Structural Analysis with Meshfree Methods. Master’s thesis
Diğer yayınlar > Diğer · 2008
Yazarlar: Mahmut PEKEDİS
Diğer, Ulusal, 2008, ss 1-218, Türkiye
Özet
<p>There is a great of interest in applying numerical methods for solution of partial differential equations of various types of engineering problems in last two decades. Numerical solution of partial differential equations consists of two main parts. Equations or unknown functions are solved approximately. Then the unknown are determined by embedding approximated solution in the governing equations in the weak or strong form and boundary conditions are applied to solve unknown functions. Accuracy and efficiency of numerical method, strictly dependent to accuracy and efficiency of these two steps. During last decade various meshfree methods have been developed, (such as EBG, SPH, PIM, MLPG) were used successfully in different engineering problems.In this study a new and popular element free Galerkin and radial point interpolation procedures of numerical methods are applied to elastic solid mechanics problem. Moving least square method and radial point interpolation method shape functions were used in solving of these problems. However, these shape functions are applied to the 1D and 2D solution domains and plotted in x-y-z coordinate system.The problem considered in this study is a 2D linear, elastic cantilever beam fixed at the end and subjected to a traction at the other free end.In this study it was compared accuracy and efficiency of different techniques like radial point interpolation method, element free Galerkin with finite elements method, numerical methods which proposed and used by researchers for approximating the solution of equation. However stress and displacement approximate values studied to reveal the efficiency of methods in various cross-sections of the beam.As a result it can be concluded that accuracy and efficiency of radial point interpolation method and element free Galerkin method are better than finite element methods. However, comparison of the numerical methods obtained by the element free Gelerkin and radial point interpolation methods shows that element free Galerkin gives more accurate result for the selected problem.</p><p>Key Words: Meshfree methods, moving least squares method, element free Galerkin method, meshless radial point interpolation method, finite elements method, approximation methods.</p>