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Finite element modeling of the signal propagation in a thin tube and comparison with experimental data
Kruisová, Alena ; Kolman, Radek ; Trnka, Jan ; Mračko, Michal
In finite element modeling of wave propagation problems, both the spatial and temporal discretization lead to dispersion errors. It means that the phase velocity of propagated wave is related to its frequency. In framework of temporal-spatial dispersion analysis, the time step size for implicit time integration method based on the Newmark method is proposed for linear and quadratic serendipity plane finite elements. In this paper, we verify the theoretical dispersion analysis by elastic wave propagation in thin tube, where experimental results are known. Such time step size was used in finite element modeling of the stress wave propagating in this thin steel tube, the results of simulations were compared with experimental results.
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SIGA 2011
Kolman, Radek ; Linkeová, I. ; Okrouhlík, Miloslav ; Pařík, Petr
The conference SIGA 2011 aimed to bring together mathematicians, physicists, computer designers and engineers dealing with splines who are using them for the numerical solutions of partial differential equations of various problems in mechanics and physics. In computational mechanics, it is isogeometric analysis (IGA) which is being dynamically developed. This numerical method employs shape functions based on different types of splines (B-splines, NURBS, T-splines and many others), and the fields of unknown quantities are consequently described the same way as the geometry of the studied domain. In addition, this approach provides a higher degree of continuity than that offered by the classical finite element (FE) method based on Lagrangian polynomials. Isogeometric analysis aims to integrate FE ideas in CAD systems without necessity to regenerate mesh. The conference intends to create a forum for further discussion in multidisciplinary scientific areas involving mathematics, computer graphics, geometry, physics, engineering and software engineering, respectively.
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