تاثير مقياس اندازه كوچك در تحليل كمانش حرارتي نانو صفحات ارتوتروپيك چهار ضلعي به روش گالركين

چكيده انگليسي :

81 Small Scale Effect on Thermal Buckling Analysis of Orthotropic Nanoplate using Galerkin Method Reza Parishani r parishani@me iut ac ir Date of Submission 26 August 2012 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 Hassan Khdemizadeh hkhademyza@cc iut ac ir Abstract Buckling analysis of orthotropic graphene monolayer and multilayer nanoplates under bi axialcompression were studied in this work Graphene has extraordinary properties such as nano scale size highmechanical stiffness and roughness high electrical and thermal conductivity flexibility ductility andmagnetic property The unique properties of this material have received a lot of attention from the scientists Because of the importance of buckling in these plates thermal buckling of the graphene sheets has beenstudied derivation of constitutive equations the small scale effects were taken into account using theEringen s nonlocal elasticity theory This theory was employed in this study because the results obtainedfrom this theory have been proved to be in good agreement with those obtained from atomic simulations The governing equations for the orthotropic nano plates buckling problem were derived using the classictheory of plates In order to solve the obtained differential equations the so called Galerkin method wasemployed Solving eigenvalue problems like current buckling one can be considered as one of the strengthpoint of Galerkin method in numerical solution The solution of algebraic equations in one and also twostages at the one stage and two stage analytical format which made it possible to study different boundaryconditions was presented The Lagrangian and harmonic shape functions are assumed in one and two stage analysis respectively Different problems with various boundary conditions were solved using adeveloped computer code in the MATLAB software environment and the effect of various parameters onthe critical load was studied As for the verifications purposes the results obtained from this work werecompared with those obtained from Navier s method and excellent agreement were found between the twosets of results For the better conclusion a new parameter called the thermal load ratio was defined Alsothe critical buckling load in the X direction was normalized For single layered nanoplates thermal effectson the buckling load were studied for the rhombic and trapezoidal geometry and the variations oforthotropic ratio and also different types of supports such as simply and clamped ones was applied inthermal stability analysis and their effects on the thermal load were investigated In addition the effect ofboth small scale coefficient at different modes and the effective geometrical parameters on the thermalbuckling load was studied In a different type of analysis a particular support was chosen and the range ofplate dimensions in which the Eringen s nonlocal elasticity is valid was found The investigated effect ofgeometry parameters such as rhomb angle trapezoid edges ratio skew angle and rectangle aspect ratio onthe buckling load was plotted in the form of separate diagrams for different scale coefficient For multilayernanoplates the effects of different parameters such as Winkler s stiffness Pasternac s stiffness andinterlayer interactions on thermal buckling variations were also investigated For the multilayer nanoplates the Winkler Pasternac s model was utilized in the simulation of interactions between the interlayerVanderwalls s and the elastic substrate Our results indicate that each of these parameters is directlyproportional to the change in buckling load Finally the effects of both the number of layers and themechanical properties of layers on stability were discussed This study shows that an increase in the numberof layers considerably increases the stability range Keywords Thermal stability Single multi layered orthotropic na

پريشاني، رضا

تاثير مقياس اندازه كوچك در تحليل كمانش حرارتي نانو صفحات ارتوتروپيك چهار ضلعي به روش گالركين

پايداري حرارتي , تئوري غير محلي ارينگن