Sharif Digital Repository

This paper is devoted to deformation theory of "anabelian" representations of the absolute Galois group landing in outer automorphism group of the algebraic fundamental group of a hyperbolic smooth curve defined over a number-field. In the first part of this paper, we obtained several universal deformations for Lie-algebra versions of the above representation using the Schlessinger criteria for functors on Artin local rings. In the second part, we use a version of Schlessinger criteria for functors on the Artinian category of nilpotent Lie algebras which is formulated by Pridham, and explore arithmetic applications  

To a hyperbolic smooth curve defined over a number-field one naturally associates "ananabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than those coming from deformations of "abelian" Galois representations induced by the Tate module of associated Jacobian variety. We develop an arithmetic deformation theory of graded Lie algebras with finite dimensional graded components to serve our purpose  

We study the deformation theory of Calabi-Yau structures in strongly pseudo-convex manifolds with trivial canonical bundles. Our approach could be considered as an alternative proof for a theorem of H. Laufer on the deformation of strongly pseudo-convex surfaces  

The response of an infinite Timoshenko beam subjected to a harmonic moving load based on the thirdorder shear deformation theory (TSDT) is studied. The beam is made of laminated composite, and located on a Pasternak viscoelastic foundation. By using the principle of total minimum potential energy, the governing partial differential equations of motion are obtained. The solution is directed to compute the deflection and bending moment distribution along the length of the beam. Also, the effects of two types of composite materials, stiffness and shear layer viscosity coefficients of foundation, velocity and frequency of the moving load over the beam response are studied. In order to... 

In this study, the energy concept along with the first- and third-order shear deformation theories (FSDT and TSDT) are used to predict the large deflection and through the thickness stress of FGM plates. These responses are studied and discussed as a function of plate thickness and the order "n" of a power law function which is considered for the through the thickness variation of the properties of the FGM plate. The results show that the energy method powered by the FSDT and FSDT is capable of predicting the effects of plate thickness on the deformation and the through the thickness stress. Here, also the effects of power "n" on the plate response is clearly depicted. Notably, the... 

This paper is devoted to mathematical modeling of anisotropic hyperelastic thick cylindrical shells like arteries by taking into account the volume compressibility and through-the-thickness deformation. To describe the hyperelastic behavior of this kind of shells and extract their constitutive relations, the modified anisotropic (MA) model is employed, which is able to characterize compressible behavior of hyperelastic materials like soft tissues. By considering the arterial segment as a thick cylindrical shell, the higher order thickness deformation shell theory together with nonlinear Green's strains are exploited to express its deformations and capture the thickness stretching effect. The... 

In this study the energy concept along with the classical plate theory (CPT), first and third order shear deformation theories (FSDT and TSDT) are used to predict the large deflection and through the thickness stresses of a FGM plate. For defining the volume fraction of the FGM constituent materials three different functions are considered; simple power-law (PFGM), exponential (E-FGM) and sigmoid (S_FGM) functions. Power-law and exponential functions are commonly used tocontrol the variations of properties of FGMs. However, with both functions, a stress concentration appears due to abruptchange of the volume fraction of the constituents. Therefore, a sigmoid FGM is used to define a new... 

In this study, based on the reduced from of elasticity displacement field for a long laminate, an analytical method is established to exactly obtain the interlaminar stresses near the free edges of generally laminated composite plates under the extension and bending. The constant parameters, which describe the global deformation of a laminate, are properly computed by means of the improved first-order shear deformation theory. Reddys layerwise theory is subsequently utilized for analytical and numerical examinations of the boundary layer stresses within arbitrary laminated composite plates. A variety of numerical results are obtained for the interlaminar normal and shear stresses along the... 

In this study, the dynamic response of the laminated composite beam with arbitrary lay-ups has been investigated within the framework of the third-order shear deformation theory using the finite element method. A new three-nodded finite element compliant with the theory is introduced next. To deal with the dynamic contact between the delaminated segments, unilateral contact constraints are employed in conjunction with Lagrange multiplier method. Furthermore, the Poisson's effect is incorporated in the formulation of the beam constitutive equation. Also, the higher-order inertia effects and material couplings (flexure-tensile, flexure-twist and tensile-twist couplings) are considered in the... 

This article presents a nonlocal sinusoidal shear deformation beam theory (SDBT) for the nonlinear vibration of single-walled boron nitride nanotubes (SWBNNTs). The surrounding elastic medium is simulated based on nonlinear Pasternak foundation. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the SWBNNTs are derived using Hamilton's principle. Differential quadrature method (DQM) for the nonlinear frequency is presented, and the obtained results are compared with those predicted by the nonlocal Timoshenko beam theory (TBT). The effects of nonlocal parameter, vibrational modes, length, and elastic medium on the nonlinear frequency of SWBNNTs... 

Based on the first-order shear deformation theory, the free vibration of the functionally graded (FG) truncated conical shells is analyzed. The truncated conical shell materials are assumed to be isotropic and inhomogeneous in the longitudinal direction. The two-constituent FG shell consists of ceramic and metal. These constituents are graded through the length, from one end of the shell to the other end. Using Hamilton's principle the derived governing equations are solved using differential quadrature method. Fast rate of convergence of this method is tested and its advantages over other existing solver methods are observed. The primary results of this study were obtained for four... 

Based on the first order shear deformation theory, free vibration behavior of functionally graded (FG) annular sector plates integrated with piezoelectric layers is investigated. The distribution of electric potential along the thickness direction of piezoelectric layers which is assumed to be a combination of linear and sinusoidal functions, satisfies both open and closed circuit electrical boundary conditions. Through a reformulation of governing equations and harmonic motion assumption, a novel decoupling method is suggested to transform the six second order coupled partial differential equations of motion into two eighth order and fourth order equations. A Fourier series method is then... 

In this paper a semi-analytical method is developed to analyze functionally graded cylindrical panels. In this method, the radial domain is divided into some finite sub-domains and the material properties are assumed to be constant in each subdomain. Imposing the continuity conditions at the interface of the adjacent sub-domains, together with the global boundary conditions, a set of linear algebraic equations are derived. Solving the linear algebraic equations, the elastic response for the thick-walled FG cylindrical panel is obtained. The method can be used for all material properties variations but in present study, material properties are assumed vary with Mori-Tanaka estimation. Results... 

In the presented research, vibrational, and amplitude behaviors of a sandwich spinning disk made of two laminated layers and graphene nanoplatelets reinforced composite (GPLRC) core has been reported. The Coriolis and centrifugal impacts have been taken into account due to its rotational feature. The stresses and strains have been obtained through the high-order shear deformable theory (HSDT). The structure’s boundary conditions (BCs) are determined using laminated rotating disk’s governing equations employing energy methods and ultimately have been solved via a computational approach called generalized differential quadrature method (GDQM). The rotational disk’s vibrations with different...