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1

Comparison of numerical testing methods in terms of impulse loading applied to structural elements

Mazurkiewicz Ł., Małachowski J., Baranowski P., Damaziak K.

Journal of Theoretical and Applied Mechanics

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2013

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Vol. 51 nr 3

615--625

EN

This paper presents comparison of numerical testing methods of an impulse loading which comes from a detonation process, i.e. blast wave propagation in a gas medium. Investigations were carried out using an analytical and numerical model based on the Finite Element Method. In order to reduce computational time, the substitute analytical model with one degree of freedom was implemented, which replaced a chosen actual system (I-section steel column). For structure modelling, the constitutive model was used, which included the strain rate effect. From the performed analyses, an acceptable similarity was noticed, although the discrete model due to greater forces gave inflated results. Nevertheless, it should be pointed out that simplified methods do not take any wave and flow around effects into consideration, which have an influence on the dynamical response of the structure and are possible to implement in the gas medium coupling.

2

I-beam structure under blast loading-Eulerian mesh density study

Mazurkiewicz Ł., Małachowski J.

Journal of KONES

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2011

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Vol. 18, No. 3

245-252

EN

Dynamic response of an I-beam structure subjected to shock wave produced by the detonation of high explosive (HE) materials is presented in this paper. LS-DYNA, a 3-D explicit, finite element computer code is used to study this behaviour. A coupled analysis between Lagrangian formulation (solid material) and Eulerian formulation (gas medium) was performed. The latest extensive research in this area indicates that the finite element analyses of such problems require complex meshes for Euler and Lagrange formulation. This research is focused on Euler mesh density influence on coupled analysis results. The principal objective of this paper is to compare various mesh density Eulerian models in respect to accuracy and computing time and asses the limit of element size. The Eulerian domains (Air and HE) were developed with various element size from 10 mm up to 30 mm. Results from all the analysis cases show how the Eulerian mesh element size influences on the global response of the column. Models with coarse meshes give much lower dynamic response then models with finer meshes. The resultant velocity vectors were also presented to illustrate the characteristic of blast wave propagation. Moreover the numerical models computational efficiency was compared are respect of CPU Time. Models with complex meshes (below 20 mm) are very computationally expensive.

3

Convection of internal variable methodology in Computational Fluid Dynamics solutions for thixoforming modelling

Macioł P.

Computer Methods in Materials Science

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2007

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Vol. 7, No. 1

112-118

EN

During thixoforming, the deformed material is in semi-solid state. From numerical point of view, such materials are difficult to simulate because of gathering some features of solid materials and some of fluids. Materials properties are history dependent like in solids, while deformations could be extremely high, like in fluids. The typical solutions of structural analysis, based on Lagrangian motion description are difficult because of remeshing, which is needed in short time intervals. Frequent remeshing operations increase time consumptions and decrease the accuracy of solution. On the other hand, typical Computational Fluid Dynamics (CFD) solutions, usually based on Eulerian motion description, are ineffective when domain borders are changing. Because of material points are detached from mesh nodes, the history dependent parameters of the material are also very difficult to introduce. On the contrary, in the third possible formulation, Arbitrary Lagrangian Eulerian (ALE), the material points are not bound with mesh nodes and domain geometry could change. In ALE formulation each time step is divided into Lagrangian and Eulerian steps, what assures that history of material could be included and the calculation domain is reproduced properly by the mesh. Therefore, ALE formulation seems to be the best solution in the most thixoforming cases. The disadvantages of this method are the time consumptions and some inaccuracy of approximation needed between both steps. In the cases when the domain of solution is unchangeable, Eulerian formulation could be more promising than ALE. The Eulerian solution is easier to implement, as well as computational round-offs are less significant. The difficulties connected with history dependent parameters could be solved with “internal variable convection”. After classical time step, when new velocities in nodes are computed, the convection step is carried out. While velocity field is known, the convection of internal variable values could be calculated. The changes of internal variable due to material processes could be included as a source stream. The internal variable convection methodology allows to adapt typical CFD codes for thixoforming simulations, with complying viscosity changes in time. This approach also makes very high deformations relatively easy to compute. In this paper, the assumption and proposition of implementation of internal variable convection into thixoforming modelling is presented.

PL

Tiksoforming jest stosunkowo nową metodą formowania. Polega ona na nadawaniu znacznego stopnia odkształcenia materiałowi w stanie stało-ciekłym. Z numerycznego punktu widzenia, procesy te są trudne do modelowania, co jest efektem występowania zjawisk charakterystycznych zarówno dla cieczy, jak i ciał stałych. Własności materiału są zależne od czasu, podobnie jak w materiałach stałych, podczas gdy odkształcenie może być bardzo duże, podobnie jak w cieczach. W artykule zaprezentowano przegląd obecnie istniejących rozwiązań numerycznych, opartych głównie na metodach dynamiki płynów, z zastosowaniem opisu kinetyki wg metody Eulera lub Arbitrary Lagrangian Eulerian (ALE). Wykazana została potrzeba opracowania nowej metody symulacyjnej dla zależnych od czasu materiałów poddawanych formowaniu tiksotropowemu. Opisana została metoda konwekcji zmiennej wewnętrznej dla eulerowskiego opisu kinetyki. Przedstawiona została implementacja metody jako procedur użytkownika komercyjnego pakietu ADINA-F. Zaprezentowano przykładowe wyniki dla prostych przepływów tiksotropowych.