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      •   BUIR Home
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      • Bilkent Theses
      • Theses - Department of Computer Engineering
      • Dept. of Computer Engineering - Master's degree
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      A three-dimensional nonlinear finite element method implementation toward surgery simulation

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      Author
      Gülümser, Emir
      Advisor
      Güdükbay, Uğur
      Date
      2011
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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      Abstract
      Finite Element Method (FEM) is a widely used numerical technique for finding approximate solutions to the complex problems of engineering and mathematical physics that cannot be solved with analytical methods. In most of the applications that require simulation to be fast, linear FEM is widely used. Linear FEM works with a high degree of accuracy with small deformations. However, linear FEM fails in accuracy when large deformations are used. Therefore, nonlinear FEM is the suitable method for crucial applications like surgical simulators. In this thesis, we propose a new formulation and finite element solution to the nonlinear 3D elasticity theory. Nonlinear stiffness matrices are constructed by using the Green-Lagrange strains (large deformation), which are derived directly from the infinitesimal strains (small deformation) by adding the nonlinear terms that are discarded in infinitesimal strain theory. The proposed solution is a more comprehensible nonlinear FEM for those who have knowledge about linear FEM since the proposed method directly derived from the infinitesimal strains. We implemented both linear and nonlinear FEM by using same material properties with the same tetrahedral elements to examine the advantages of nonlinear FEM over the linear FEM. In our experiments, it is shown that nonlinear FEM gives more accurate results when compared to linear FEM when rotations and high external forces are involved. Moreover, the proposed nonlinear solution achieved significant speed-ups for the calculation of stiffness matrices and for the solution of a system as a whole.
      Keywords
      Tetrahedral element
      Deformation
      Finite element method
      GreenLagrange strain
      Surgery simulation
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      http://hdl.handle.net/11693/15603
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