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

By Chia-Shun Yih

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9) gives (GI:’ - crOcb) 6u = A’ = cb + >-(A- A;) Csu = 0. 11) into + ... + ‘e”’u2 2 0 + Agu + “A”’u2 + ... 8b) for cr, to get seb 6 u + {(go+ S ) E ~ iA6)u 6u + ;((go + AA~}V’6u + ;{(G,,+ - iAk}u3 6u + ... = 0. 12) by ~11:: ~(uIJ, CSU lim(q/ilui\). 13) 44 Bernard Budiansky where the subscript c denotes evaluation at A = 'A on the fundamental path. 7b) may be expanded as 00 +s= and so cancellation of OIEO + 'I] = 0 0 + ob'I + f0;;'I + ... 15) 0;c1. Similarly, the strain-displacement relation ( 5 .

58) [ K0': = P, 1. : ds $Pc L = '0 and 1. 0: L (jy2 1 - - ds = -1 2L. ' 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 = (

Has been used insrcad. Buckliiig Behauior qf Elastic Structures admissible variations in 6it. 8), wherein 6u can be chosen as u, . 21) and expressions for the successive coefficients i3, i4, . . 16) can also be found in a straightforward way. It is seen that the post-buckling coefficient 2 , depends only on the buckling mode i i , , but the calculation of 2 , would generally require the determination of u2 as well, and so on. I t is now evident that the relations between iand found for the bifurcated path are entirely similar to those illustrated in Fig.

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