Papers by Keyword: Nonlocal Elasticity

Abstract: Torsional vibration analysis of the axially functionally graded carbon nanotubes has been carried out. Nonlocal stress gradient elasticity theory has been used in continuum mechanics model of the carbon nanotube. Variation of the material properties of the axially graded nanostructure has been assumed in exponential form. Differently from the majority of literature works, viscous damping and nonlocal parameters have been assumed in grading form. Energy functional for the carbon nanotube has been achieved with minimum potential energy principle and weak form solution has been obtained with the Ritz Method. Effects of material grading, nonlocality and viscoelasticity to the torsional dynamics of axially graded carbon nanotube have been investigated. Results of the present work could be useful in modeling and production of axially functionally graded nanostructures.

Abstract: Computational prediction damage in cementitious composites, as steel fibre reinforced ones, under mechanical, thermal, etc. loads, manifested as creation of micro-fractured zones, followed by potential initiation and evolution of macroscopic cracks, is a rather delicate matter, due to the necessity of bridging between micro-and macro-scales. This short paper presents a relatively simple approach, based on the nonlocal viscoelasticity model, coupled with cohesive crack analysis, using extended finite element techniques. Such model admits proper verification of its existence and convergence results, from the physical and mathematical formulation up to software implementation of relevant algorithms. Its practical applicability is documented on a sequence of representative computational examples.

Abstract: Vibration problem of variable cross-sectional nanorods have been investigated. Analytical solutions have been determined for the variable cross-sectional nanorods for a family of cross-sectional variation. Cross-sectional area variation has been assumed as power function of the axial coordinate. Nonlocal governing equation of motion has been obtained as a second order linear differential equation. Bessel functions have been used in analytical solution of the governing differential equation. Effect of nonlocal and area variation power parameters on dynamics of nanorods have been analyzed. Mode shapes of nanorod have been depicted in various cases and boundary conditions. Present results could be useful at design of atomic force microscope’s probe tip selection.

Abstract: The present paper investigates the nonlocal buckling of Zigzag Triple-walled carbon nanotubes (TWCNTs) under axial compression with both chirality and small scale effects. Based on the nonlocal continuum theory and the Timoshenko beam model, the governing equations are derived and the critical buckling loads under axial compression are obtained. The TWCNTs are considered as three nanotube shells coupled through the van der Waals interaction between them. The results show that the critical buckling load can be overestimated by the local beam model if the small-scale effect is overlooked for long nanotubes. In addition, a significant dependence of the critical buckling loads on the chirality of zigzag carbon nanotube is confirmed, and these are then compared with: A single-walled carbon nanotubes (SWCNTs); and Double-walled carbon nanotubes (DWCNTs). These findings are important in mechanical design considerations and reinforcement of devices that use carbon nanotubes.

Abstract: The higher order Haar wavelet method (HOHWM) introduced recently by workgroup is utilized for vibration analysis of nanobeams. The results obtained are compared with widely used Haar wavelet method. It has been observed that the absolute error has been reduced several magnitudes depending on number of collocation points used and the numerical rate of convergence was improved from two to four. These results are obtained in the case of the simplest higher order approach where expansion parameter k is equal to one. The complexity issues of the HOHWM are discussed.

Abstract: Vibration of an axially loaded viscoelastic nanobeam is analyzed in this study. Viscoelasticity of the nanobeam is modeled as a Kelvin-Voigt material. Equation of motion and boundary conditions for viscoelastic nanobeam are provided with help of Eringen’s Nonlocal Elasticity Theory. Initial conditions are used in solution of governing equation of motion. Damping effect of the viscoelastic nanobeam structure is investigated. Nonlocal effect on natural frequency and damping of nanobeam and critical buckling load is obtained.

Abstract: In the present study, buckling of eccentrically loaded nanobeams in which the load is not applied at the centroid of cross section, has been studied. Eringen’s Nonlocal Elasticity Theory has been used in the formulation of governing equation of motion of the nanobeam. Simply supported and free boundary conditions for nanobeam have been taken consideration. The effect of nonlocal parameter, eccentricity of the load, nanobeam length on the buckling deflection and critical buckling load on nanobeam have been investigated. Present results can be useful in the design of nano-structures.

Abstract: The fracture analysis for two-dimensional nonlocal elasticity is presented by the numerical approaches i.e. the Local Integral Equation Method (LIEM). Based on the Eringen’s model, the nonlocal stresses at the crack tip are regular. Numerical simulation by LIEM is proposed for the nonlocal elasticity fracture problems. A rectangular cracked plate subjected to tensile load is observed numerically to demonstrate the convergence and accuracy of LIEM.

Abstract: This study deals with the frequency analysis of Nano-sandwich-structure with nonlocal effect. The model takes into account the flexibility of the sandwich core while the faces are treat as beams. The different stiffness of core will impart different vibration characteristic of the structure. To examine free vibrations of Nano-sandwich-structure, nonlocal elasticity theory has been applied. In this paper an investigation is carried out to understand the small-scale effects in the free vibration. The boundary conditions of simply-supported conditions are described here. Further the effects of scale coefficient and stiffness parameter are studied in this manuscript.

Abstract: In this article surface effects are considered to study the electromechanical coupling behavior of piezoelectric nanobeams with the non-local Euler-Bernoulli beam theory. The equation of motion for piezoelectric nanobeams with considering both surface effect and nonlocal effect is achieved and exact term for natural frequencies is derived for simply supported conditions. In the following the axial load effect on the natural frequencies piezoelectric nanobeams has been studied.