{
  "id": "1601.04912",
  "version": "v1",
  "published": "2016-01-19T13:20:36.000Z",
  "updated": "2016-01-19T13:20:36.000Z",
  "title": "Thin elastic plates supported over small areas. II. Variational-asymptotic models",
  "authors": [
    "G. Buttazzo",
    "G. Cardone",
    "S. A. Nazarov"
  ],
  "comment": "31 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "An asymptotic analysis is performed for thin anisotropic elastic plate clamped along its lateral side and also supported at a small area $\\theta_{h}$ of one base with diameter of the same order as the plate thickness $h\\ll1.$ A three-dimensional boundary layer in the vicinity of the support $\\theta_{h}$ is involved into the asymptotic form which is justified by means of the previously derived weighted inequality of Korn's type provides an error estimate with the bound $ ch^{1/2} \\left | \\ln h\\right| .$ Ignoring this boundary layer effect reduces the precision order down to $\\left| \\ln h\\right| ^{-1/2}.$ A two-dimensional variational-asymptotic model of the plate is proposed within the theory of self-adjoint extensions of differential operators. The only characteristics of the boundary layer, namely the elastic logarithmic potential matrix of size $4\\times4,$ is involved into the model which however keeps the precision order $h^{1/2}\\left| \\ln h\\right| $ in certain norms. Several formulations and applications of the model are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-19T13:20:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "74K20",
      "74B05"
    ],
    "keywords": [
      "thin elastic plates",
      "small area",
      "precision order",
      "thin anisotropic elastic plate",
      "elastic logarithmic potential matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}