By Chia-Shun Yih
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Additional resources for Advances in Applied Mechanics, Vol. 14
Indeed, it is particularly convenient to choose the norm IluIl = ( u , u)”’, for then ( u l , u l ) = 1 , and this choice will be assumed henceforth. 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,.
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.
40) these become - 7c4Et5 32a2 t A possible inconsequential linear contribution to F , is ignored. 50) independent of the ratio of Px and P,. Note that wmaX% ( l t )for small l,so that we have the result A/& % 1 + i ( 1 - v2)(wm,,/t)2 + ".. ], Eq. 52) For uniaxial loading, P, = 0, and K I K , = 4,independent of v. For P, = P,. 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.