Browsing by Subject "Finite element method."

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Open Access
Finite element method based simulations of low frequency magnetic field in seawater
(2013) Şimşek, Fatih Emre
Propagation properties of the electromagnetic waves in seawater are different than in air (vacuum) due to electrical conductivity (σ) and high relative permittivity (εr) of the seawater. Numerically it is hard to solve the electromagnetic waves in seawater for the complex geometries. With the help of the advances in the Finite Element Method (FEM) tools as well as the personal computers, we have chance to analyze magnetic field of the complicated and complex geometries of physical systems in seawater. In this thesis; an air-cored multilayer transmitting coil is designed. Then the low frequency magnetic flux density of this coil in different studies in seawater in COMSOL Multiphysics is solved. In the first study; the magnetic flux density of the coil in air and in seawater for different frequencies on different observation points is solved. In the second study; the shielding effect of the material of the case of the coil as well as the thickness of the case is analyzed. Specific materials as well as thickness for the case are proposed. In the third study; the perturbation of the magnetic flux density of the coil due to a metal plate is analyzed. The material of the metal plate is taken iron and copper. Iron has high relative permeability (  r) and high electrical conductivity (σ). Copper has unity permeability (  0) and high electrical conductivity (σ). Effect of the high electrical conductivity on the perturbation of the magnetic flux density on the observation point is analyzed. Effect of high relative permeability on the phase shift of the field on the observation point is observed. A detection region for the plate and coil geometries according to the attenuation of the secondary fields caused by the eddy currents on the metal plate is proposed. In the last study; perturbation of ambient Earth magnetic field due to a submarine is solved and how this perturbation can be imitated by an underwater system, which tows a DC current carrying wire is analyzed. These underwater systems are used to test detection performance of magnetic anomaly detector (MAD) equipped aircrafts.
Open Access
A three-dimensional nonlinear finite element method implementation toward surgery simulation
(2011) Gülümser, Emir
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.