M.Sc Student | Clara Sussmann |
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Subject | A Finite Element Method for Effective Models Representing Thin Layers in Heat Conduction |

Department | Department of Aerospace Engineering |

Supervisors | Full Professor Givoli Dan |

Full Professor Yaakov Benbenisti | |

Full Thesis text |

Thin layers with material properties which differ signiﬁcantly from those of the adjacent media appear in a variety of applications, as in the form of ﬁber coatings in composite materials or protecting surface layers in the case of external coating . The full modeling of thin layers by standard ﬁnite element (FE) analysis is often associated with complex meshing and high computational cost. An alternative has been known in the literature for some time in the form of asymptotic procedures which model such thin domains by an interface of no thickness on which appropriate interface conditions are devised .

In this thesis, it is shown how the ﬁrst-order asymptotic interface model proposed by Bövik in 1994, and later generalized by Benveniste in 2006 , ? can be incorporated in a FE formulation, to yield an accurate and efficient computational scheme for problems involving thin layers. This is done here for linear scalar elliptic problems in two dimensions, prototyped by steady-state heat conduction .

While the formulation was developed for an interphase of general shape , the ﬁrst step was chosen to consider a thin layer of circular shape which would enable the model to be presented in the simplest possible setting and form. Later chapters examine thin layers of general shape as well as another possible application of thin layers, external coating. In that case , the outer medium is removed such that the layer itself is the outermost medium .

It is also shown that by somewhat modifying the formulation of the Bövik-Benveniste asymptotic model, the proposed formulation is, in the interphase problem, made to preserve the self-adjointness of the original three-phase problem, thus leading to a symmetric FE stiffness matrix. Numerical examples are presented that demonstrate the performance of the method , and show that the proposed scheme is more cost-effective than the full standard FE modeling of the layer .