تحليل ارتعاشي يك ورق مركب لايه به لايه به كمك تئوري دو متغيره ي پالوده شده به روش المان هاي محدود سلسله مراتبي

چكيده انگليسي :

108Hierarchical FEM Based Vibration Analysis of a Laminated Composite Plate by Using Two Variable Refined Plate Theory Amir Hosain Eshaghian Ah eshaghian@me iut ac ir Date of Submission 2015 14 1 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisor Hamid Reza Mirdamadi hrmirdamadi@cc iut ac irAbstractIn this dissertation classical plate theory first order shear deformation theory and two variable refinedplate theory are discussed for free vibration problem by using standard finite element and hierarchical finiteelement methods The two variable refined plate theory is an equivalent single layer theory in whichbending components would not have any influence in shear forces while shear components does not haveinfluence in bending moments By eliminating the shear component this theory would become the same asclassical plate theory Furthermore this theory considers shear strains along thickness direction as parabolicand consequently it does not need any shear correction factor The hierarchical finite element is a meshrefinement technique which does not change the number of nodes This is done by increasing the order ofshape functions for approximating displacements In this research advantages of hierarchical finite elementmethods are explained and 1D element shape functions are described Then the application of 2D elementshape functions will be presented In the sequel the formulations of standard and hierarchical finite elementmethods are derived for classical laminated plate theory and their natural frequencies for different boundaryconditions and different numbers of layers are compared with exact solutions It is observe that by usingless number of degrees of freedom the hierarchical finite element method converges to more accuratesolutions as compared to standard finite element method Furthermore the formulations of standard andhierarchical finite element methods are derived for the first order shear deformation theory and the effect ofshear locking is investigated by the change in thickness ratio of plate Together with preventing shearlocking using hierarchical finite element method results in more accurate natural frequencies for plate ascompared to standard finite element In the following two variable refined plate theory is presented and theequations of motion and formulations of standard and hierarchical finite element methods are derived Inthis theory the fundamental and higher are obtained from exact solutions standard and hierarchical finiteelement methods for symmetric and unsymmetric laminated orthotropic plates With comparing the results the superiority of hierarchical finite element method is shown with respect to standard finite elementmethod Then changing different parameters of angle ply and cross ply laminated orthotropic plates suchas modulus ratio thickness ratio aspect ratio and different boundary conditions of the plate the solutionsare obtained for standard and hierarchical finite element methods and they are compared with those of exactmethods Key words Classical plate theory First order shear deformation theory Two variable refined plate theory Standardfinite element method Hierarchical finite element method

اسحاقيان، اميرحسين

تحليل ارتعاشي يك ورق مركب لايه به لايه به كمك تئوري دو متغيره ي پالوده شده به روش المان هاي محدود سلسله مراتبي

تئوري كلاسيك , تئوري تغيير شكل برشي مرتبه اول , روش المان محدود استاندارد