ar X iv : c on d - m at / 9 60 80 50 v 1 9 A ug 1 99 6 The von Karman equations , the stress function , and elastic ridges in high dimensions . Eric
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چکیده
The elastic energy functional of a thin elastic rod or sheet is generalized to the case of an M -dimensional manifold in N -dimensional space. We derive potentials for the stress field and curvatures and find the generalized von Karman equations for a manifold in elastic equilibrium. We perform a scaling analysis of an M − 1 dimensional ridge in an M = N − 1 dimensional manifold. A ridge of linear size X in a manifold with thickness h ≪ X has a width w ∼ h1/3X2/3 and a total energy E ∼ μhM (X/h)M−5/3, where μ is a stretching modulus. We also prove that the total bending energy of the ridge is exactly five times the total stretching energy. These results match those of A. Lobkovsky [Phys. Rev. E 53, 3750 (1996)] for the case of a bent plate in three dimensions. Typeset using REVTEX 1
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تاریخ انتشار 1996