Bending Theory of Circular Cylindrical Shells Under Axisymmetric Loads
In addition to internal pressure, circular cylindrical shell structures are often subject to concentrated or localized bending moments and forces of varying nature (external loads, loads arising from the interaction between structural components of differ
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Bending Theory of Circular Cylindrical Shells Under Axisymmetric Loads
10.1 General Considerations and Fundamental Relations In addition to internal pressure, circular cylindrical shell structures are often subject to concentrated or localized bending moments and forces of varying nature (external loads, loads arising from the interaction between structural components of differing stiffness, loads due to constraint reactions, and so forth), distributed symmetrically around the rotational axis. This occurs in pressurized aeronautical and aerospace structures consisting of assembled axisymmetric substructures with different geometries, in cylindrical pressure vessels with closures consisting of flatplate closures or formed heads, in boilers and heat exchangers, and in tubular shell structures with stiffening rings spaced at a predetermined distance along the axis, such as in the ribbed monocoque fuselages, structures and hulls used in the aeronautical, shipbuilding and submarine industries, for example, or the penstocks in hydroelectric powerplants, the cylindrical vessels under external pressure reinforced with circumferential stiffeners and distillation columns in oil refineries, the vessels used in the chemical and nuclear industries, missiles, etc (see Brownell and Young 1968, Jaward and Farr 1989). If only the membrane theory discussed in Sect. 1.6 were to be used in analyzing such structures, discontinuity areas would be found where the compatibility of deflections (displacements and rotations) would not be satisfied. At locations where the deflections are restricted, or there is a change in geometry, the membrane theory is inadequate. Bending loads (forces and moments), also called discontinuity loads, are generated in these localized areas which, together with the membrane loads, restore the compatibility of displacements and rotations. Though these discontinuity loads are local, they are sufficiently intense to cause significant alterations in the stress distributions in the immediate vicinity of the area where they are generated. In addition, these stresses are localized over a small area of the shell, and dissipate rapidly along the structure (Houghton 1960, Meyer 1961). To determine the relations governing the stress and strain states of these structures, we will assume that the intensity of the loads is such that the material works in the linear elastic range and that the displacements are small compared to V. Vullo, Circular Cylinders and Pressure Vessels, Springer Series in Solid and Structural Mechanics 3, DOI: 10.1007/978-3-319-00690-1_10, Springer International Publishing Switzerland 2014
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Bending Theory of Circular Cylindrical Shells Under Axisymmetric Loads
the radius. We will consider a circular cylinder under internal pressure pi and having a geometry of revolution, small thickness s such that the cylinder can be regarded as thin-walled as defined in Chap. 1, and mean radius R (Fig. 10.1a and b). As the thickness is small, the inner radius ri , outer radius re and mean radius
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