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چكيده انگليسي :

Buckling Analysis of Shallow Nano Arches using Nonlocal Elasticity Theory Parvaneh Sadat Mortazavi Nasiri ps mortazavi@me iut ac ir Date of Submission 2014 01 22 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language FarsiSupervisor Alireza shahidi shahidi@cc iut ac irAbstractDeformable structures such as beams and arches are used widely in modern engineering applications Thesestructures have found vast applications in different field such as mechanical engineering robotics and civilengineering Besides the mentioned applications in macro scale these structures are also used in micro andnano scales For instance they are used in biosensors atomic force microscope and micro nanoelectromechanical systems Due to the importance of arches and nano arches because of their wide applicationin different engineering fields and also the importance of the stability concepts in designing differentconfigurations of structures the present study is concerned with the stability analysis of arches and nano arches It should be noted that some recently published articles shows that the reinforcing nanotubes used in compositematerials are curved in their own planes So modeling them using curved beam models would yield in morerealistic results than the results obtained from straight beam models The governing equations are derived usingthe variational principles and the principle of stationary value of the total potential energy In the nano archproblem the effect of small scale is included in the governing equation using nonlocal elasticity theory Analytical solution of governing differential equations of structures is only possible for specified loading geometric and boundary conditions and sometimes these analytical solutions is so complicated that it is difficultto use them in daily engineering applications So it is needed to use general approaches to solve easily theproblems with arbitrary loading and boundary conditions Thus the obtained equations are tried to be solvednumerically in order to be able to study different states of the considered problem The equations are descretizedusing finite difference method and a displacement control method called the GDC method is used to solve thesystem of nonlinear algebraic equations In this method two parameters named the general stiffness parameter GSP and the incremental load parameter are used to detect the change in loading direction Based on thesolution used a program is developed in MATLAB R2011a and the stability of arches and nano arches has beenstudied The solution is verified through comparing the results with the available analytical solution for thespecified situations Finally the buckling and post buckling behavior of arches and nano arches is studied andthe effect of different parameters such as the Winkler and Pasternak modulus the initial shape boundaryconditions load distribution and initial imperfections on buckling load and critical initial height is investigated KeywordsArch Nano arch Shallow Buckling Post buckling Finite difference Method Nonlocalelasticity theory

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