Get Advances in Applied Mechanics, Vol. 14 PDF

By Chia-Shun Yih

ISBN-10: 0120020149

ISBN-13: 9780120020140

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Extra resources for Advances in Applied Mechanics, Vol. 14

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If A1 = 0, Eq. :. Consequently, [j = ( - 3 i 2 $;u:)t2+ O(5“) ( n 2 3) at A = ,Ic and , since > 0, we have stability for sufficiently small t > 0. To sum up, for sufficiently small imperfections, stability, as assessed by the sign of the second variation, has been verified along imperfect-structure equilibrium paths emanating from 1 = 0, up to the snapping load in imperfection-sensitive structures; and, up to some load higher than Ac in imperfection-insensitive structures. [Similar conditions hold for the imperfection-insensitive perfect structure, except that the second variation is inadequate to determine stability at /1 = 2 , .

0 = and so it is verified that the column Consequently, Eq. 22') gives is not imperfection sensitive. 60) g 2 , but a possibly more useful representation for P/Pc would be in terms of the amplitude of displacement rather than rotation. Since the lateral deflection w is related to 0 by dwlds = sin 0 z 0 + . . , w = (

In the case of an imperfection-insensitive structure (Fig. 9b,d) the same conclusion clearly applies for A < A,. 8 1) ;-ro where L' is the displacement increment along the bifurcated path originally defined in Eq. 3). 79) for A > A, is now about u = uo u and LI = 0, and this gives + $"(6U)Z = (b"[uo + v(A); )L](6t/)2 + $""uo + L'(A); 149 - + ... I~)(dU)Z + ~ ~ " * [+u uo , o ; A];l(6U)' + . ' = 0. 83) z. + = (du, 6 u ) = I l f i ~ (and / ~ AuT = 1, with respect to an admiswhere sible (6u). 83) be stationary with respect to variations in w implies that w and p are solutions of the eigenvalue problem 6''~ 6~ - j 3 A 6~ ~ = 0 on the bifurcated path.

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Advances in Applied Mechanics, Vol. 14 by Chia-Shun Yih


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