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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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Comparative study of finite element method, isogeometric analysis, and finite volume method in elastic wave propagation of stress discontinuities
Berezovski, A. ; Kolman, Radek ; Blažek, Jiří ; Kopačka, Ján ; Gabriel, Dušan ; Plešek, Jiří
A comparative study of Finite Element Method, Isogeometric Analysis, and Finite Volume Method in numerical simulation of one-dimensional wave propagation problems of stress discontinuities in elastic solids is presented. The special attention is paid to accuracy, convergence, and stability of tested numerical methods and the appearance of spurious oscillations and damping effects occurring close to theoretical sharp wavefronts.
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Component-wise partitioned finite element method in linear wave propagation problems: benchmark tests
Kolman, Radek ; Cho, S.S. ; Červ, Jan ; Park, K.C.
A novel explicit time scheme for nite element computations of wave propagation problems in solids is presented. The presented algorithm, with the component-wise partition of equations of motion to the longitudinal and shear parts, is designed to more precisely integrate wave propagation in accordance with their dierent propagation wave speeds. The suggested three-time step integrator is fully explicit with the diagonal mass matrix, of second-order accuracy, conditionally stable and it exhibits minimal sensitivity behavior on time step size satisfying the stability limit. We present two numerical tests of wave propagation phenomena to show accuracy and performance of the proposed method.
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