بررسي مسائل خمش و ارتعاش آزاد ورق هاي ضخيم كامپوزيت با استفاده از توابع پايه نمايي

چكيده انگليسي :

On Bending and Free Vibration Problems of Thick Laminated Composite Plates through Exponential Basis Functions Mina Shahbazi Mina shahbazi65@yahoo com Date of Submission April 6 2011 Department of Civil Engineering Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language FarsiSupervisor Dr Bijan Boroomand boromand@cc iut ac ir Advisor Dr Mojtaba Azhari Mojtaba@cc iut ac ir AbstractIn this dissertation the bending and free vibration problems of thick laminated composite plates based onclassical and shear deformation theories have been considered The problems are based on the classical platetheory CLPT first order shear deformation theory FSDT and third order shear deformation theory TSDT A mesh free approach in both the global and local form has been exploited for the static problems whereas another mesh less method has been proposed for free vibration problems All these methods sharethe common fact that the unknown variables are approximated by the summation of an appropriately selectedset of exponential basis functions EBFs The imposition of the boundary conditions is performed by acollocation method through a discrete transformation technique In static problems the governing differential equations are satisfied over the problem domain directly in aglobal or local form In this method the solution is first split into homogenous and particular parts and thenthe homogenous part is approximated by the summation of an appropriately selected set of exponential basisfunctions EBFs that are restricted to satisfy the governing differential equation The process of finding theEBFs for CLPT FSDT and TSDT are described and the explicit expressions are given for special cases oflaminated plates Two different methods are also proposed for approximating the particular solutionincluding the Fourier series solution and a method using another series of EBFs with a similar transformationtechnique to the homogenous solution Comparison of the results of these two methods reveals significantsupremacy of the latter over the former in many problems regarding the computational costs The boundaryconditions are enforced through a collocation approach on a set of boundary points In this sense the methodmay be classified as mesh less boundary point methods such as the method of fundamental solutions MFS Comparing with the fundamental functions needed in MFS the EBFs can be easily found for PDEs withconstant coefficients This is the case for variety of plate problems formulated by CLPT FSDT or TSDTusing Cartesian coordinates Moreover the in plane and out of plane actions may appear in a coupledformulation depending on the configuration of the layers Nevertheless this does not create any restrictionsfor the proposed method in this paper since the system of equation is of constant coefficient type Contrary to the adopted approach for static problems a variational form of the differential equations issatisfied in an iterative way for the case of free vibration problems In this method the basis functions forapproximating the unknown variables are selected by enforcing the boundary conditions on a set of boundarypoints directly The frequency parameters are obtained by solving the eigenvalue problem of the weak orstrong form of the differential equations The solutions of several bending and free vibration laminated plate problems with various geometries boundary conditions and plate lamination schemes are presented to validate the accuracy efficiency andapplicability of the proposed methods It has been observed that the presented methods can performexcellently in a wide range of problems defined for the bending and free vibration analysis of laminatedplates based on various plate theories Key words Laminated composite plates Exponential basis functions Shear deformation theories

شهبازي، مينا

بررسي مسائل خمش و ارتعاش آزاد ورق هاي ضخيم كامپوزيت با استفاده از توابع پايه نمايي

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