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چكيده انگليسي :

Stress Analysis of Nanorings Arches Based on Nonlocal Elasticity Theory Azam Arefi azam arefy @yahoo com March 5 2012 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language FarsiSupervisor Dr Mahmoud Salimi salimi@cc iut ac ir Abstract Nanotechnology has great potential applications in many fields such as chemistry physics material science etc In the recent years nanostructures due to their extraordinary properties are used in a wide range of nanodevicessuch as nanosensors nanoactuators and nanocomposites So appropriate physical and mechanical analysis of thesestructures should be under investigation for proper design and useful handling of them After the invention of carbonnanotubes CNTs a large number of researches using experimental and theorical approaches have been directed toanalyze micro and nanostructures Atomistic modelings are expensive for large sized atomic systems andconducting experiments at the nanoscale are difficult and sometimes not applicable Consequently continuummodels which are proposed may be used for a larger system while they are able to include nanoscale size effect Since the classical continuum theory is free scale and cannot capture the size effect hence modified continuumtheories are considered These methods are beneficial from the computational efficiency of classical continuummodeling while they are accurate enough comparable to atomistic models The most widely reported theory foranalyzing small scale structures is the nonlocal elasticity theory In the nonlocal continuum mechanics it is assumedthat the stress at a reference point is a function of strains at all points in the continuum thus in nonlocal mechanics the long range force between atoms and internal length scales are introduced into the constitutive relations of ahomogeneous and isotropic material as a material parameter The nonlocal constitutive equations have been used tostudy wave propagation in composites fracture mechanics surface tension fluids etc In this thesis buckling andvibration analysis of nanorings and nanoarches is investigated based on nonlocal elasticity theory Thesenanostructures have many applications in microelectromechanical MEMS and nanoelectromechanical NEMS systems The principle of virtual displacement is implemented to circular nanorings and nanoarches to derive thegoverning differential equations which are solved analytically Inextensibility constraint exerted using Lagrange smultiplier method initialized from the unbuckled state to the adjacent buckled equilibrium state The effects ofdimensions opening angle mode number load behavior and nonlocal parameter on buckling loads are investigatedand then the effect of shear deformation on buckling load and natural frequencies are studied Carbon nanotubesmay have some defects which cause obvious changes in their behaviors Geometrical imperfection is one type ofthese defects which may occur during CNTs manufacturing Generally this type of CNTs may be applied in acurved configuration in other nanostructures such as nanocomposites In this case these nanotubes cannot bemodeled as straight components In the present work stability and vibration of an embedded single walled carbonnanotube with small initial curvature under lateral loading has been investigated based on Eringen s nonlocalelasticity theory Euler Bernoulli beam theory EBT is used to model the behavior of nanotubes Winkler Pasternaktype elastic foundation has been used to estimate the effect of matrix Governing equations have been derived usingthe principle of virtual work The relationship among critical buckling load nonlocal parameter and mode numbersare investigated by parametric studies It has seen that nonlocal parameter contribute to the mechanical properties ofnanostructures and should be considered Key Words Nonlocal elasticity theory Circular nanoring Nanoarch Stability analysis Vibration Lagrange s multiplier method

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آناليز تنش نانو حلقه/نانو قوس به كمك تئوري الاستيسيته نا موضعي

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