Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundary Layer Analysis of the Ridge Singularity in a Thin Plate   Large deformations of thin elastic plates and shells present a formidable
problem in continuum mechanics which is generally intractable except by
numerical methods. Conventional approaches break down in the limit of small
plate thickness due to appearance of discontinuities in the solution which
require boundary layer treatment. We examine a simple case of a plate bent by
forces exerted along its boundary so as to create a sharp crease in the limit
of infinitely small thickness. We find a separable boundary layer solution of
the von Karman plate equations which is valid along the ridge line. We confirm
a scaling argument (T. A. Witten and Hao Li, Europhys. Lett. 23 51 (1993)) that
asserts that the ridge possesses a characteristic radius of curvature $R$ given
by the thickness of the sheet $h$ and the length of the ridge $X$ {\it viz.} $R
\sim h^{1/3} X^{2/3}$. The elastic energy of the ridge scales as $E \sim \kappa
(X/h)^{1/3}$ where $\kappa$ is the bending modulus of the sheet. We determine
the dependence of these quantities on the dihedral angle of the ridge $\pi -
2\alpha$. For all angles $R \sim \alpha^{-4/3}$ and $E \sim \alpha^{7/3}$. The
framework developed in this paper is suitable for determination of other
properties of ridges such as their interaction or behavior under various types
of loading. We expect these results to have broad importance in describing
forced crumpling of thin sheets.

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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga