Inextensional approximations in cylindrical shells.

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Introduction I is well-known that the deformation in many thin shells with unsupported edges may be characterized as inextensional. (For example, see Refs. 2 or 3.) Recently, Williams' presented a number of comparisons between the homogeneous Donnell equations and the inextensional theory for the radial deformation in open end cylindrical shells. Williams showed that for certain cylindrical shell geometries subjected to the boundary conditions u = 1.0, v = w = dw/dx — 0 at x = 0 and Tx = Sx = Nx — Mx = 0 at x = /,t the inextensional theory and the solution to the homogeneous Donnell equations are within 95% agreement. It was shown that the 95% demarcation lines could be represented by (l/a) = (CSIn*)(alh) (1) for some geometries, and