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The two boundary conditions at the shell contour can be as well considered as link conditions to a special outer cylinder; the geometry resulting from a shell clamped in an outer cylinder is called a vase shell. We assume hereafter that the cross-section dimensions of this outer cylinder are small compared to the radius rN so the effects of the load q on it can be neglected. Furthermore, the displacement w due to the axial compression or extension Qr of the cylinder does not intervene in the shape of the optical surface for which r < rN. Hence, from (6.30f), the tangential strain of the cylinder - numbered N +1 - can be simply represented by £tt = u/rN instead of u/rN — w/<R>. From these two assumptions we may characterize the cylinder elastic link to the outermost meniscus shell element N at r = rN by the two relations dw = aMrN+1 + ß N,N+1 , u = YMrN+1 + 8Nr,N+l , dr rN

rN+1

Particular values of a, f},y, 5 coefficients allow analysis with various boundary conditions [cf. (6.32)]. Some of these coefficient sets are determined below.

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