Document Type



Master of Science (MS)


Mechanical Engineering

First Advisor's Name

Igor Tsukanov

First Advisor's Committee Title

Major advisor

Second Advisor's Name

Ibrahim Tansel

Second Advisor's Committee Title


Third Advisor's Name

Yiding Cao

Third Advisor's Committee Title

Committee member


mesh-free method, finite element method, conforming mesh, no conforming mesh, solution structure, heat transfer, plates, buckling, r-functions, transfinite interpolation.

Date of Defense



In the process of engineering design of structural shapes, the flat plate analysis results can be generalized to predict behaviors of complete structural shapes. In this case, the purpose of this project is to analyze a thin flat plate under conductive heat transfer and to simulate the temperature distribution, thermal stresses, total displacements, and buckling deformations. The current approach in these cases has been using the Finite Element Method (FEM), whose basis is the construction of a conforming mesh. In contrast, this project uses the mesh-free Scan Solve Method. This method eliminates the meshing limitation using a non-conforming mesh. I implemented this modeling process developing numerical algorithms and software tools to model thermally induced buckling. In addition, convergence analysis was achieved, and the results were compared with FEM. In conclusion, the results demonstrate that the method gives similar solutions to FEM in quality, but it is computationally less time consuming.





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