Journal ArticleDOI
Stresses in Narrow Regions
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In this article, a method for calculating the stress distribution in a narrow region of an elastic plate is presented, which consists in treating the narrow region by beam theory, treating the rest of the plate by any computational or analytical method, and matching the results of these two calculations.Abstract:
A method for calculating the stress distribution in a narrow region of an elastic plate is presented. It consists in treating the narrow region by beam theory, treating the rest of the plate by any computational or analytical method, and matching the results of these two calculations. It is illustrated by finding the stress distribution in the narrow region of a plate, between a straight edge and a nearby hole, when the plate is under tension. The same method can be applied to three-dimensional bodies with thin plate-like or shell-like regions.read more
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Journal ArticleDOI
An elliptic regularity result for a composite medium with “touching” fibers of circular cross-section
Eric Bonnetier,Michael Vogelius +1 more
TL;DR: A classical regularity result due to DeGiorgi and Nash is improved, which asserts that the solution of the elliptic equation u is in the Holder class $C^\gamma$ for some positive exponent $\gamma$.
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Gradient estimates for solutions to the conductivity problem
TL;DR: In this paper, the authors derived very precise gradient estimates for solutions to the conductivity problem in the case where two circular conductivity inclusions are very close but not touching, and they gave very specific information about the blow up of the gradient as the conductivities of the inclusions degenerate.
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Estimates for Electric Fields Blown Up between Closely Adjacent Conductors with Arbitrary Shape
TL;DR: The blow‐up results on the stresses specialized only for disks to the general case of arbitrary shapes are extended and a novel representation for the solution on conductors by a probability function is established.
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Gradient Estimates for the Perfect and Insulated Conductivity Problems with Multiple Inclusions
TL;DR: In this paper, the authors studied the gradient estimates for the perfect and the insulated conductivity problems with multiple inclusions imbedded in a bounded domain in ℝ n, n ≤ 2.
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Asymptotics and computation of the solution to the conductivity equation in the presence of adjacent inclusions with extreme conductivities
TL;DR: In this article, the singular term of the solution is characterized explicitly when two circular inclusions with extreme conductivities are adjacent, and it is shown through numerical computations that the characterization can be used efficiently for computation of the gradient in the presence of adjacent inclusions.