كمانش ورق سوپر بيضوي ساخته شده از مواد مدرج هدفمند ﴿FGM﴾ تحت فشار يكنواخت صفحه اي

چكيده انگليسي :

Buckling of FGM Super Elliptical Plates Under In plane Uniform Pressure Ahmad Karimzade Babaki a karimzadebabaki@me iut ac ir Date of Submission 2012 03 04 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language FarsiSupervisors Hasan Khademizadeh hkhademyza@cc iut ac ir Alireza Shahidi shahidi@cc iut ac irAbstract In this thesis the buckling of simply supported and clamped Functionally Graded super elliptical platesis investigated The periphery shape of plate is defined by a super elliptical function with a power corresponding to shapes ranging from an ellipse to a rectangle Such a plate shape has practicalapplications as the advantageous curved corners help to diffuse stress concentrations The loadingconsidered for the buckling problem is that of in plane uniform pressure along the periphery Functionallygraded materials FGMs are one of the advanced high temperature materials capable of withstandingextreme temperature environments FGMs are composite and microscopically inhomogeneous in which themechanical properties vary smoothly and continuously from one surface to the other This is achieved bygradually varying the volume fraction of the constituent materials It is assumed that the material propertiesof the plate vary through the thickness of the plate as a power function Based on the classical plate theory Kirchhoff theory the equilibrium and stability equation and the total potential energy are obtained forFunctionally Graded Plates FGP The computations are carried out by both of the Rayleigh Ritz andGalerkin method Rayleigh Ritz use is based on the Trefftz criterion which defines the critical load as thesmallest load for which the second variation of the potential energy assumes a stationary value TheGalerkin s method is proved to provide solutions of significant accuracy with minimal manual effort andcomputer execution time for various problems In the Galerkin s method accuracy of the results depends onthe selected shape function Converging solutions can be obtained much faster by satisfying all of thegeometrical and kinematical boundary conditions of the problem by the assumed series expression of theplate surface Galerkin s method can be applied to small and large deflection theories linear and nonlinearproblems of plates provided that differential equations of the problem under investigation have already beendetermined The study is performed for a wide range of super elliptical plates The critical buckling loadsare obtained for a super elliptical plate with different super elliptical powers various powers of FGM andsome aspect ratio It is concluded that the equilibrium and stability equations are identical with thecorresponding equations for homogeneous isotropic plates the critical buckling load for the functionallygraded plates is generally lower than the corresponding value for homogeneous plates Functionally gradedplates have many advantages as a heat resistant material but it is important to check its resistance tobuckling the critical buckling load for the functionally graded plates is reduced when the power law indexk increases the critical buckling load for the functionally graded plates decreases with increasing aspectratio a b the critical buckling load for the super elliptical plates decreases with increasing power of supperellipse n By equating power of FGM to zero predicted relations are reduced to the relations ofhomogeneous plates The detailed parametric studies are carried out to investigate the influences of aspectratio super elliptical power and power of FGM on the critical buckling load Keywords Buckling Super elliptical plate FGM Rayleigh Ritz method Galerkin method Classicalplate theory

كريم زاده بابكي، احمد

كمانش ورق سوپر بيضوي ساخته شده از مواد مدرج هدفمند ﴿FGM﴾ تحت فشار يكنواخت صفحه اي

روش ريلي-ريتز , روش گالركين , تئوري كلاسيك