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

By Chia-Shun Yih

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Extra resources for Advances in Applied Mechanics, Vol. 14

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For 2, < I,,&/$A again approaches K O . As in the modified simple model, bifurcation with 1, < 1,implies the possibility of snap buckling (Fig. 8c) for an increasing A imposed on the structure, whereas an increasing I leads to snap buckling for all I , < 0. Values of K for I , > 0 are useful in assessing the load-carrying capacity of structures that continue to carry loads after buckling without snapping. As in the simple model, snap buckling under imposed shortening for I , # 0 is always possible for sufficiently small when ?

Again, with F' 6U = 4"u; It] 6u + vA"u] 8 u + A [ u ] 8v = 0 as the governing variational statement of the problem, it follows that all of the preceding results remain valid with the replacement of Q, by F , and u by U . Exaniplr 1-Euler Column Although the post-buckling behavior of an Euler column has long been understood on the basis of the exact elasticu solution, this problem usefully provides an elementary, yet nontrivial example of the application of the general theory. The usual uniform-column theory based on inextensional bending deformation gives the potential energy where (see Fig.

10). If the assumptions (i)-(iii) apply, then Eqs. 33) Under assumption (iv) [and not necessarily any of (i)-(iii)] 3, = - ( l/A,)0, i;,= and since we also have [Eq. 35) Example 3-Flut plute Consider a square, simply supported, flat, plate of uniform thickness compressed normally along all edges as shown in Fig. 14, by means of rigid, 49 Buckling Behavior of Elastic Structures lubricated loading heads. 'F/2s2, N , , = - ? 2 F / ? \,. The generalized stresses of this problem are the bending F-IG.

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