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چكيده انگليسي :

108Exponential Basis Functions in the Analysis of Laminated Thick Plates Using a Higher order Zig Zag Deformation Theory Fatemeh Azhari fatemeh azhari@gmail com Date of Submission September 19 2012 Department of Civil Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisor Dr Bijan Boroomand boromand@cc iut ac ir Abstract In this dissertation a meshfree method is developed for the bending analysis of thick laminated composite plates with different shapes and various boundary conditions using a higher order Zig Zag deformation theory In the higher order Zig Zag theory proposed by Cho and Parmerter a linear Zig Zag variation of in planedisplacement is combined with a cubic variation of in plane displacement field The Zig Zag term represents theshear strain discontinuity between layers resulted from the transverse shear stress continuity conditions Moreover the cubic part accounts for the overall parabolic transverse shear stress as in Reddy s third order shear deformationtheory By satisfying the transverse shear stress continuity as well as the shear free surface conditions the Zig Zagunknowns of each layer are derived in terms of the global unknown displacements of the mid plane therefore thenumber of unknowns does not change as the number of layers increases Consequently for the thick laminates with high transverse anisotropy this theory is suitable and computationally efficient Furthermore the details of imposing different boundary conditions including free simply supported andclamped are given In order to define the boundary conditions for free and simply supported edges a variationalapproach combined with conventional conditions pertaining to displacements is used However for clamped edges we show that satisfying the conventional Dirichlet conditions may lead to disappearance of transverse shear stress at the clamped edges Therefore a new set of conditions are proposed to avoid such an unwanted effect The solution method used in this dissertation is a Trefftz type which falls in the category of meshfree methods In this method exponential basis functions EBFs with complex valued exponents are used The solution is splitinto homogenous and particular parts The homogenous part is approximated by a series of EBFs and the unknowncoefficients are determined by satisfaction of the boundary conditions through a collocation method using a discretetransformation technique The way that one can generally evaluate the EBFs for a laminated plate using a Zig Zagtheory is demonstrated Apart from giving explicit form of EBFs for single layer isotropic plates useful for solutionon relatively thick plates we present similar explicit relations for three layer sandwich plates with in plane isotropy having wide applications in structural mechanical engineering In addition two different methods are proposed forapproximating the particular solution including a method using another series of EBFs by means of thetransformation used in the homogenous solution and the Fourier series solution In this study the first method is employed due to its great convergency in bending analysis of plates with uniform loadings Moreover the results of our numerical experiments including the bending analysis of composites withdifferent boundary conditions and different configurations are provided and compared with those available in theliterature to validate the results It has been observed that the present method can perform excellently in a widerange of problems defined for the bending analysis of laminated plates In addition some results for a sandwich composite plate as a new benchmark using the Zig Zag theory are presented for further sudies Key words Laminated composite plates Exponential basis functions Higher order Zig Zag deformation theory

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تحليل خمشي ورق هاي كامپوزيت لايه اي ضخيم بر اساس تئوري زيگزاك مرتبه بالا و با استفاده از روش بدون شبكه توابع پايه نمايي

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