External Pressure and Stressed in the Linear Elastic Range
1.1 Foreword Circular cylinders are generally divided into two families, according to the equations governing their stress state. If the wall thickness is small compared to the inside diameter, within the limits indicated below, it is assumed that the stresses are uniformly distributed through it, which simplifies the treatment to a considerable extent (Bickell and Ruiz 1967, Iurzolla 1981, Burr 1982, Ventsel and Krauthammer 2001, Ugural and Fenster 2003). In this case, we are dealing with a cylindrical membrane shell, i.e., a thin-walled circular cylinder, where the axial dimension is large, and a thin-walled circular ring where the axial dimension is small. In this chapter, we will discuss thin-walled circular cylinders with large axial dimension, or in other words, tubular structures having an annular cross-section of small radial thickness stressed in the linear elastic field. Assuming that the stresses are uniformly distributed through the wall thickness makes it possible to address the problem using only the equilibrium equations. It is this not necessary to employ the compatibility equations or advance hypotheses regarding the stress state or strain state. Geometrical axisymmetry and the uniform distribution of stresses through the wall thickness means that the radial, circumferential (or tangential) and axial directions are the principal directions of both stresses and strains. The stress and strain states of thin-walled circular cylinders under internal and external pressure are analyzed here by assuming that displacements are small and strains are infinitesimal. Consequently, the geometrical magnitudes characterizing deformation mechanics remain essentially unchanged after the loads associated with pressure are applied. It will also be assumed that the material is homogeneous and isotropic. If the wall is thick, it is no longer possible to assume that stresses are uniformly distributed through it. In this case, the approach to the problem is more complex, as it involves simultaneously employing the equilibrium equations and the compatibility equations, both of which must be satisfied, as well as the boundary conditions. Here we are dealing with vessels or, more generally, thick-walled circular cylinders and rings, depending on whether their axial dimensions are large or small. V. Vullo, Circular Cylinders and Pressure Vessels, Springer Series in Solid and Structural Mechanics 3, DOI: 10.1007/978-3-319-00690-1_1, Springer International Publishing Switzerland 2014
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1 Thin-Walled Circular Cylinders Under Internal and/or External Pressure
It should be specified that there is no difference between the two families of thin-walled and thick-walled circular cylinders from the standpoint of continuum mechanics. The difference is purely conventional. Here, we will follow the more common international convention, whereby the ratio of wall thickness s and inside diameter di for the family of thin
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