Sharif Digital Repository

In the present study, free vibrations and stability of rotating single walled carbon nanotubes (SWCNT) is investigated by nonlocal theory of elasticity; while the CNT is partially resting on an elastic foundation. The governing equations of motion are presented by using Love's shell assumptions. An exact series expansion method of solution is employed and very accurate results are obtained. Some parameter studies including the effects of rotating speed, foundation stiffness, slenderness ratio and nonlocal parameter on the natural frequency and stability margins of the current model are studied. The studies show that rotation rates and foundation elasticity can contribute significantly in the... 

Many authors simply use band structure of infinite photonic crystals to predict the beam's direction in a finite structure. The validity of this approximation for high frequencies has been questioned by Felbacq (PRL 92, 193902) and instead a dressed (by evanescent waves) transfer matrix has been suggested. In this work, we show through numerical examples that the direction obtained by conventional band structure is more accurate than that of dressed transfer matrix of Felbacq et. al. We also demonstrate that this approximation can be improved by taking the effect of evanescent Bloch modes into consideration. The effect of these modes leads to a constant shift of beam's center inside and far... 

In this study, we numerically investigate the size effect of a bluff body, embedded inside a combustor, on the formation of carbonaceous nano-particulate matter (PM). The combustor is fed with a jet propulsion fuel. We first evaluate our extended numerical tool by simulating a turbulent kerosene/air nonpremixed flame in a combustor. The achieved results are then compared with those of experiment. The comparisons show that there are good agreements between them. Next, we embed an O-ring type flame holder inside the combustor to change its configuration, i.e., to extend it to a bluff-body burner. Assuming a constant air mass flow rate, we investigate the blockage ratio effects of the burner... 

A continuum implementation of stress gradient plasticity is established to analyze passivated thin films under tension. It is verified and evaluated by investigation of the tensile response of passivated Cu films with different thicknesses and grain sizes. The material parameters are fitted to the stress-strain experimental data, while the length scale parameter is directly characterized from the corresponding available discrete dislocation predictions. The numerical solutions give rise to boundary layers near the interface between film and passivation. This prediction is consistent with the formation of dislocation pileups at the film-passivation interface and also is responsible for the... 

In the present study, free vibrations of single walled carbon nanotubes (SWCNT) on an elastic foundation is investigated by nonlocal theory of elasticity with both beam and shell models. The nonlocal boundary conditions are derived explicitly and effectiveness of nonlocal parameter appearing in nonlocal boundary conditions is studied. Also it is demonstrated that the beam model is comparatively incapable of capturing size effects while shell model captures size effects more precisely. Moreover, the effects of some parameters such as mechanical properties, foundation stiffness, length and radius ratios on the natural frequencies are studied and some conclusions are drawn  

Classical continuum mechanics fails to give accurate solution near the crack tip, moreover, it implies that a solid is able to sustain an infinite stress at the Griffith-Inglis crack tips. Among other critical issues is the inability of the classical approach to sense the size effect. For these reasons, for more in-depth understandings and accurate behavioral predictions, it is essential to develop some atomistic methods which properly accounts, not only for the structure but also the long and short range atomic interactions effectively. In this work the interaction of inhomogeneity and crack under polynomial loading is simulated by using the many body Rafii-Tabar and Sutton potential... 

The continuum theory of dislocations is applied to formulate the problem of a double ended dislocation pileup under quadratic applied stress. Accordingly, a second order stress gradient plasticity model is presented to address the contribution of the first and the second stress gradients in the effect interpretation. The model is employed to predict the initial strengthening and subsequent hardening in curved and straight thin foils under pure bending within the continuum framework. It is shown that the so-called stress gradient plasticity model that ignores the second stress gradient may not give sound interpretations of the size effects. The plastic response of thin foils is affected by... 

Due to inadequacy of the classical continuum theories at the nano-scale when dealing with defects, stress concentrators, and relevant deformation phenomena in solids, a refined approach that can capture the discrete atomic features of solids is essential. The inability to detect the size effect, giving unrealistically high values for some components of the stress field right on the edge of the stress concentrators, and infirmity to address the complex interaction between small inhomogeneities, cracks and as such when they are only a few nanometers apart, are among some of the drawbacks of the classical approach. An atomistic study which employs atomic finite element method in conjunction... 

This paper presents the results of an experimental and analytical study on the improvements gained in the axial compressive behavior of confined concrete. Among several parameters affecting compressive ductility of confined concrete, including confinement mechanical volumetric ratio, shape and size effect, number of confinement layers, strength of plain concrete and ductility of confining material, the latter was found to play the most important role in determining the ultimate strain and post peak behavior of concrete. Axial compressive tests were performed on small-scale circular or square section concrete columns, which were retrofitted either by CFRP jacket or by two types of... 

A new expression for the shear capacity of reinforced concrete beams without stirrups was derived by calculating the aggregate interlock capacity across the major diagonal crack of the beam, a procedure somewhat similar to those based on the modified compression field theory. Two formulas were obtained from the simplification of this expression. All three relations capture the dependence of shear strength on the size of the beam, the ratio of shear span to beam depth, longitudinal reinforcement ratio, maximum aggregate size, and concrete strength. The limits of these formulas agree well with the limit solutions of shear failure load for very small and very large beams based on plastic and... 

The classical continuum theory is neither able to accurately model the mechanical behavior of micro/nano-scale structures nor capable of justifying the size-dependent behavior observed in these structures; so the non-classical continuum theories such as the strain gradient theory have been emerged and developed. In order to enable the finite element method (FEM) to more accurately deal with the problems in micro/nano-scale structures, a size-dependent Euler-Bernoulli beam element is developed based on the strain gradient theory. Compared to the classical Euler-Bernoulli beam element, the nodal displacement vector of the new Euler-Bernoulli beam element has an additional component, i.e. the... 

In this paper, a size-dependent formulation is developed for Timoshenko beams made of functionally graded materials (FGMs). The developed formulation is based on the strain gradient theory; a non-classical continuum theory able to capture the size-effect in micro-scaled structures. Five new equivalent length scale parameters are introduced as functions of the constituents' length scale parameters. It is shown that the size-dependent static and dynamic behavior of FG micro-beams can be described using these equivalent length scales. The governing differential equations of motion and both classical and non-classical sets of boundary conditions are derived for the proposed strain gradient FG... 

In this paper, the strain gradient theory, a non-classical continuum theory capable of capturing the size effect observed in micro-scale structures, is employed in order to investigate the size-dependent mechanical behavior of microbars. For a strain gradient bar, the governing equation of motion and classical and non-classical boundary conditions are derived using Hamilton's principle. Closed form solutions have been analytically obtained for static deformation, natural frequencies and mode shapes of strain gradient bars. The static deformation and natural frequencies of a clamped-clamped microbar subjected to a uniform axial distributed force are derived analytically and the results are... 

The elastic behavior of an edge dislocation, which is positioned outside of a nanoscale elliptical inhomogeneity, is studied within the interface elasticity approach incorporating the elastic moduli and surface tension of the interface. The complex potential function method is used. The dislocation stress field and the image force acting on the dislocation are found and analyzed in detail. The difference between the solutions obtained within the classical-elasticity and interface-elasticity approaches is discussed. It is shown that for the stress field, this difference can be significant in those points of the inhomogeneity-matrix interface, where the radius of curvature is smaller and which... 

The couple stress theory is a non-classical continuum theory which is capable to capture size effects in small-scale structures. This property makes it appropriate for modeling the structures in micron and sub-micron scales. The purpose of this paper is the derivation of the governing motion equations and boundary conditions for the geometrically nonlinear micro-plates with arbitrary shapes based on the modified version of the couple stress theory. The consistent boundary conditions are provided at smooth parts of the plate periphery and also at the sharp corners of the periphery using variational approach  

The properties of W-15 wt.%Cu composites were investigated by preparing two distinct composites of micrometer and nanoscale structures. Micrometer composite was produced by mixing elemental W and Cu powders and nanometer one was synthesized through a mechanochemical reaction between WO3 and CuO powders. Subsequent compaction and sintering process was performed to ensure maximum possible densification at 1000-1200 °C temperatures. Finally, the behavior of produced samples including relative density, hardness, compressive strength, electrical conductivity, coefficient of thermal expansion (CTE) and room temperature corrosion resistance were examined. Among the composites, nano-structured...