تحليل ارتعاش و كمانش نانو صفحات مثلثي ارتو تروپيك بر اساس تئوري الاستيسيته غير محلي و با استفاده از روش گالركين

چكيده انگليسي :

95 Buckling and Vibration Analysis of Orthotropic Triangular Nano Plates Using Nonlocal Theory and Galerkin Method Sayed Hossein Shahidi s shahidi@me iut ac ir Date of Submission 2012 3 13 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language FarsiSupervisor Alireza shahidi shahidi@cc iut ac irAbstract The small scale effect on the elastic buckling and vibration of triangular orthotropic single layeredgraphene sheets is studied employing nonlocal continuum mechanics Superior mechanical chemical andelectrical properties of nanostructures cause their wide usage in different nano devices such as nano sensors nano actuators and nano composites Due to their discrete structure atomistic methods such as moleculardynamic simulations density functional theory are more proper for the accurate mechanical analysis ofnanostructures As controlled experiments in nano scale are difficult and molecular dynamic simulations arecomputationally expensive theoretical modeling of nanostructures would be an important issue as long as theapproximate analysis of nanostructures is concerned Although classical continuum elasticity is a scale freetheory and cannot foretell the size effects however continuum modeling of nanostructures has gained ever broaden attention Using local theory for the small size analysis leads to the over predicting results To predictmicro nano structures correctly it is necessary to consider the small scale effects Some size dependentcontinuum theories that take small scale effects into consideration are couple stress elasticity theory straingradient theory and modified couple stress theory However the nonlocal elasticity theory initiated byEringen is the most common continuum theory used for analyzing the small scale structures In order tocapture the small scale effects in nonlocal continuum theory it is assumed that the stress at a point depends onthe strain at all points in the domain This is contray to the classical continuum theory in which it is assumedthat the stress at a point is just a function of the strain at that point So dimensions of a system reduce to thesmall scale they become comparable to the inter atomic or inter molecular spacing of the system and so thematerial can no longer be modeled as a continuum In addition at small scale the influence of long rangeinter atomic and inter molecular cohesive forces on the static and dynamic responses of nanostructures tendsto be significant and cannot be neglected In this present work the principle of virtual work is emploied toderive the govering equation The Galerkin method in conjuction with the area coordinates of the nanoplate isused as a basis for the analysis The straight sided triangular domain is mapped into a right angled triangledomain in the computational space using a three nod element The solution procedure views the entiretriangular nano plate as a single super continuum element Nonlocal theories are emploied to bring out theeffect of the nonlocal parameter on natural frequencies and buckling parameter of the nanoplates Effects ofnonlocal parameter lengths of nano plate aspect ratio mode number material properties and differentboundary condition on the nano plate buckling loads and natural frequency are investigated It is shown thatthe buckling loads and natural frequency depend on the non locality of the micro nano plate especially at thesmall dimensions and clamped boundary condition Also the effects of geometrical parameters such as aspectratio and mode numbers on the buckling loads and natural frequencies decrease when nonlocal parameterincreases for all arbitrary triangular plates Keywords Buckling and Vibration analysis Nonlocal elasticity theory Triangular nano plate Galerkinmethod different boundary condition

شهيدي، حسين

تحليل ارتعاش و كمانش نانو صفحات مثلثي ارتو تروپيك بر اساس تئوري الاستيسيته غير محلي و با استفاده از روش گالركين

آناليز ارتعاشي و كمانش , نانو صفحه مثلثي , شرايط مرزي ساده و گيردار