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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61) Moderately large displacements are thus produced by small excursions beyond the initial load. 1, A i34/2P = L - J, cos 8 (1s. The results of this analysis agree with those found from an expansion about P, of the classical exact solution in terms of elliptic integrals. Exumplr 2-Inextmsioizal Ring The uniform thin ring shown in Fig. 13 is presumed to be loaded by pressure q that remains normal to the surface. 3. Thin ring. 64) The strain energy is +El Jin(dt)lds)2ds, and the potential energy of the pressure is - q(AA), where AA is the reduction of enclosed area given exactly by AA = +R2 [ 2rr [-2w - w2 - v2 + 2u(dw/da)] da.

85) appear appropriate, where, without loss of generality, (w,,u l ) = 0 for I I 2 2. 84) about j. = 2, and I' = 0, and writing A w (h= (w,(h), gives t{&w2 R , &u, q5e,u: - A u , j 6w + + + <2j45:w3 + A, 4:w2 + A 2 & h l + fA:$:u, + (je,u2u, + + A~$;U: + $&"u: - Aw2 /j2Aul) 6w + . . = 0. 86) t In fact, d ' ' ( 6 ~is) ~then positive-definite with respect to 11 11. 39 Buckling Behavior qf Elastic Structures Setting 6w = u 1 in the coefficient of [I1 = < gives A1&hl + qyu:, where use has been made of the fact that Au: = (ul, u l ) [Eq.

Ac . For below the transition load, say, 2,4: w2 > 0 for all w,and above w2 < 0 for some w's; we will assume that at A = 1,4: w2 = 0 vanishes for at least one w = W,t remains non-negative for all other w, and, therefore. as a function of w,is stationary at w = W; thus the eigenvalue equation 4; k 6w = 0 must be satisfied at A = 1;and therefore, since 2 is the lowest possible eigenvalue, i= ,Ic. Furthermore, if u1 is unique, W is proportional to u l . ,, it follows that 4eu: 5 0. However, the special case &u: = 0 will not be considered explicitly, although a separate treatment can be executed without essential difficulty.

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


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