A Hierarchy of Plate Models Derived from Nonliinear Elasticity by T-Convergence

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Golipoor, Javad | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 43712 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Bahraini, Alireza
Abstract:
In this thesis the elastic energy of plates is computed. Primarily, some physical related concepts such as stress, strain and strain energy density are defined. Then based on rigidity estimate theorem, the gradient map on bounded Lipschitz domains is approximated by a constant rotation map R.Thanks to this approximation theorem,we prove the precompactness of sequences of finite bending energy, and the limiting energy of two dimensional thin plates is shown to be an elastic energy. This limit innovation is called Γ –convergence introduced in 1993. It will indeed be revealed that the induced elastic energy of a deformable body is the limit of the sequence of stored energy of body under deformations of body along with boundary conditions. Finally, we will observe that elastic energy of plates is that kinds of curvature functionals
Keywords:
Strain Energy Density ; Limiting Energy ; Gamma-Convergence Method ; Second Fundamental Form

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