M

2p2D

Using cosh2ocos2o + sinh2osin2o = 2(cosh2o + cos2o), the coefficients are

M coshocos o M sinh osino

1 = JD cosh2o + cos2o ' 2 = — JD cosh2o + cos2o . (. )

With these coefficients, the slope of the flexure at the edge of the cylinder is s = /dr\ = M sinh2o + sin2o = Ml / 8 + \ (562) cyl \dz)z=/2 2jDcyl cosh2o + cos2o 2Dcyl V 15 / '

In order to obtain a basic formulation, we can restrict the term in parentheses to unity by choosing enough small values of o. Taking H o4 < 10—2, we obtain the inequality

acVc2yl 10

From (5.62), we see that the first-order term of the slope scyl does not depend on the cylinder mean radius acyl = a + \ tcyl. Making acyl equal to a in the above inequality, the condition on length for the cylinder is l2 < atcyl . (5.64)

Since the rigidities are related by Dcyl = y3D, if using the same material for the plates and cylinder, (5.54) and (5.62) give respectively

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