M.Sc. Tezi Görüntüleme | |||||||||||||||||||||
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| Summary: In this thesis, The Element Free Galerkin and The Meshless Local Petrov-Galerkin methods are formulated and applied to one dimensional linear problems. Shape functions, which are very important for solution procedure of the Element Free Galerkin and the Meshless Local Petrov-Galerkin method, are obtained using the moving least squares procedure. The effectiveness of the shape functions are tested over predefined functions.One dimensional boundary value, Eigenvalue, Initial Boundary value problems are solved with the Element Free Galerkin and Meshless Local Petrov-Galerkin methods. Boundary value problems considered in this study are a bar fixed at one end and a tip load applied at the other end, and rigid body displacement problems.Eigenvalue problems considered are a bar fixed at one end and a beam fixed at both ends. For both of the problems the first four eigenvalues and mode shapes are evaluated. Initial boundary value problems considered in this thesis cover the parabolic equations, which includes the first derivative of the displacement vector with respect to time and hyperbolic equation which includes the second time derivative of the displacement vector. For both methods time integration schemes are evaluated.Comparison of the numerical solutions obtained by the Element Free Galerkin and the Meshless Local Petrov-Galerkin methods shows that the Meshless Local Petrov-Galerkin method gives rise to more accurate results for at least solved problems. Key Words : Meshfree Methods, Moving Least Squares, Element Free Galerkin Method, Meshless Local Petrov-Galerkin Method, Boundary Value Problems, Initial Value Problems , Initial Boundary Value Problems, Free Vibration, Time Integration Methods. | |||||||||||||||||||||