A three-dimensional nonlinear finite element method implementation toward surgery simulation

buir.advisorGüdükbay, Uğur
dc.contributor.authorGülümser, Emir
dc.departmentDepartment of Computer Engineeringen_US
dc.descriptionAnkara : The Department of Computer Engineering and the Graduate School of Engineering and Science of Bilkent University, 2011.en_US
dc.descriptionThesis (Master's) -- Bilkent University, 2011.en_US
dc.descriptionIncludes bibliographical references leaves 93-98.en_US
dc.description.abstractFinite 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.en_US
dc.description.statementofresponsibilityGülümser, Emiren_US
dc.format.extentxi, 103 leaves, illustrationsen_US
dc.publisherBilkent Universityen_US
dc.subjectTetrahedral elementen_US
dc.subjectFinite element methoden_US
dc.subjectGreenLagrange strainen_US
dc.subjectSurgery simulationen_US
dc.subject.lccT385 .G85 2011en_US
dc.subject.lcshComputer simulation.en_US
dc.subject.lcshComputer animation.en_US
dc.subject.lcshThree-dimensional display systems.en_US
dc.subject.lcshFinite element method.en_US
dc.subject.lcshDeformations of singularities.en_US
dc.subject.lcshApproximation theory.en_US
dc.subject.lcshNonlinear theories.en_US
dc.titleA three-dimensional nonlinear finite element method implementation toward surgery simulationen_US


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