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

By Chia-Shun Yih

ISBN-10: 0120020149

ISBN-13: 9780120020140

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Extra info for Advances in Applied Mechanics, Vol. 14

Example text

13) where (C;, u l ) = 0. (A) - u o ( i L )between the displacements on the bifurcated path and the fundamental path, at a given value of A. This amount depends, of course, on the particular choice made for the inner-product norm, but for any choice, 4 + O for A+&. 13), for A + 2,. 6) of the variational equation of equilibrium will now, in turn, be expanded about 3,. We will use the notation $$) = p ) [ u O ( i ) ;4, d 4‘0)EE dx d2 &? = d i 2 J;$ A], pJ[llO(n); $01) 0 1A = & , = p0 Ii . 14) and so on.

With U representing the state variables w, c, and the variational equation 0'6 U = 0 is satisfied in the fundamental state by 11, wg = uo vo = 2, = 0 (as well as by rigid-body displacements, which may be suppressed). 69) with the mode w , = cos 20, el = -4 sin 20, v 1 = 3 cos 20. 70) It i s clear that the bifurcation is symmetric, and A, = 0. For the purpose of calculating U , by means of Eq. 70). 71) become d4w2 da4 d2w, da2 + - d3v2 d3w2 + 3 dw, da3 dcl dv, v, = 9 cos 48, + 2 d2v2 --z + dv, da da = 9 .

And v = K / K , = $; this shows that, for balanced biaxial compression, the stiffness associated with change in area of the plate is reduced by a factor of 4 after buckling. 4, D. 1. ,~ is an appropriate curvature tensor, where z is the normal distance to a reference plane; and the metric tensor ya0is calculated in the flat space of the reference plane. In Donnell-Mushtari-Vlasov theory, the same equations are used, but b,, and y, are curvature and metric tensors computed on the surface. 56) where now iis a scalar multiplier of a prescribed external edge and surface loading distribution.

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