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Dispersion properties of finite element method: review
Kolman, Radek ; Okrouhlík, Miloslav ; Plešek, Jiří ; Gabriel, Dušan
Review of the dispersion properties of plane square bilinear finite element used in plane elastic wave propagation problems is presented. It is assumed the grid (spatial) dispersion analysis and, further, the temporal-spatial dispersion analysis for explicit direct time integration based on the central difference method. In this contribution, the dispersion surfaces, polar diagrams and error dispersion graphs for bilinear finite element are depicted for different Courant numbers in explicit time integration. Finally, recommendation for setting the mesh size and the time step size for the explicit time integration of discretized equations of motion by the bilinear finite element method is provided.
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Isogeometric contact analysis: a study of an explicit dynamic contact algorithm
Kopačka, Ján ; Gabriel, Dušan ; Kolman, Radek ; Plešek, Jiří
The isogeometric NURBS based variant of symmetry preserving explicit FE contact-impact algorithm, has been proposed. The algorithm was studied by means of a numerical example, which involves 2d frictionless dynamic Hertz contact problem of two equally shaped cylinders. The attention was paid to the influence of different lumping techniques on the oscillations of contact force and contact pressure. The standard Lagrange finite elements were compared with the NURBS isogeometric elements. Both the first and second order were considered.
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