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A modified van der Pol equation with delay in a description of the heart action

Zduniak B., Bodnar M., Foryś U.

International Journal of Applied Mathematics and Computer Science

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2014

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Vol. 24, no. 4

853--863

EN

In this paper, a modified van der Pol equation is considered as a description of the heart action. This model has a number of interesting properties allowing reconstruction of phenomena observed in physiological experiments as well as in Holter electrocardiographic recordings. Our aim is to study periodic solutions of the modified van der Pol equation and take into consideration the influence of feedback and delay which occur in the normal heart action mode as well as in pathological modes. Usage of certain values for feedback and delay parameters allows simulating the heart action when an accessory conducting pathway is present (Wolff–Parkinson–White syndrome).

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Numerical Aspects of Penetration Simulation

Morka A., Zduniak B., Niezgoda T.

Problemy Mechatroniki : uzbrojenie, lotnictwo, inżynieria bezpieczeństwa

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2011

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Vol. 2, Nr 3 (5)

21-30

EN

Several numerical methods were studied as means of solution to a penetration problem. The Element Free Galerkin (EFG), Smooth Particle Hydrodynamics (SPH), Finite Element Analysis (FEA) methods were considered. The above mentioned algorithms implemented in the LS-DYNA code were applied. Additionally, the mesh density was taken into consideration. The reference case assumed an average node to node distance of 1 mm. The finer and coarser mesh densities were analysed. The full 3D models of the projectile and target were developed with a strain rate and temperature dependent material constitutive relations. An impact of 12.7x108 mm B32 armour piercing projectile on a 80 mm thick block of 7017 aluminium alloy was modelled. The results obtained by a computer simulation were validated and then verified by experimental data. The study of the erosion criteria involves defining the most efficient and reliable way of removing the failed and extremely deformed parts of the projectile and targets. Generally, EFG method applied to solve the perforation/penetration problems can be characterized as a very stable, reliable and effective method.

3

Study of FEM model for tension and compression test for aluminum alloys samples in order to set materiał data

Zduniak B., Morka A., Gieleta R.

Journal of KONES

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2010

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Vol. 17, No. 3

527-532

EN

The purpose of this paper is to conform an available material data for aluminum alloy material (P A11). This task was filled with the aid of computer modeling techniques, which are based on Finite Element Method (FEM), and our own experimental tests of quasistatic tension/compression material samples. For this kind of research FEM is most commonly used, but there are also other numerical methods that can be applied. The idea of FEM is the division of the given continuous area into a finite number of subareas (finite elements) connected with one another in nodal points and approximation of solution inside the finite elements using interpolation functions and function values in nodes. Numerical analysis was performed with the LS-Dyna commercial software. Reconstruction of conditions of experiment required application of implicit method of numerical integration in time, so called implicit solver. At this stage of work the aluminum alloy P A11 with respect to Johnson-Cook model was researched. A further work for fmding a good material data for WHA, U12A steel for other constitutive models will be performed. A good agreement of the numerical and experimental results is received. Other material data used in modeling, which were not determined by experiment, assumed according to literature sources.