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#### Asymmetric wave propagation in a transversely isotropic half-space in displacement potentials

, Article International Journal of Engineering Science ; Volume 46, Issue 7 , 2008 , Pages 690-710 ; 00207225 (ISSN) ; Rahimian, M ; Eskandari, M ; Pak, R. Y. S ; Sharif University of Technology
2008

Abstract

With the aid of a complete representation using two displacement potentials, an efficient and accurate analytical derivation of the fundamental Green's functions for a transversely isotropic elastic half-space subjected to an arbitrary, time-harmonic, finite, buried source is presented. The formulation includes a complete set of transformed stress-potential and displacement-potential relations that can be useful in a variety of elastodynamic as well as elastostatic problems. The present solutions are analytically in exact agreement with the existing solutions for a half-space with isotropic material properties. For the numerical evaluation of the inversion integrals, a quadrature scheme...

#### Displacement potentials for functionally graded piezoelectric solids

, Article Applied Mathematical Modelling ; Volume 52 , 2017 , Pages 458-469 ; 0307904X (ISSN) ; Eskandari, M ; Ahmadi, S. F ; Sharif University of Technology
Abstract

Two new displacement potential functions are introduced for the general solution of a three-dimensional piezoelasticity problem for functionally graded transversely isotropic piezoelectric solids. The material properties vary continuously along the axis of symmetry of the medium. The four coupled equilibrium equations in terms of displacements and electric potential are reduced to two decoupled sixth- and second-order linear partial differential equations for the potential functions. The obtained results are verified with two limiting cases: (i) a functionally graded transversely isotropic medium, and (ii) a homogeneous transversely isotropic piezoelectric solid. The simplified relations...

#### Torsional surface wave propagation in a transversely isotropic FG substrate with piezoelectric over-layer within surface/interface theory

, Article Acta Mechanica ; Volume 231, Issue 6 , 2020 , Pages 2203-2216 ; Mohamadi Shodja, H ; Sharif University of Technology
Springer
2020

Abstract

Propagation of the torsional surface waves in a medium consisting of a functionally graded (FG) substrate bonded to a thin piezoelectric over-layer has been analytically formulated in the mathematical framework of surface/interface elasticity theory. In the cases where the wavelength and/or the thickness of the over-layer are comparable to the surface/interface characteristic length, then the surface/interface effects are not negligible. It is assumed that the over-layer is made of hexagonal 622 crystals with a single axis of rotational symmetry coinciding with the axis of polarization. The half-space is made of an FG transversely isotropic material in which the elasticity tensor and the...

#### Lateral Translation of a Flexible Disk Embedded in a Transversely Isotropic Half-Safe

, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor) ; Eskandari, Morteza (Supervisor)
Abstract

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...

#### Elastic Analysis of a Surface Stiffened Transversely Isotropic Half-space Under a Buried Horizontal Point Load

, M.Sc. Thesis Sharif University of Technology ; Eskandari, Morteza (Supervisor)
Abstract

In this study, the interaction between thin plate completely bonded to the transversely isotropic halfspace and a concentrated force applied horizontally (Mindlin-type force) are considered. This problem has been solved analytically. This problem is used as sample for thin solid films and surface coating technology, where the surface of solid is covered by thethin plate for increasing its stiffness. Moreover, this problem is a good sample when homogenous solid is subjected to contact loading and can be seen that mechanical properties of material which is near the solid surface varies; consequently, a two-phase solid is created.Because of the influence of noted inhomogeneity, solid is...

#### Composites with superspherical inhomogeneities

, Article Philosophical Magazine Letters ; Volume 89, Issue 7 , 2009 , Pages 439-451 ; 09500839 (ISSN) ; Avazmohammadi, R ; Shodja, H. M ; Weng, G. J ; Sharif University of Technology
2009

Abstract

In contrast to the traditional study of composites containing ellipsoidal inclusions, we highlight some calculated results for the effective moduli when the inclusion shape can be described by the superspherical equation, [image omitted], such that when p = 2 it reduces to a sphere and when p it becomes a perfect cube. We consider the cases of both aligned and randomly oriented superspherical inclusions with isotropic, cubic, and transversely isotropic properties, and show how the shape parameter, p, affects the overall moduli of the composites during the spherical to cuboidal transition

#### Consistent Strain Energy Functions for Transversely Isotropic and Orthotropic Hyperelastic Materials

, M.Sc. Thesis Sharif University of Technology ; Naghdabadi, Reza (Supervisor) ; Sohrabpour, Saeed (Supervisor) ; Arghavani, Jamal (Co-Advisor)
Abstract

Process Variation is seen as statistical variations in leakage current and delay of transistors in nano-scale technologies. The amount of process variations increase as the size of transistors decrease by technology scaling such that those effects can be seen in frequency of MPSoC (Multi-Processor System-on-Chip) cores and their leakage power deviation. These variations cause the tasks duration and power consumption fluctuate in different processors in an MPSoC instance. Consequently, some chip instances of the same MPSoC may consume more time and power than their considered limitations. Hence considering the process variation is necessary and required for MPSoC optimization at different...

#### Elastic Analysis of Brazilian Test of Transversely Isotropic Material

, M.Sc. Thesis Sharif University of Technology ; Eskandari, Morteza (Supervisor)
Abstract

In Former research we determinate elastic response of Brazilian Test of transversely Isotropic material . In Bio-mechanic science surveying mechanical properties and modeling biological organ such as bone , tooth and bio-material such as titanium, zirconium with application in joint replacement is very important . One of method to determine properties of bio-material which mostly has transversely Isotropic behavior is Brazilian Test. Also most rocks has transversely Isotropic behavior, so choosing efficient test is so important. In current issue , load apply in limited area and it is also considered friction in area of jaw loading area .By use of displacement potential function ...

#### Mixed Boundary Value Problems in Transversely Isotropic Materials

, Ph.D. Dissertation Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

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...

#### Vertical Forced Vibration of a Rigid Disk in a Transversely Isotropic Full-Space

, M.Sc. Thesis Sharif University of Technology ; Eskandari, Morteza (Supervisor) ; Mohammadi Shodja, Hossein (Co-Advisor)
Abstract

This research is concerned with the investigation of forced time–harmonic vertical vibration of a rigid disk embedded in a transversely isotropic full space medium. By properties of integral transform methods, the generalized mixed boundary–value problem is formulated as a set of dual integral equations, which in turn, are reduced to a Fredholm equation of the second kind. The obtained Fredholm integral equation is solved by well-known numerical methods. Selected results for the load distribution on the disk and complex compliance are presented for various ranges of frequency.

#### Axisymmetric Response of a Transversely Isotropic Half-space Stiffened by a Thin Plate Considering Refined Interaction Theory

, M.Sc. Thesis Sharif University of Technology ; Eskandari, Morteza (Supervisor)
Abstract

In this paper, the elastic response of a surface-stiffened transversely isotropic half-space subjected to a surface normal load is addressed. The half-space is reinforced by a Kirchhoff thin plate bonded to its surface. Two different boundary conditions are considered across the plate-half-space interface: (i) the classic approach in which the plate in-plane deformation is neglected by writing the interfacial boundary conditions across the plate mid-plane, and (ii) the refined approach that considers the in-plane deformation of plate due to bending by writing the boundary conditions across the bottom face of plate. By virtue of appropriate displacement potentials, the complete set of elastic...

#### A hyperelastic constitutive model for fiber-reinforced rubber-like materials

, Article International Journal of Engineering Science ; Volume 71 , 2013 , Pages 36-44 ; 00207225 (ISSN) ; Naghdabadi, R ; Arghavani, J ; Sharif University of Technology
2013

Abstract

In this paper, a Strain Energy Function (SEF) is proposed to characterize the hyperelastic behavior of transversely isotropic incompressible fiber-reinforced rubbers. The kinematics of the deformation is based on a strain measure consistent with the physics of the deformation. The SEF consists of an isotropic part and an anisotropic one where a simple form of SEF is used for both parts. In order to investigate the capabilities of the proposed model, two fiber-reinforced rubbers under homogeneous deformations are examined. The predictions of the model show a good agreement with the experimental data for both tensile and shear deformations. Also, torsion of a fiber-reinforced rubbery circular...

#### Green's functions of a surface-stiffened transversely isotropic half-space

, Article International Journal of Solids and Structures ; Volume 49, Issue 23-24 , 2012 , Pages 3282-3290 ; 00207683 (ISSN) ; Ahmadi, S. F ; Sharif University of Technology
2012

Abstract

Green's functions of a transversely isotropic half-space overlaid by a thin coating layer are analytically obtained. The surface coating is modeled by a Kirchhoff thin plate perfectly bonded to the half-space. With the aid of superposition technique and employing appropriate displacement potential functions, the Green's functions are expressed in two parts; (i) a closed-form part corresponding to the transversely isotropic half-space with surface kinematic constraints, and (ii) a numerically evaluated part reflecting the interaction between the half-space and the plate in the form of semi-infinite integrals. Some limiting cases of the problem such as surface-stiffened isotropic half-space,...

#### Axial Stiffness of a Detached Anchor Plate in a Transversely Isotropic Solid

, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shoja, Hossein (Supervisor) ; Eskandari, Morteza (Co-Advisor)
Abstract

In this study, the analytical treatment of an anchor plate buried in a transversely isotropic half-space and subjected to a normal point load is addressed. In reality, the tension face of the anchor plate is detached from the soil and the edges of the detached zone extend to a region greater than the anchor plate area. To simulate this situation, the anchor plate is modeled as a rigid circular disk located in a penny-shaped crack and it is in smooth contact with only single face of the crack. With the aid of an appropriate displacement potential function and Hankel transform, the governing equations of the problem are written as a set of triple integral equations. Employing some mathematical...

####
Numerical Modeling of Fracture Mechanics in Isotropic/ Orthotropic FGMs by XFEM

,
M.Sc. Thesis
Sharif University of Technology
;
Kazemi, Mohammad Taghi
(Supervisor)
Abstract

Nowadays, regarding to knowledge progresses in various fields,advanced materials for which have acceptable performance in sensitive and special conditions must be used. Functionally graded materials are advanced multiphase composite materials that are characterized by continues spatial variations in mechanical and thermal properties. Clearly, studying on fracture mechanics of FGMs is important because they are used in igh-tech and sensitive applications.In this research, numerical modeling of fracture mechanics in isotropic/orthotropic/ transversely isotropic FGMs via interaction integral method is performed. Both incompatible and non-equilibrium formulations of interaction integral are...

#### The Response of Transversely Isotropic Half-Space Stiened by a Surface Thick Plate

, M.Sc. Thesis Sharif University of Technology ; Eskandari, Morteza (Supervisor)
Abstract

In this study the axisymmetric and asymmetric problem of interaction between a transversely isotropic half-space and various rst order shear deformation plate theories including Mindlin, Reissner and Vasil'ev are addressed. In order to improve the accuracy of solution, the surface boundary conditions of the half-space are modied.Moreover, the results compared with the exact solution and the most appropriate result is identied. The displacement Green's functions are obtained for both cases, modied and unmodied boundary conditions which can be expressed in a closed form and a numerically evaluated part. The latter is calculated exploiting Built-in numerical interrelation function of...

#### A Tilt of a Surface Rigid Circular Foundation Due to an Inclined Buried Point Load in a Transversely Isotropic Half-Space

, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor) ; Eskandari, Morteza (Supervisor)
Abstract

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...

#### Elastic Responses of a Transversely Isotropic Half-Space Reinforced by a Buried Extensible Membrane under Internal Loading

, M.Sc. Thesis Sharif University of Technology ; Eskandari, Morteza (Supervisor)
Abstract

In this research, a homogeneous elastic half-space with transversely isotropic behavior, reinforced by an isotropic thin membrane is investigated under static loading with an analytical approach. The membrane is considered as an infinite plane with a thickness of negligible and buried at the arbitrary depth from the surface of the half-space, also its flexural strength is neglected and only the in-plane stiffness is considered for it. The reinforced half-space is investigated under several concentrated and distributed static loads, which are applied to the surface of the half-space or buried at the depth of the membrane. The membrane is first modeled as a three-dimensional elastic layer and...

#### 3D Elasticity Buckling Solution for Transversely Isotropic Functionally Graded Rectangular Plates by Displacement Potential Function

, M.Sc. Thesis Sharif University of Technology ; Khaloo, Alireza (Supervisor) ; Navayi Neya, Bahram (Co-Supervisor)
Abstract

The importance of transversely isotropic and functionally graded materials and also plates in industry necessitates studies on these kinds of structures. This study works on the buckling of simply supported rectangular transversely isotropic FGM plates subjected to in-plane uniaxial or biaxial static loads. For this purpose, discretization method is applied and the aforesaid inhomogeneous plate is divided into arbitrary number of sublayers parametrically (N). With the help of displacement potential functions, coupled different equations for each sublayer are simplified to two uncoupled different equations in terms of the potential functions. These governing equations for transversely...

#### Three-dimensional dynamic Green's functions in transversely isotropic tri-materials

, Article Applied Mathematical Modelling ; Volume 37, Issue 5 , March , 2013 , Pages 3164-3180 ; 0307904X (ISSN) ; Rahimian, M ; Eskandari, M ; Sharif University of Technology
2013

Abstract

An analytical derivation of the elastodynamic fundamental solutions for a transversely isotropic tri-material full-space is presented by means of a complete representation using two displacement potentials. The complete set of three-dimensional point-load, patch-load, and ring-load Green's functions for stresses and displacements are given, for the first time, in the complex-plane line-integral representations. The formulation includes a complete set of transformed stress-potential and displacement-potential relations in the framework of Fourier expansions and Hankel integral transforms, that is useful in a variety of elastodynamic as well as elastostatic problems. For the numerical...