engleski

Hyperbolic problems for metric graphs - tools for analyzing vibrations of frame like structures

This talk is motivated by numerical problems in modeling and simulation of elastic stents. To this end, we will present a general approach to the dynamic (hyperbolic problem) and stationary simulation of elastic frame structures. As prototypes we will present two 1D models of an endovascular stent. Endovascular stents are biomedical devices made of struts and are used for treating arterial stenosis. The state of the system in both models is described by a vector valued function on a metric graph which satisfies a system of ODEs and a set of algebraic constraints. Both models are obtained, and thus theoretically validated, by Γ-convergence from 3D nonlinear elasticity. As a result of asymptotic analysis, solutions are contained in a space of functions which are constrained by a set of algebraic conditions in the nodes of the graph and by requiring that the middle line of a strut does not extend. Finally, we present validation experiments for the method by comparing it empirically to the 3D model solved by the standard legacy finite element code.

finite elements, endovascular stents, hyperbolic problems, metric graphs

nije evidentirano