| Summary: In this thesis, The Element Free Galerkin Mesh Free Method formulated and applied to two dimensional plate bending problems due to moving temperature loads. Shape functions, which are very important for solution procedure of the Element Free Galerkin Method are obtained using forth order spline functions with the moving least squares procedure. In this study, as the boundary value problems, the bending behavior of a simply supported plate under sinusoidal and uniform surface temperature distributions are considered. Initial boundary value problems that cover the parabolic equations containing the first derivative of the displacement vector with respect to time and hyperbolic equations which include the second time derivative of the displacement vector are also considered. In the formulation and solution of the both problems time integration schemes are evaluated. The solution of the Plate bending problem due to the Moving Heat Source is divided into two subsections; the first section involves the thermal analyses to predict the temperature distribution on the plate surface due to moving heat source and the second section contains the solution of the elasticity problem to predict the plate bending behavior due surface temperature distribution obtained in the first section. The temperature distributions, the plate bending deformations and the stress distributions on the plate are depicted. Investigating the numerical solutions obtained by using the Element Free Galerkin Method for the plate bending problems under moving temperature loads shows that the Element Free Galerkin Method is an alternative method to the other numerical methods that are available for the numerical solutions of problems including the moving heat source and the plate bending. As a conclusion, it can be said that the numerical solutions obtained with the Element Free Galerkin Method are reliable and compatible with the data available in the literature.
Key Words : Meshfree Methods, Moving Least Squares, Element Free Galerkin Method, Boundary Value Problems, Initial Value Problems , Initial Boundary Value Problems, Time Integration Methods, Moving Heat Source Problems, Line Heating.
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