تحليل كمانش حرارتي نانو صفحات بر پايه تئوري دو متغيره اصلاح شده با بكارگيري تاثير مقياس كوچك غير محلي به روش سنجش وزني مشتق

چكيده انگليسي :

Thermal Buckling Analysis of Nanoplate Based on Two Variable Refined Plate Theory via Nonlocal Small Scale Effect by DQM Gholam Ghorbani gho ghorbani84@yahoo com Date of Submission 22 January 2013 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisors Ali Reza Shahidi Shahidi@cc iut ac ir Abstract In this work the mechanical stability of nanoplates under thermal loading was studied Graphene isthe two dimensional 2D counterpart of graphite with superior properties High hardness excellent electricaland thermal conductivity high mechanical strength flexibility and unique magnetic properties are among themost important properties of nanometer sized graphene These unique properties have attracted a lot ofattention in different areas of science Buckling is one of the most important issues on the mechanicalanalysis of plates So buckling of plates especially those made of graphene was studied in this thesis Thermal buckling is one type of buckling that is caused due to the temperature rise in the parts and it is amajor challenge in the construction of new electronic components Today s electronics is silicone based andgraphene is a potential alternative for the future electronic devices Therefore the phenomenon of thermalbuckling has also been considered in this thesis In order to take the small scale effects into account Eringen s non local elasticity theory was employed to derive the constitutive equations as the results obtainedfrom this theory has been reported to match well with atomic simulation results Also two variable refinedplate theory was utilized to derive the governing buckling equation of orthotropic plate This theory takes thetransverse shear effects into account and assumes a parabolic distribution for the transverse shear strainsthrough the plate thickness Therefore the results obtained from this theory are more accurate than thoseobtained from the classical plate theory The DQ method was then used to solve the governing equations This method converts the differential equation into a set of algebraic equations within the problem domain The main advantage of DQ method over the analytical method is its ability to consider any arbitraryquadrilateral geometry and various boundary conditions Buckling of arbitrary straight sided quadrilateralplates with both simply supported and clamped boundary conditions was investigated The boundaryconditions were imposed using the Shu s direct method For the sake of convenience and generality thegoverning equations were non dimensionalized A computer program was coded in MATLAB software andit was used to study the effect of various parameters on the buckling load As for the verification purposes the numerical solution was compared with the Navier s solution exact solution and excellent agreement wasobserved The effect of small scale factor for different modes and geometrical parameters that influence thethermal load was also studied The effect of geometrical parameters including the aspect ratio of trapezoid angle of parallelogram and aspect ratio of rectangle on the buckling load were plotted for different scalecoefficients It was observed that the DQ method is an effective method in terms of both accuracy and rate ofconvergence for analysis of nanostructures Moreover it was found that the critical load ratio is equal to thecritical temperature ratio in similar situations It was also proven that the dimensionless buckling load isindependent of the elasticity modulus for isotropic material and it is dependent on the orthotropic ratio E2 E1 for orthotropic materials not on the moduli Keywords Thermal buckling Orthotropic nanoplate Nonlocal theory Differential quadrature method Twovariable refined plate theory

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تحليل كمانش حرارتي نانو صفحات بر پايه تئوري دو متغيره اصلاح شده با بكارگيري تاثير مقياس كوچك غير محلي به روش سنجش وزني مشتق

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