PSI - Issue 48

Udaya B Sathuvalli et al. / Procedia Structural Integrity 48 (2023) 207–214 Sathuvalli and Suryanarayana/ Structural Integrity Procedia 00 (2019) 000–000

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Fig. 4. Limiting axial strain and force (abscissae) as a function of external pressure for elastic perfectly plastic thick-walled cylinders

3. Tension Collapse of a Thin-Walled Cylinder Tests (by Maruyama et al. 1990) and numerical simulations (by Toscano and Dvorkin, 2011) show that thin-walled casings can resist significant biaxial loading (external pressure and tension, Fig. 5). These pressures are much greater than the theoretical ratings predicted by elastic stability theory for thin-walled cylinders, and by the API equations (API TR 5C3 2007). A full discussion of these test data in light of results from finite element analyses is presented by Suryanarayana et al. (2020). Here we propose a method to determine the collapse resistance of a thin-walled cylinder subjected to axial load or strain (Fig. 5), with a view to design and analyze casings during “cold collapse” in geothermal and steam wells (Fig. 1b). The deformed cross section (i.e. the median surface, Fig. 5) can be described by tangential and radial displacement (Timoshenko and Gere,1989, section 7.2). The analysis assumes that the tangential displacement is given by ( ) sin2 2 o u v θ θ = (5) where u o is the amplitude of the radial displacement indicated in Fig. 5. We now apply Rayleigh’s inextensional; criterion which states that the perimeter of the median surface is constant during bending deformations of thin-walled shells. Under this assumption, we can show that the radial displacement takes the form (Paslay et al. 2006) ( ) 2 9 cos2 16 o o o u u u R θ θ =− − . (6)

Fig. 5. Deformation of thin-walled cylinder subjected to external pressure and axial load