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چكيده انگليسي :

Small Scale Effect on the Buckling Behavior of Circular Nanoplates Ali Farajpour oderji a farajpouroderji@me iut ac ir Date of Submission 2012 1 28 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisor Alireza Shahidi Shahidi@cc iut ac irAbstractNanomaterials have been attracted the attention of many researchers due to their superior mechanical chemical and electronic properties These desirable properties have led to its applications as componentsin nano electro mechanical systems Continuum modeling of nanostructures has received the great deal ofattention of scientific community because controlled experiments in nanoscale are difficult and moleculardynamic simulations are highly computationally expensive Since the classical continuum elasticity is ascale free theory the use of classical continuum models may be uncertain in the analysis of structuralelements in nanoscale such as carbon nanotubes and graphene sheets There are various modified classicalcontinuum theories which capture size effects such as couple stress theory strain gradient elasticitytheory modified couple stress theory and nonlocal elasticity theory Among all size dependent theories the nonlocal elasticity theory has been commonly used in the theoretical investigations of structures atsmall scale Nonlocal theory is based on this assumption that the stress tensor at an arbitrary point in thedomain of nanomaterial depends not only on the strain tensor at that point but also on strain tensor at allother points in the domain Both atomistic simulation results and experimental observations on phonondispersion have shown the accuracy of this observation This research presents a formulation of nonlocalelasticity theory for the axial vibration analysis of tapered nanorods Solutions for natural frequencies arenumerically computed using the differential quadrature method DQM for clamped clamped andclamped free boundary conditions Furthermore the buckling behavior of nanoscale circular plates underuniform radial compression is studied Small scale effect is taken into consideration using nonlocalelasticity theory This thesis also presents an investigation on the buckling characteristics of nanoscalerectangular plates considering non uniformity in the thickness Based on the nonlocal continuummechanics governing differential equations are derived Numerical solutions for the buckling loads areobtained using Galerkin method The vibration characteristic of variable thickness nanoplates embeddedin an elastic medium is also investigated The nonlocal governing equations of motion are derived takinginto account the influences of the small scale based on the first order shear deformation theory FSDT ofplates Numerical solution for the vibration frequencies of nanoplates are obtained by employing thedifferential quadrature method DQM as a simple efficient and accurate numerical tool for differentialequations with variable coefficients In another problem attempt is made to study the buckling behavior oforthotropic graphene sheets under various linearly varying in plane normal forces Based on the nonlocalelasticity theory the small scale effects are introduced Using the equilibrium equations of a differentialelement of a rectangular plate the governing equations of single layered graphene sheet SLGS arederived Differential quadrature method DQM is used to solve the governing equations for simplysupported boundary conditions clamped boundary conditions and various combinations of them Toverify the accuracy of the DQM solutions the governing equation is also solved by the power seriesmethod PSM of Frobenius In addition the postbuckling of single layered graphene sheet subjected toaxial compression based on the nonlocal continuum mechanics is investigated The geometricalnonlinearity is modeled with the use of von Karman s assumptions Galerkin method is applied to solvethe governing nonlocal equations for postb

فرج پور اودرجي، علي

بررسي اثر مقياس كوچك بر كامنش نانو صفحات دايره اي

روش سنجش وزني مشتقات , الاستيسيته غير محلي