Sharif Digital Repository

In this research, circular and elliptic inhomogeneities are modeled using a numerical meshless method named RKPM. A newly developed accurate and simple method called augmented corrected collocation method, which was previously applied in order to model material discontinuities in the framework of classical continuum theory, is used in combination with the penalty method, considering couple stress elasticity and in micro or nano scales for the first time, where the classical continuum theory has certain shortcomings in predicting the behavior of materials. Simulating nano-composites subjected to anti-plane stresses and comparing the analytical and numerical results show that the augmented... 

The axisymmetric contact problem of a rigid inclusion embedded in the piezoelectric biomaterial frictionless interface subjected to simultaneous far-field compression and electric displacement is addressed. With the aid of a robust technique, the coupled governing integral equations of this mixed boundary-value problem are reduced to decoupled Fredholm integral equations with a constraint equation. A useful limiting case for the contact problem of transversely isotropic bimaterials is addressed. The present solution is analytically in agreement with the existing solution for an isotropic bimaterial. Selected numerical results of interest to engineering applications including the radius of... 

The aim of this work is to study a cohesive crack in an elastic solid with meshless method. The procedure uses Reproducing Kernel Particle Method (RKPM) formulation in conjunction with Penalty method for implementing all constraints, including the Essential Boundary Conditions (EBCs) and the constraints related to cohesive crack. Meanwhile subdomain technique is employed to diminish the compiling process to facilitate one. Study of Stress Intensity Factor (SIF) at the tip of the cohesive crack has also been dealt with particular interest  

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... 

One important problem in all, particularly in developing countries, is shortage of funds to invest in infrastructure projects. One way to lessen this difficulty is to benefit from the private sector participation in this respect. Build-Operate-Own-Transfer (BOT) is a Public-Private-Partnership (PPP), in which the private sector invests and builds a (e.g. road) project, operates it for a specified period of time to collect the tolls to return the investment cost plus the specified attractive rate on it, and then transfer it to the public sector. This research, which is a continuation of previous endeavors in this area, formulates the problem, discusses the multiplicity of the solutions, and... 

It is proposed to obtain the mode I plastic zone size and shape at the crack-tip in a work-hardening material using reproducing kernel particle method (RKPM). RKPM is a meshless technology which has proven very useful for solving problems of fracture mechanics. Ramberg-Osgood stress-strain relation is assumed. In this project the crack-tip stress intensity factor (SIF) before and after formation of the plastic zone will be examined. To impose the essential boundary conditions, penalty method is used. To construct the shape functions in the vicinity of the crack and crack-tip, both the diffraction and visibility methods are employed. The effects of different dilation parameters on SIF under... 

During the past decade, element free methods have achieved great successes. One of these methods is the so called RKPM which has a suitable structure for use in fracture mechanics problems. Despite all characteristic abilities of element free methods; these methods due to their higher order continuous differentiable approximations fail to model discontinuous material properties of the subjected domains. In this study by improving the collocation method in RKPM treatment of such conditions have been achieved. Also in this study performance of a new meshfree method in fracture mechanics problems has been analyzed. GRKPM is one of these methods which its suitable accuracy and convergence has... 

Within the surface/interface elasticity, two following problem are solved: First the elastic behavior of an edge dislocation located inside the core of a core-shell nanowire which is embedded in an infinite matrix is studied within the surface/interface elasticity theory. The corresponding boundary value problem is solved exactly by using complex potential functions. The stress field of the dislocation, image force acting on the dislocation, and the dislocation strain energy is calculated by considering the interface effect. Second, the surface/interface elasticity approach is applied to the case of a misfit core-shell nanowire system in which the misfit strain is adjusted through the... 

This thesis presents an analytical solution for determination of the
electro-elastic media subjected to an anti plane shear harmonic wave containing a multi-phase cylindrical fiber whose electro-elastic properties differ from those of the matrix. Both the matrix and the coated-fiber system are transversely isotropic piezoelectric materials with symmetry and poling axes parallel to the fiber axis. The coating can have variable thickness. The dynamic electro-mechanical equivalent inclusion method (DEMEIM) is presented and employed as an extension of dynamic equivalent inclusion method (DEIM) in order to take into account the electro-mechanical coupling. Accordingly, the coating-fiber... 

By employing first principles density functional theory-based (DFT) molecular dynamics (MD), the influences of dangling and floating bonds as well as distorted tetrahedral bonds are studied on the mechanical, physical, and electronic properties of amorphous Si (a-Si). For further examination of the effects of these geometrical defects, two distinct amorphous samples, namely as-quenched and annealed are generated and examined. To verify the validity of the representative cells, the obtained radial distribution function, pair correlation function, and cohesive energy are compared with those corresponding results presented in the literature. Moreover, the surface energy is calculated at final... 

By virtue of a robust and efficient method, the solution of triple and quadruple integral equations which are the keys of various mixed boundary value problems corresponding to half-space and full-space media is addressed. These multiple integral equations are reduced to a well-known Fredholm integral equation of the second kind. In order to write the governing integral equations of the problem, Green’s functions play an important role. Therefore, Green’s functions of homogeneous and non-homogeneous transversely isotropic media in the form of line integrals including Bessel functions are obtained. Three interesting mixed boundary value problems in transversely isotropic materials are... 

Reproducing kernel particle method (RKPM) is a meshfree method for solving various differential equations. RKPM is based on pure mathematics; therefore, it is in the center of attention of many scientists. One major problem in RKPM is satisfying the essential boundary conditions (EBCs) involving the derivative of the field function. This problem is considered herein and its solution is proposed. To this end, two actions should be undertaken. First, the concept of Hermitian interpolation is employed to add the derivative term to the reproducing equation of RKPM and a new meshless method called gradient RKPM (GRKPM) is introduced. Second, the corrected collocation method is modified so... 

In addition to enhancement of the results near the point of application of a concentrated load in the vicinity of nano-size defects, capturing surface effects in small structures, in the framework of second strain gradient elasticity is of particular interest. In this framework sixteen additional material constants are revealed, incorporating the role of atomic structures of the elastic solid. In this work, the analytical formulations of these constants corresponding to fcc metals are given in terms of the parameters of Sutten-Chen interatomic potential function. The constants for ten fcc metals are computed and tabulized. Moreover, the exact closed-form solution of the bending of a... 

The present study aims at determining the elastic fields of ultra-small flaws and defects. These defects are often introduced undesirably in elastic solids during fabrication and their sizes are normally in the order of couple of nano-meters. In this work, the elastic fields around a circular nano-void subjected to a uniform farfield uniaxial tension, also the elastic fields of a nano-sized mode I crack under remote uniform loading are studied. In this paper the strain gradient theory developed by Mindlin and co-workers in 1960s is employed. According to this theory, the strain energy density assumes the form of a positive-definite function of the strain components and their first gradient.... 

In many problems, the traditional elasticity cannot predict phenomenon such as nano-scale defects, surface effects, and stress concentration correctly. For example, analysis near the crack tip, dislocation and inhomogeneity shows inconsistent results because in this case values of stress go to infinity. Therefore for solving these kinds of problems, higher order continuum theories were introduced. The appearance of additional constants in the equations of motion can represent the atomic nature of materials. Furthermore, they can be utilized for determining properties of materials vibration with high frequency, granular materials, and polymers.First strain gradient theory introduced by... 

In this thesis an analytical solution is introduced for finding the elastic fields of stress and strain in a confocal elliptic ring at the state of general plane problem. A confocal elliptic ring is a doubly connected region which its external and internal boundaries are ellipses with the same focal points. We used the method of complex variables, the functions of Kolosov-Muskhelishvili potentials, Laurent series expansion for analytical functions, the method of the analytic continuation of Milne-Thomson, elliptic hyperbolic coordinates, and two dimensional conformal mapping to do this study. the importance of this analysis is because we can simulate some problems of the elasticity by... 

During recent years, many researches on meshfree methods to solve differential equations and crack problem have been accomplished, and acceptable results have been obtained. One of these methods which is widely used in fracture mechanics specially in problems including crack is RKPM (reproducing kernel particle method). RKPM is one of the modern numerical methods in solving differential equations that has been lately introduced and developed. In this method, the genuine response of the system is replaced with a good approximation of the real response called ‘Reproduced Function’. The formulation of this method obviates the need for discretizing the domain by meshing with elements. In this... 

It is well known that the classical continuum theory does not consider size effect in predicting material’s behavior, however at the micro and nano scales, this effect is not negligible and the classical theory has deficiencies at these scales. To take into account the size effect, higher order continuum theories introduce new material constants into the formulation. One famous version of these theories is couple stress which is applied in this research. This theory considers size effect of inhomogeneity by employing Characteristic length of materials. Quasi-static couple stress and classical dynamic approaches do not include explicitly the size of the material unit cell in the formulation... 

Recently, there has been a strong interest in the development of a new class of meshfree methods. As an alternative to the finite element method (FEM), mainly due to elimination of high cost mesh generation processes. In addition, the size effect is currently a subject of increasing interest since it is an important parameter in predicting, correctly, the mechanical behavior of materials with microstructure. It was well established that classical linear elastic continua which neglects the higher order terms is not able to describe size effects. In contrast, enhanced continuum theories such as nonlocal or gradient-dependent models do involve an internal length scale. Thorough this length...