كمانش نانو صفحات مدور با استفاده از روش تفاضل محدود

چكيده انگليسي :

67 Buckling of Circular Annular Nanoplates Using Finite Difference Method Ebad Amini e amini@me iut ac ir Date of Submission 2014 01 18 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisors Alireza Shahidi Shahidi@cc iut qc irAbstractNanotechnology is a fast growing field of science and technology which deals with thedevelopment of materials structures and devices at the nanoscale Nanoplates are pivotalbranches of nanostructures with vast applications including their usage in making batteries chemical and biological sensors and also in nanocars and many other applications Though fewstudies have been investigated the behavior of these structures and this shortage of efforts ispossibly related to the troubles in their productions In this regard understanding the vibrationand buckling behaviors of nanoplates is the most important steps to the design of thesestructures Due to high dependencies in static and dynamic stability equations providing ananalytical solution for free vibration and buckling of nanoplates is very difficult so in moststudies numerical or semi numerical methods such as finite element Rayleigh Ritz and areutilized various recent experimental results have shown that as the size of the structure reducesto compareable to micro nanoscale the influences of atomic forces and small scales play asignificant role in their mechanical properties Thus neglecting these effects in some cases mayresults in completely incorrect solutions and hence wrong designs Some methods such asmolecular dynamics involve solving a large number of equations so they have difficulties inhandling systems with large length and time scales Therfore modeling of the large systems isleft to continuum mechanics approaches One of the well known continuum mechanics theorythat includes small scales effects with acceptable accuracy is the nonlocal theory of Eringen Using local theory for the small size analysis leads to the over predicting results In order tocapture the small scale effects in nonlocal continuum theory it is assumed that the stress at apoint depends on the strain at all points in the domain This is contrary to the classical local continuum theory in which it is assumed that the stress at a point is just a function of the strainat that point So the nonlocal theory contains information about long range interactions betweenatoms and internal scale length In this study using nonlocal theory is attempted to modelisotropic circular annular and sector nanoplates and provide an exact numerical solution fortheir buckling using finit difference method It should be noted that Kirchhoff plate theories isutilized to model the thin plates It is shown that nonlocal effects are very important in ananoplate The affects of nonlocal parameter and the plate size have been studied for eachcombination of boundary conditions The obtained results are in good agreement with the otherstudies and the reality The results also convince that the finite difference method is a powerfulmethod for solving the problems corresponding to nanoplate mechanical behaviors Keywords Nanoplate Nonlocal elasticity Buckling Solid disks Circular annularplates Sector plates Finite difference method

اميني، عباد

كمانش نانو صفحات مدور با استفاده از روش تفاضل محدود

تئوري غير محلي ارينگن