Augmented RKPM Modeling of a Glide Edge Dislocation Near a Grain Boundary in the Framework of Surface/Interface Elasticity
- Type of Document: M.Sc. Thesis
- Language: English
- Document No: 43040 (53)
- University: Sharif University of Technology, International Campus, Kish Island
- Department: Science and Engineering
- Advisor(s): Mohammadi Shoja, Hossein
- Traditional continuum theory of elasticity becomes remarkably inaccurate in the vicinity of singularities, and when the size eect is of concern. For example in the study of ultra-small objects and ultra-thin lms, near defects, near point of application of a concentrated load and as such, the classical solutions are not reliable. This work focuses on determination of the elastic elds of an edge dislocation near the grain boundary of two perfectly bonded nano-size crystals. It is proposed to study this problem in the context of surface/interface elasticity, and incorporate the eect of the grain boundary on the elastic elds. In contrast to the surface/interface elasticity theory, traditional elasticity does not ncorporate the interface stresses which are present at the grain boundaries. This aspect of the traditional approach is mentionable source of in accuracy. It is proposed to solve the problem under consideration numerically by the so-called Reproducing Kernel Particle Method(RKPM), which is a meshfree method.Meshfree methods which have proved to be instrumental for the solution of partial dierential equations and for treating various engineering and scientic problems have signicantly matured over the past two decades. One of the early incentives to develop meshfree Galerkin methods was due to its advantages in addressing crack growth, a critical issue in computational fracture mechanics. It is fair to say that, at least in 2D crack growth simulation, meshfree Galerkin procedure oers considerable advantages over the traditional nite element methods, because remeshing is avoided. Another area where meshfree Galerkin methods have clear edge over usual nite element computations is its ability to handle large deformation problems. Reproducing Kernel Particle Method (RKPM) is a well-known version of meshfree methods which incorporates a correction function in the kernel of integral transformation to impose the reproducing conditions
- Reproducing Kernel Particle Method (RKPM) ; Meshless Method ; Surface/Interface Elasticity ; Glide Edge Dislocation ; Nanolaminated Beam
- محتواي کتاب
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- List of Figuresto.44em.
- List of Tablesto.44em.
- Chapter 1 Introduction to.44em.
- Chapter 2 Reproducing Kernel Particle Method to.44em.
- 2.1 Review of 1D RKPM Formulation
- 2.2 Review of 2D RKPM Formulation
- 2.3 Assign Essential Boundary Condition With Collocation
- 2.4 RKPM with Augmented Corrected Collocation
- Chapter 3 Solving Some Problems in a RKPM Framework to.44em.
- Chapter 4 Review Of Beam Theories to.44em.
- Chapter 5 Review of Surface/Interface Elasticity to.44em.
- Chapter 6 Review of Dislocation to.44em.
- Chapter 7 Conclusion and Future Work to.44em.
- AppendixChapter A to.44em.