آناليز ارتعاش و كمانش گرافين صفحه چند لايه بر روي بستر الاستيك بر پايه تئوري الاستيسيته غير محلي با استفاده از روش هاي عددي المان محدود وريتز

چكيده انگليسي :

Vibration and Buckling Analysis of Multilayered Graphene Sheets onElastic Foundation Based on Nonlocal Elasticity Theory Using Numerical Finite Element and Ritz Methods Amin Anjomshoa a anjomshoa@me iut ac ir Date of Submission 2012 3 12 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language FarsiSupervisor Ali Reza Shahidi shahidi@cc iut ac irAbstract Graphene G is a two dimensional plate like nanostructure with remarkable and extraordinary physicalproperties The intrinsic mechanical properties make graphene one of the most applicable structures indifferent nano engineering systems as sensors or reinforcements In the present study vibration and bucklinganalysis of multilayered graphene sheets MLGSs surrounded by two parameter elastic foundation areinvestigated using the finite element method and the Ritz functions Since the classical continuum theoriescannot take account of the small scale effects on the mechanical behavior of structures at nano scale thesequantum effects are introduced through the modified size dependent Eringen s nonlocal continuum theory Employing the nonlocal constitutive equation for planar orthotropic structures and adopting classical platetheory CLPT assumptions the load displacement relation associated with each graphene layer of a MLGSis obtained The Lennard Jones and Winkler Pasternak models are used to simulate the interlayer interactionsand foundation pressure respectively The intensity of Van der Waals forces between each two adjacent andnon adjacent layers is calculated by a relation obtained from linearization of the Lennard Jones interactionequation Also the springy and shear effects of elastic medium are considered by the two parameter Winkler Pasternak elastic model Decoupled forms of governing vibration and buckling equations based on thenonlocal continuum theory are obtained for the current extended model of embedded MLGS Variationalprinciple is introduced via an inverse approach using the governing equations to make a basis for numericalanalysis of MLGSs and other plate like nanostructures Finite element solutions for natural frequencies andcritical in plane loads of embedded MLGS are obtained through minimizing the introduced nonlocalpotential term There is also a study on the application of the Ritz functions in vibration and bucklinganalysis of elliptical nanoplates on elastic foundation using a similar approach The Ritz functions eliminatethe need for mesh generation and thus large numbers of degrees of freedom arising in discretization methodssuch as finite element method FEM Small scale effects on natural frequencies and critical buckling loadsof MLGS and elliptical nanoplate are investigated for different nonlocal parameters lengths aspect ratios inter layer interactions foundation parameters mode numbers and boundary conditions It is shown that bothnatural frequencies and buckling loads depend obviously on the non locality of the nano plates especiallywhen the dimensions decrease Also it is seen that classical continuum mechanics overestimates the naturalfrequencies and buckling loads of MLGS which leads to deficient in precision required for frequency andstability design of these load bearing structures for application in different nano mechanical systems Consequently it is seen that small scale effects play an important role in dynamic behavior of nanostructuresand should be considered via size dependent theories such as nonlocal elasticity theory The nonlocalcontinuum mechanics and finite element model developed in this work provide designers efficient tools topredict mechanical responses of plate like nanostructures in different nano devices Finally it should benoted that current FE and Ritz methods can be applied for analyzing nanoplates with arbitrary geometries variations in thickness and boundary conditions KeywordsMultilayered graphene sheet Elliptical nanoplate Small scale effects Nonlocal elasticity theory Tw

انجم شعاع، امين

آناليز ارتعاش و كمانش گرافين صفحه چند لايه بر روي بستر الاستيك بر پايه تئوري الاستيسيته غير محلي با استفاده از روش هاي عددي المان محدود وريتز

نانو صفحه بيضوي , اثرات مقياس كوچك , بستر الاستيك دو پارامتري , اصل تغييرات