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Numerical Modeling of Two Interacting Circular Holes Using a Gradient Elasticity Based Meshless Method
Ramhormozian, Shahab | 2010
697
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- Type of Document: M.Sc. Thesis
- Language: English
- Document No: 40687 (53)
- University: Sharif University of Technology, International Campus, Kish Island
- Department: Science and Engineering
- Advisor(s): Mohammadi Shoja, Hossain
- Abstract:
- A theory of gradient elasticity is used and numerically implemented by a meshless method that is called reproducing kernel particle method (RKPM) to model size effects. Some of the problems are modeled under the consideration of gradient elasticity for the first time and all of them are also modeled with classical elasticity to compare with gradient elasticity. First of all, the RKPM formulation and computing the amount of shape functions and requisite derivatives will be explained with details and a mathematical innovation that will decrease the computational cost seriously proposed for the first time. Several 1D and 2D shape functions with first and second derivatives that are resulted from codes are written by the author with visual FORTRAN 90 programming language and they will be plotted. Then all of the needed procedures to model a problem will be explained step by step. They are computing stiffness matrix of the system, imposing natural and essential boundary conditions, numerical integrating methods and extra necessary processes to solve a problem numerically according to gradient elasticity formulation. Finally several boundary value problems which show the capability of gradient elasticity theory to capture size effects ‘that is considerable in nanosized specimens’ and ability of RKPM will be considered. At last some of the results will be plotted expressively in various aspects.
- Keywords:
- Shape Function ; Gradient Elasticity Theory ; Meshless Method ; Size Effect ; Reproducing Kernel Particle Method (RKPM) ; Nano Sized
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