Numerička metoda za model lineariziranog stenta

Iveković, Josip (2015) Numerička metoda za model lineariziranog stenta. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

Stent is usually modelled as a three-dimensional elastic body. In this paper, we have defined the stent net as a non-directed graph, in which the slender metallic rods, modelled by the linearized Antman-Cosserat model for inextensible, unshearable rods, represent the edges of the graph. In that way, we have transformed a three-dimensional problem into a one-dimensional problem, which is computationally cheaper and easier to handle. We have shown that under certain conditions the mixed formulation of our model has a unique solution. For the approximation of the middle line shift of the stent struts and infinitesimal rotation of the cross-section of the stent struts, we have used polynomial spaces. In addition, to make the calculus simpler, we have taken the stent struts, which are actually curved, to be straight. We have established that the numerical method we use converges, and the scale of convergence depends on the polynomial space we use to approximate the functions. However, there is no difference between the convergence scale of P2P1 elements and that of P3P2 elements. Moreover, the solutions obtained by P2P1 elements are just slightly different from the solutions obtained by P2P1 elements. It would be interesting to give some theoretical background to these observations, and also to see what rate of convergence is actually possible to achieve with this approach.

Item Type: Thesis (Diploma thesis)
Supervisor: Tambača, Josip
Date: 2015
Number of Pages: 67
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 03 Jun 2015 08:38
Last Modified: 03 Jun 2015 08:38
URI: http://digre.pmf.unizg.hr/id/eprint/3951

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