Sharif Digital Repository

The following dissertation examines the interaction between the free surface of a homogenous transversely isotropic half-space and a rigid circular foundation. The whole system is under a vertical and an inclined point loads applied simultaneously on the foundation and at the specified depth of the medium, respectively. Determination of the Green’s functions for the proposed mixed boundary value problem is of interest. By employment of the boundary conditions, the governing equations are represented in terms of a dual integral equation which are subsequently solved analytically. Furthermore, the exact closed-form expressions of the tilt (rotation and settlement) of the loaded rigid foundation... 

This work examines the problem of the fully coupled magneto-electro-elastic (MEE) scattering of SH-waves incident upon a heterogeneous MEE scatterer which is embedded in an unbounded medium. The scatterer consists of a circular core and a circular encapsulator with eccentricity. All three regions: the core, encapsulator, and the surrounding matrix have distinct MEE properties and fully coupled constitutive relations. The generated coupled MEE fields coexist simultaneously in all these regions without resort to any simplifying assumptions. The precise description of the multifunctionality involves the solution of three fully coupled partial differential equations in three different regions.... 

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 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... 

In this thesis, concerning Eigenstrain Theory, the micromechanical formulation of dental implants has been derived for the first time in the fields of Mechanics and Medical Science. The proliferation of using dental implants as a prosthesis for the people who lost their teeth because of poor maintenance and smoking cigarette results in scientists think more about the design of these implants and their stress fields inside the mandible. It is crystal clear that these stress fields cause stress shielding, which is a phenomenon that brings about bone loss or decrement in the bone density. Hence, if we know the stress that is produced by the implants inside the mandible, we can optimize the... 

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... 

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... 

This work focuses on developing a theoretical approach for the calculations of the surface elastic constants for (100) planes of fcc crystals. Using this method, the surface elastic constants, as well as the surface residual stress of the (100) planes of Al, Ag, Ni, Pt, and Cu fcc crystals, are evaluated using quantum calculations and VASP code. Surface effects are important in nanostructures and the considered metals are the most applicable ones in nanostructures especially in optic and electronic fields. For verification of the obtained values for surface elastic constants and residual stress, other surface parameters including the equilibrium lattice parameter, the energy per atom of the... 

Since the classical continuum theory fails to deal with the problems associated with defects, stress concentrators, and relevant deformation phenomena in solids, alternative approaches that can detect the atomistic nature of materials' fracture are required. The deficiency of the capture the size effect which yields delusively high values for some components of the stress field right on the edge of the stress concentrators, and its weakness in describing the complex interaction between small inhomogeneities, cracks and the like when they are only a few nanometers apart, are among some of the disadvantages of the classical approach. In recent years, however, atomistic methods are emerging to... 

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... 

The electro-elastic fields of nano-sized piezoelectric structures are considered based on the non-classical continuum theory. Nowadays because of increasing the application of piezoelectric materials in nano technology and exclusive properties of this kind of materials, they can use as the ingredients of electromechanical systems. Therefore, the determination of induced electro-mechanical fields is important. In this study the constitutive equations based on non-classical continuum theory and general anisotropy for the elastic, piezoelectric and dielectric tensors are considered, and the electromechanical fields are determined using the micromechanical method. Furthermore, the size effects... 

In this thesis, pull-in of nano/micromirrors under effects of capillary, Casimir and van der Waals (vdW) forces is investigated based on two models. In the first model, only rotation of torsional beams of mirror is considered. In the second model, effect of bending of the torsional beams is also considered. The static behavior of the mirror under capillary, Casimir and vdW loading are also studied using these models. Results show that neglecting bending effect, can lead to considerable overestimation in predicting the pull-in limits of the nano/micromirrors under these forces. Results reveal that the static behavior of the nano/micromirrors under these forces highly depends on 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... 

Nowadays, by adding a small amount of a desired nanomaterial to a matrix having certain properties one may design a multifunctional nanocomposites with a remarkably improved macroscopic properties of interest. The capability of conventional continuum theories in treating the problems of embedded ultra-small inhomogeneity with any of its dimensions comparable to the characteristic lengths of the involved constituent phases is questioned, mainly, on the grounds of the accuracy and the size effect. In this work, effort is firstly directed at the prediction of the macroscopic shear modulus of composites consisting of nano-/micro-size fibers of elliptic cross-sections via couple stress theory, a... 

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... 

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... 

Meshless Methods using kernel approximation like Reproducing Kernel Particle Method (RKPM) are methods for solving partial differential equations that require only nodal data and a description of the geometry without requiring element connectivity data and mesh producing. An innovative method of nonplanar material partitioning method (NMPM) with implementation of RKPM is employed to calculate the stress intensity factor (SIF) at the tip of an anticrack sited in an isotropic plate under a remote applied loading. Numerical examples in comparison with the exact closed form expressions show that accurate SIF for mode I can be obtained.

 

Nowadays, the excellent technological applications of composites have attracted the attentions of industry and numerous scientists. They are advantageous for their high tensile modulus, strength, and promising electrical and thermal properties. In applying the approach of lamellar inhomogeneity to real composites, the micro-geometries of the reinforcement must be considered such that they can be approximated as limiting case of an ellipsoid. In vapor grown carbon nanofiber, the fiber may have a diameter of about 150nm and length of 10-20 µm [1]. The modulus of carbon nanofiber is normally in the range of 100-600 GPa and sometimes even higher, whereas the modulus of some polymers is usually... 

It is the main idea of present thesis to provide a micromechanical method as a general treatment for several fundamental problems of the piezoelectric inhomogeneities. For initial demonstration of pertinent methodology, a single piezoelectric inhomogeneity of ellipsoidal geometry, under non-uniform far-field loading is considered. Accordingly, it is taken equivalent to elastic and dielectric inclusion problems connected by proper eigenstrain-electric field. This approach is named the electro-mechanical equivalent inclusion method (EMEIM) and requires that the electroelastic fields of the inhomogeneity to be equal to fields of the equivalent inclusions. Afterwards, the complex problem of... 

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...