Národní úložiště šedé literatury Nalezeno 15 záznamů.  1 - 10další  přejít na záznam: Hledání trvalo 0.04 vteřin. 
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.
Numerical solution of a secular equation for rayleigh waves in a thin semi-infinite medium made of a composite material
Červ, Jan ; Adámek, V. ; Valeš, František ; Parma, Slavomír
The traditional way of deriving the secular equation for Rayleigh waves propagating along the stress-free edge of a thin semi-infinite composite is presented. It means that it is necessary to find a general steady-state solution that vanishes at infinity. The secular equation is then obtained by vanishing of the surface traction at the stress-free edge. For the solution of such secular equation it is necessary to precompute some roots of characteristic quartic equation. The method shown in this paper, based on displacement formulation, leads to the so-called implicit secular equation. The numerical approach to the solution is shown.
Transient response of layered orthotropic strip to transverse load
Adámek, V. ; Valeš, František ; Červ, Jan
This work concerns the transient response of an infinite two-layered strip subjected to a transverse load of impact character. The material of each layer is assumed to be specially orthotropic, i.e. the material and geometric axes coincide. Moreover, the material is modelled as linear viscoelastic using the model of standard linear viscoelastic solid such that the damping behaviour of the strip for long wavelengths and long times can be addressed. The non-stationary wave phenomena in the strip are studied using analytical approach. The system of equations of motion for the case of 2D plane-stress problem is solved using the classical method of integral transform. Once the formulas for the Laplace transforms of fundamental mechanical quantities are derived, the numerical inverse Laplace transform is used to obtain the response in time domain for a strip with free-fixed boundaries. The results for a strip composed of two orthotropic layers of specific material properties are presented in this work. Finally, this solution is confronted with the results of numerical simulations reached by a professional FE code.
Performance and implementation aspects of an isogeometric mortar-based 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 3d frictionless impact of two equally shaped cylinders. The attention was paid to performance and implementation aspects of the mortar-based contact algorithm.
Case study using the creep probabilistic exponential model and explicit integration method with time step control
Gabriel, Dušan ; Hrubý, Zbyněk ; Masák, Jan ; Plešek, Jiří ; Kopačka, Ján ; Pařík, Petr ; Straka, F. ; Albl, P.
The issues concerning accuracy and stability control of original explicit algorithm for integration of differential systems arising from viscoplastic or creep finite element analyses was explored. The attention was focused on the investigation of the numerical stability for complex creep probabilistic exponential model with damage.
Convergence study of isogeometic analysis in poisson problem
Cimrman, R. ; Kolman, Radek ; Vejchodský, Tomáš
In this contribution, we use isogeometric analysis for numerical solution of the the Poisson problem with homogeneous Dirichlet boundary conditions. We analyze the influence of this continuity, together with the spline order and parameterization, on the convergence rates of numerical solutions to analytic ’exact’ solution.
Využití numerické zpětné laplaceovy transformace při řešení úloh elastodynamiky
Adámek, V. ; Valeš, František ; Červ, Jan
Laplaceova transformace představuje jednu z nejvíce užívaných transformací v časové oblasti. Existují dva přístupy při hledání inversní Laplaceovy transformace, analytický a numerický. Analytická metoda je založena na exaktním vyjádření inversního integrálu pomocí Cauchyovy residuové věty. Podstata druhé metody spočívá v numerickém řešení inversního integrálu. Ukazuje se, že numerický přístup je rychlejší nežli analytické řešení. V neposlední řadě může být tento přístup využit ve složitějších případech, kde např. existence bodů rozvětvení činí inversní proces, založený na analytickém přístupu, mnohem komplikovanější.
Isogeometrický kontaktní analýza: studie explicitního dynamického kontaktního algoritmu
Kopačka, Ján ; Gabriel, Dušan ; Kolman, Radek ; Plešek, Jiří
V této práci byla navržena isogeometrická varianta explicitního konečnoprvkového kontaktního algoritmu, který zachovává symetrii kontaktních hranic. Upravený algoritmus byl testován na numerickém příkladu 2d dynamické Hertzovy úlohy rázu dvou válců bez tření. Pozornost byla věnována vlivu různých metod diagonalizace matice hmotnosti na oscilace kontaktní síly a kontaktního tlaku. Standardní Lagrangeovy konečné prvky byly porovnány s NURBS isogeometrickými elementy. Byly uvažovány prvky prvního a druhého řádu.
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.
On the diminishing of spurious oscillations in explicit finite element analysis of linear and non-linear wave propagation and contact problems
Kolman, Radek ; Cho, S.S. ; Park, K.C.
A nearly non-spurious oscillations explicit time integration scheme for finite element solution of linear and non-linear wave propagation of stress discontinuities in solids and contact problems is presented and tested. The main concept of the diminishing spurious oscillations time scheme is based on a modification of the conventional central difference method.

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