Study of Size Effect via Strain-gradient Elasticity Based RKPM in Nano-Structures

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Arshadi, Amir | 2010

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 41175 (09)
University: Sharif University of Technology
Department: Civil Engineering
Advisor(s): Mohammadi Shoja, Hossein
Abstract:
In this thesis one of the mesh-free methods called RKPM is employed to solve the differential equations of strain-gradient elasticity. To this end the corresponding weak form is laid down. Subsequently the relevant stiffness-matrix is obtained by discretization of the weak form. To be sure about the accuracy of the relations, the problem of a plate weakened by a hole under uniform far-field tension, for which the exact solution is available in the literature, is solved. The obtained numerical result is in good agreement with the solution of Eshel and Rosenfeld. Afterwards, a plate containing a crack of finite length subjected to uniform far-field tension (mode I) is considered. This problem is solved in the framework of first strain gradient theory; the obtained result follows the trend of the approximate strain gradient theory presented by Aifantis and coworkers. It is interesting to note that, in the context of usual theory of elasticity, the stress field is independent of the material properties, whereas in the framework of the first strain gradient the stress field varies with the material properties
Keywords:
Charachteristic Length ; Crack ; Shape Function ; Reproducing Kernel Particle Method (RKPM) ; Strain Gradient Elasticity