REINFORCEMENT OF THE POISSON EQUATION BY A THIN LAYER
2011 ◽
Vol 21
(05)
◽
pp. 1153-1192
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Keyword(s):
We consider the problem of reinforcing an elastic medium by a strong, rough, thin external layer. This model is governed by the Poisson equation with homogeneous Dirichlet boundary condition. We characterize the asymptotic behavior of the solution as the shear modulus of the layer goes to infinity. We find that there are four types of behaviors: the limiting solution satisfies Poisson equation with Dirichlet boundary condition, Robin boundary condition or Neumann boundary condition, or the limiting solution does not exist. The specific type depends on the integral of the load on the medium, the curvature of the interface and the scaling relations among the shear modulus, the thickness and the oscillation period of the layer.
1997 ◽
Vol 34
(10)
◽
pp. 101-114
2013 ◽
Vol 284-287
◽
pp. 3131-3134
2017 ◽
Vol 139
◽
pp. 23-36
◽
2004 ◽
Vol 2004
(16)
◽
pp. 807-825
◽
2021 ◽
Vol 2021
◽
pp. 1-9
2017 ◽