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1

Analyzing the Impact of Population Size in AI-Based Reconstruction of the Thermal Parameter in Heat Conduction Modeling

Gawrońska Elżbieta, Zych Maria, Dyja Robert, Kowalkowski Michał

Advances in Science and Technology. Research Journal

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2024

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Vol. 18, no 2

349--364

EN

The research shows how to use swarming algorithms to rebuild the heat transfer coefficient, especially in regard to the continuous border condition. The authors utilized their application software to do numerical computations, employing classical variants of swarm algorithms. The numerical calculations employed a functional determining error to assess the accuracy of the estimated result. The functional minimization was conducted with the swarm algorithms (especially ABC and ACO). The geometry analyzed in this study consisted of a square shape referred to as the cast, enclosed within another square shape known as the casting mold. These two squares were separated by a layer facilitating heat conduction, characterized by the coefficient κ. The coefficient of the thermally conductive layer was recalibrated utilizing swarm methods within the range of 900 - 1500 [W/m^2K] and subsequently compared to a predetermined reference value. A finite element mesh consisting of 576 nodes was used for the calculations. The study involved simulations with populations of 5, 10, 15, and 20 individuals. Furthermore, each scenario also took into account noise of 0%, 2%, and 5% of the reference values. Results make evident the reconstructed value of the κ coefficient, cooling curves, and temperatures for the ABC and ACO algorithms are physically correct. The consequences indicate a notable level of satisfaction and strong concurrence with the anticipated of the κ parameter values. The results from the numerical simulations demonstrate considerable promise for applying artificial intelligence algorithms in optimizing production processes, analyzing data, and facilitating data-driven decision-making.

2

Numerical modeling of the solidification process with consideration of shrinkage cavities formation and the influence of solid phase content on the feeding of the casting

Węgrzyn-Skrzypczak Ewa, Skrzypczak Tomasz

Journal of Applied Mathematics and Computational Mechanics

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2023

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Vol. 22, nr 2

75--86

EN

The paper focuses on the numerical modeling of the three-dimensional solidification process of steel using the finite element method (FEM). The model includes and discusses the formation of shrinkage cavities and the influence of the solid phase content on the feeding of the casting through the riser. The analysis assumed a critical value of the solid phase content, at which the transport of liquid phase from the riser to the casting is interrupted. The results of numerical simulation are presented to investigate the influence of this factor on the final quality of the casting. The model neglects the fluid motion in the liquid and solid-liquid regions and replaces the influence of the mold with appropriate boundary conditions.

3

Impact of input parameters on numerical calculations optimized by swarming algorithms during computer simulations of the heat conduction phenomenon

Zych Maria, Gawrońska Elżbieta, Dyja Robert, Krawiec Piotr

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 4

107--118

EN

The article presents the application of swarming algorithms in heat conduction, taking into account the continuity of the boundary condition (type IV). The influence of the input parameters of the bee and ant algorithm and tessellation on the selection of the heat conduction coefficient between the casting mold and the casting in computer simulations was presented. The results were compared for two different finite element grids, a different number of individuals, and a different number of iterations. The study also considered the magnitude of the reference temperature disturbance as the input temperature for numerical calculations. The analysis showed that the relative error of reproducing the value of the thermal conductivity coefficient in the continuity condition did not exceed 1.5% of the reference value of this coefficient.

4

Investigations on an influence of the material properties on vibrations of active rocker-bogie suspension

Sokół Krzysztof, Pierzgalski Maciej

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2022

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Vol. 70, nr 1

art. no. e138239

EN

Unmanned vehicles are often used in everyday life, mostly by rescue teams or scientists exploring new terrains. In those constructions, the suspension has constant dimensions, which leads to many disadvantages and limits the application area. The solution to these problems can be creating a six-wheeled mobile platform that can dynamically change the wheelbase in relation to the area of action or terrain inclination angle. The active change in location of the center of gravity gives a possibility to access sloppy obstacles not available with classical suspensions. The main scope of this study is to investigate the influence of material properties on vibration frequency at different lengths of suspension members. The obtained results will allow finding the optimum material for producing a prototype unit.

5

Estimation of strength properties of functionally graded structures with elliptical stress concentrators

Stotsko Z.A., Kuzin B., Kuzin M.O., Mechanik V.A.

Archives of Materials Science and Engineering

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2022

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Vol. 113, nr 1

35--41

EN

Purpose: The purpose of this paper is to elaborate new calculation schemes for evaluating the strength parameters of railway rolling stock parts with non-local properties of surface layers in the presence of elliptical stress concentrators. Design/methodology/approach: Using the proposed approaches of developed mathematical modelling and open software for calculating FEniCS, it were established the most dangerous angles of stress concentrator orientation and the required thickness of the hardened zones of parts, which ensures their minimum softening during operation. Findings: It is shown that for an elliptical stress concentrator with any orientation angle, there is a certain key size of surface hardening thickness, the exceeding the value of which does not have influence on the operational strength of the parts, but rise the price of technological operations. Research limitations/implications: In this paper proposes a method for computation the impact of the orientation of the surface elliptical stress concentrators on the contact strength of parts under conditions of dominate friction power loads. Practical implications: The obtained results were used to set the modes of plasma hardening, which increase the contact strength of railway parts with elliptical stress concentrators. Originality/value: Using the approaches of contact mechanics, mathematical and computer modelling, methods of controlling the contact strength of the parts with the surface elliptical stress concentrators were proposed for the first time.

6

Application of computational mechanics approaches for increasing of tribosystem operational parameters by using plasma hardening method

Kopylov Viacheslav, Kuzin Oleg, Kuzin Nickolai

Journal of Applied Mathematics and Computational Mechanics

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2021

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Vol. 20, nr 1

61--70

EN

On the basis of the mathematical model of the continual description of functionalgradient metal systems, taking into account their structure, a computational computer scheme has been developed that makes it possible to assess the stress-strain state of local volumes of parts taking into account their spatial inhomogeneity. With the use of modern software components of computational mechanics - FEniCS finite element analysis package and its implementation in Python, the optimal structural characteristics of wheelsets of railway locomotive tires after plasma treatment have been established. It is shown that, depending on the value of the load, hardening of products must be carried out to a depth of 4.5 mm; with a further increase in thickness, the parameters of operational strength do not change.

7

Application of numerical methods for solving the non-Fourier equations. A review of our own and collaborators’ works

Majchrzak E., Mochnacki B.

Journal of Applied Mathematics and Computational Mechanics

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2018

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Vol. 17, nr 2

43--50

EN

Thermal processes occuring in the solid bodies are, as a rule, described by the well-known Fourier equation (or the system of these equations) supplemented by the appropriate boundary and initial conditions. Such a mathematical model is sufficiently exact to describe the heat transfer processes in the macro scale for the typical materials. It turned out that the energy equation based on the Fourier law has the limitations and it should not be used in the case of the microscale heat transfer and also in the case of materials with a special inner structure (e.g. biological tissue). The better approximation of the real thermal processes assure the modifications of the energy equation, in particular the models in which the so-called lag times are introduced. The article presented is devoted to the numerical aspects of solving these types of equations (in the scope of the microscale heat transfer). The results published by the other authors can be found in the references posted in the works cited below.

8

Diagnosis of vortex induced vibration of a gravity damper

Scappaticci L., Castellani F., Astolfi D., Garinei A.

Diagnostyka

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2018

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Vol. 19, No. 2

31--39

EN

A gravity damper is a one-way valve, employed for regulating the airflow rate in ducts, generally constituted by a series of rectangular panels (closure sections), connected to an articulated quadrilateral synchronizing the movements. If the device needs to process large masses of high speed air, as common in the case of energy conversion systems, disadvantageous dynamic effects can occur. In this study, vortexinduced vibration (VIV), occurring on a gravity damper for high values of the Reynolds number, is investigated. The analysis of this work couples numerical methods (Computational Fluid Dynamics with Large-Eddy Simulation turbulence model and Finite Element Method) to experiments: a full-scale accelerometric measurement campaign is actually performed at the wind tunnel facilities of the University of Perugia. VIVs are diagnosed and quantified through the experimental vibration analysis, which is interpreted through numerical simulations. The large amplitude of VIV is interpreted as due to a tendency towards lockin because of the approaching of the vortex shedding frequency to a natural vibration mode of the system. The integrated numerical and experimental framework finally inspires two different design solutions for mitigating the amplitude of VIV: these strategies are tested at the wind tunnel and they are indeed shown to be effective.

9

Modeling of mechanical phenomena in the platinum-chromium coronary stents

Idziak-Jabłońska A., Karczewska K., Kuberska O.

Journal of Applied Mathematics and Computational Mechanics

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2017

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Vol. 16, nr 4

29--36

EN

This study discusses the geometrical model of a coronary stent with known design and strength analysis using the finite element method. The coronary stent model was made of platinum and chromium alloy. Static analysis based on compression of the coronary stent was also performed. The aim of the analysis was to examine the strength of the stent structure. The study analyzed stresses, plastic strains and displacements after applying a constant load to the stent walls. The mechanical phenomena such as percentage degree of shortening (foreshortening), relative narrowing and area of stent covering were also determined.

10

Peridynamics for damage modelling and propagation via numerical simulations

Martowicz A.

Diagnostyka

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2017

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Vol. 18, No. 1

73--78

EN

The present work provides an overview on the selected applications of peridynamics to damage modelling and simulations of its propagation in mechanical structures. The theoretical fundamentals of the method are briefly described to highlight its advantages and the scope of practical use in the field of computational mechanics. Selected results of numerical analyses are provided to illustrate demanded capabilities. The perspectives of nonlocal and integral based problem formulations for dynamics are discussed.

PL

Artykuł stanowi przegląd wybranych zastosowań perydynamiki w modelowaniu uszkodzeń i symulacji zjawisk ich propagacji w konstrukcjach mechanicznych. Przedstawiono podstawy teoretyczne metody ze szczególnym uwzględnieniem specyfiki zalet perydynamiki w zastosowaniach w mechanice komputerowej. Opisywane zalety metody są zilustrowane wybranymi przykładami analiz numerycznych. Artykuł przedstawia możliwości obliczeniowe nielokalnych sformułowań dla dynamiki bazujących na całkowych równaniach ruchu.

11

Modeling of thermal contact through gap with the use of Finite Element Method

Węgrzyn-Skrzypczak E., Skrzypczak T.

Journal of Applied Mathematics and Computational Mechanics

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2015

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Vol. 14, nr 4

145--152

EN

In the paper the mathematical and numerical descriptions of the general case of thermal contact between two flat bodies are presented. The numerical model of the problem is based on the Finite Element Method (FEM). Variable width of the contact gap between interacting bodies is considered. The model allows the use of independent spatial discretization of the contacting components, which means that the edges of the finite elements lying on the both sides of the contact gap need not be matched. The algorithm of treatment of the fourth kind boundary condition is described in details.

12

Modeling of selected load-bearing structures using the truss and beam elements

Jaskot A., Śpiewak S.

Journal of Applied Mathematics and Computational Mechanics

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2015

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Vol. 14, nr 3

37--47

EN

The article presents the methodology of adjusting the usable properties of rodlike and beam elements for modeling the complex load-bearing structures. The basic object of consideration was the single-row slewing ball bearing. In this paper the mapping issues of usable qualities of the slewing bearings are summarized in relation to use of the finite element method. The emphasis is primarily on using the rod-like and beam elements for modeling the contact phenomena in the ball-raceway contact zone. In addition, ideas for use of the beam elements to modeling bearing bolts were presented.

13

Errors of stress numerical integration for cross-sections with straight and curved boundaries

Matuszak A.

Computer Assisted Methods in Engineering and Science

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2015

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Vol. 22, no. 2

153--176

EN

Internal forces are integrals of stress in a section area. Integrating the stress for an arbitrary cross-section shape and for the nonlinear stress-strain law σ(ε) is tedious and the use of the boundary integral approach can simplify computations. Numerical integration when applied to the computations of such integrals introduces errors in many cases. Errors of numerical integration depend on the adopted integration scheme, the type of σ(ε) and the shape of the cross-section boundary. In the case of adaptive numerical integration what is very important are the properties of the sequence of errors produced by a given integration scheme in the increasing order of the numerical quadrature or the increasing number of subdivisions. This paper analyses errors caused by different integration schemes for the typical σ(ε) either for a straight or curved boundary. Special attention is paid to the properties of the error sequence in each case. The outcome of this paper is important from the viewpoint of the reliability and robustness of the software developed for nonlinear simulations of bar structures.

14

Pyramidal ceramic armor ability to defeat projectile threat by changing its trajectory

Stanislawek S., Morka A., Niezgoda T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2015

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Vol. 63, nr 4

843--849

EN

This paper presents a numerical study of a multilayer composite panel impacted by an AP (Armor Piercing) 14.5×114 mm B32 projectile. The composite consists of alternating layers of hard ceramic and a ductile aluminum alloy. While the alloy layer consists of typical plate, ceramics confront projectiles in the form of ceramic pyramids. The studied models are compared with a reference structure, which is a standard double layer panel. The problem has been solved with the usage of modeling and simulation methods as well as a finite elements method implemented in LS-DYNA software. Space discretization for each option was built with three dimensional elements ensuring satisfying accuracy of the calculations. For material behavior simulation, specific models including the influence of the strain rate and temperature changes were considered. A steel projectile and aluminum plate material were described by the Johnson-Cook model and a ceramic target by the Johnson-Holmquist model. The obtained results indicate that examined structures can be utilized as a lightweight ballistic armor in certain conditions. However, panels consisting of sets of ceramic prisms are a little easier to penetrate. Despite this fact, a ceramic layer is much less susceptible to overall destruction, making it more applicable for the armor usage. What is most important in this study is that significant projectile trajectory deviation is detected, depending on the impact point. Such an effect may be utilized in solutions, where a target is situated relatively far from an armor.

15

Badanie wpływu sformułowania elementu skończonego oraz schematu rozwiązywania równania ruchu na wyniki analizy MES na przykładzie niesymetrycznie obciążonej płyty

Krzeszowiec M., Małachowski J.

Biuletyn Wojskowej Akademii Technicznej

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2015

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Vol. 64, nr 1

139-159

PL

Komputerowe metody symulacji zjawisk fizycznych obecnie są powszechne zarówno w obszarze nauki, jak i przemysłu. Możliwość przybliżonego rozwiązywania skomplikowanych układów równań różniczkowych, opisujących zagadnienia z dziedziny mechaniki, fizyki czy chemii, pozwala na znaczne skrócenie czasu projektowania i wdrażania nowych projektów. Często dzieje się to przy jednoczesnym zmniejszeniu zapotrzebowania na kosztowne badania eksperymentalne lub wytwarzanie prototypów. Jednak wspomniana powszechność tych metod, w szczególności metody elementów skończonych, spowodowała, że symulacje oraz analizy przeprowadzane z ich wykorzystaniem są często z góry za dokładne. Celem tego artykułu jest przedstawienie na przykładzie prostej analizy wytrzymałościowej, jak duży wpływ na wyniki symulacji mają takie parametry jak gęstość siatki elementów skończonych, sformułowanie elementu skończonego czy schemat całkowania równania ruchu. Dodatkowo autorzy zdecydowali się pokazać, jak łatwo jest uzyskać wyniki, które nie przedstawiają sensu fizycznego, pomimo tego, że wszystkie podstawowe założenia poprawnej analizy (odpowiednie warunki brzegowe, zachowana energia układu etc.) zostały spełnione. Wyniki przeprowadzonych badań mogą być przestrogą przed pochopnym wyciąganiem wniosków z obliczeń przeprowadzonych za pomocą MES.

EN

Computer simulations of physical phenomena are at the moment common both in science and industry. The possibility of finding approximate solutions for complicated systems of differential equations, mathematically describing issues in the fields of mechanics, physics or chemistry, allows for shorten design and research time, often significantly reducing the need for expensive experimental studies or costly production of prototypes. However, the mentioned prevalence of these methods, particularly the Finite Element Method, resulted in analysis outcomes to be often in advance regarded as accurate ones. The purpose of the article is to showcase, on a simple stress analysis problem, how parameters such as the density of the finite element mesh, finite element formulation or integration scheme significantly influence on the simulation results and how easy it is to end up with the results that do not hold any physical sense, despite the fact that all the basic assumptions of correct analysis (suitable boundary conditions, total system energy stored etc.) have been met. The results of this study can serve as a warning against premature conclusion drawing from calculations carried out by means of FEM simulation.

16

The identification of degenerated systems in the impact energy dissipation process

Bocian M., Jamroziak K.

Journal of Achievements in Materials and Manufacturing Engineering

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2013

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Vol. 57, nr 1

23--30

EN

Purpose: The article presents an analysis of impact energy dissipation process with selected non-classical dynamic models. Design/methodology/approach: Identification of impact energy dissipation phenomena in mechanical systems with a layered structure (eg. composite ballistic shields) is quite a challenge, because on the one hand it is sought to the model, whose parameters are as much as possible responsible for the energy dissipation, on the other hand, the number of parameters should be optimized. Searched model should be reduced to a simple description of the whole phenomenon and completely imitate entire mechanical system. Description of the impact energy dissipation was modeled with selected degenerated systems in this case. Models were subjected to hammer extortion the specified impulse of force. The mathematical description of pulsed extortion was carried out by using the energy and balance equation of power. Verification of mathematical identification equations for selected model parameters was performed by computer simulation technique. Findings: This is original analytical method, which uses the degenerated systems in various configurations. It involves the use of specially derived identification equations, which are described by the decrease of potential energy of the system during the vibrations induced by a single impulse load. Research limitations/implications: Method of identification requires the use of appropriate input function. Input function could be a periodic type or a type of step function. Practical implications: Estimation of the energy consumption objects in terms of method of identifying the parameters of the model. Originality/value: Presented work includes the identification of piercing the ballistic shield, and it is a part of work on the implementation of the degenerated models to describe these phenomena.

17

Wpływ uproszczeń w badaniach symulacyjnych zderzeń pocisków z tarczą na dokładność wyników

Stanisławek S., Morka A., Niezgoda T.

Biuletyn Wojskowej Akademii Technicznej

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2013

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Vol. 62, nr 3

137-143

PL

Artykuł omawia zagadnienie możliwości stosowania określonych uproszczeń w symulacji komputerowej. Stanowi on niezbędny warsztat dla każdego badacza stosującego opisane sposoby modelowania. Weryfikacja uproszczeń numerycznych polegała na przeprowadzeniu trzech testów zderzeniowych dla rdzenia pocisku 7,62 × 51 WC oraz czwartej symulacji polegającej na porównaniu efektów uderzenia pełnego modelu pocisku oraz jedynie jego rdzenia. Opracowane modele tarczy symulowały materiał stalowy z wprowadzonymi typowymi parametrami, natomiast pocisk był opisany modelem Johnsona-Cooka. Prędkość początkowa pocisku wynosiła 854 m/s, zaś tarcza pozostawała nieruchoma i zamocowana w płaszczyźnie prostopadłej do kierunku lotu. Opisane badania potwierdzają możliwość stosowania modelu materiału nieodkształcalnego oraz sprężystego do uproszczonego opisu ciał materialnych. Pozwala to na uproszczenie i przyspieszenie obliczeń numerycznych w sytuacjach, gdzie materiały zderzających się ciał mają znacznie różne właściwości mechaniczne. Z dużą ostrożnością powinno się odnosić do odczytywania sił rejestrowanych na ściance nieodkształcalnej. Analiza sił oraz energii pokazuje natomiast, że sabot i płaszcz pocisku nie odgrywają zasadniczej roli przy uderzeniu w nieruchomą tarczę. Doznaje ona większego popędu, jednak nie jest to różnica zasadnicza.

EN

The paper presents the possibility of applying certain simplifications for computer simulations. It is the essential knowledge for each scientist employing the described methods of modelling. Verification of numerical simplifications consisted in conducting three impact tests for a 7.62 × 51 WC projectile core and a forth one which referred to a comparison of a full model of the penetrator with its core only. The target was described with a simple steel material while the projectile with an advanced Johnson-Cook model. Projectile initial speed was 854 m/s while a target remained motionless and fixed in a plane perpendicular to the motion direction. The performed tests confirm the possibility of using rigid and elastic materials for a simplified material body description. It allows simplification and shortening of computational time when materials are characterized by very different strength. However, a user should be very careful when analyzing the forces recorded on a rigid wall. Furthermore, analysis of the forces and energies shows that both a sabot and a jacket do not play a significant role during the impact into a motionless target. It register a bigger force impulse but it is not a substantial difference.

18

Analiza przestrzennych ścianowych konstrukcji usztywniających budynki wysokie z dodatkowymi sztywnymi belkami

Wdowicki J., Wdowicka E.

Biuletyn Wojskowej Akademii Technicznej

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2013

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Vol. 62, nr 1

215-233

PL

Praca przedstawia analizę przestrzennych niesymetrycznych ścianowych konstrukcji usztywniających budynki wysokie z dodatkowymi sztywnymi belkami. Sztywne, wysokie belki zastosowane nawet na niewielu poziomach ścianowej konstrukcji z nadprożami znacznie zwiększają sztywność układu konstrukcyjnego. W analizie wykorzystano pewien wariant metody ciągłych połączeń, opracowany dla przestrzennych ścianowych konstrukcji usztywniających, mających skokowe zmiany sztywności wzdłuż wysokości. W podejściu ciągłym nadproża są zastępowane równoważnymi pionowymi pasmami ciągłych połączeń. Równania zgodności przemieszczeń są zapisane w punktach znajdujących się w środkach rozpiętości nadproży i sztywnych belek. Układy równań różniczkowych dla stref układów usztywniających o stałym przekroju poprzecznym są rozdzielane przy wykorzystaniu ortogonalnych wektorów własnych. Wyniki obliczeń dla proponowanej metody zostały porównane z wynikami uzyskanymi przy wykorzystaniu różnych metod obliczeniowych, zarówno analitycznych jak i numerycznych, oraz z opublikowanymi wynikami badań doświadczalnych. Stwierdzono dobrą zgodność wyników.

EN

The paper presents the analysis of non-planar asymmetric shear wall structures with stiffening beams. The stiff deep beams incorporated at various levels of coupled shear walls improve the stiffness of the structural system of a tall building. The analysis is based on a variant of the continuous connection method for three-dimensional shear wall structures having stepwise changes in a crosssection. In the continuous approach, the connecting beams are replaced by equivalent continuous connections. The compatibility equations have been written at the midpoints of connecting and stiffening beams. The differential equation systems for shear wall structure segments of the constant cross-section are uncoupled by orthogonal eigenvectors. The results obtained by the presented method have been compared with those obtained experimentally and analytically, given in literature, and a good match has been observed.

19

Numerical analysis of a multi - component ballistic panel

Stanisławek S., Morka A., Niezgoda T.

Journal of KONES

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2012

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Vol. 19, No. 4

585-588

EN

The paper presents a numerical study of a two layer composite panel impacted by an AP (Armour Piercing) 14.5x118mm B32 projectile. The panel consists of a number of pyramid ceramic components supported by an aluminium plate. The studied model is compared with a reference structure in which ceramic layer is in a form of a plate. The problem has been solved with the usage of modelling and simulation methods as well as a finite elements method implemented in LS-DYNA software. Space discretization for each option was built with three dimension elements guaranteeing satisfying accuracy of the calculations. For material behaviour simulation, specific models including the influence of the strain rate and temperature changes were considered. A steel projectile and aluminium plate material were described by Johnson-Cook model and a ceramic target by Johnson-Holmquist model. In the studied panels, the area surrounding back edges was supported by a rigid wall. The obtained results show interesting properties of the examined structures considering their ballistic resistance. All tests have given clear results about ballistic protection panel response under AP projectile impact. Panels consisting of sets of pyramids are slightly easier to penetrate. Despite this fact, a ceramic layer is much less susceptible to overall destruction what makes it more applicable for the armour usage. Furthermore, a little influence of the projectile impact point and consequently a part of the pyramid, which is first destroyed, is proved.

20

Numerical analyses of ceramic/metal ballistic panels subjected to projectile impact

Morka A., Nowak J.

Journal of KONES

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2012

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Vol. 19, No. 4

465-472

EN

The paper concerns research and development on modern, ceramic-based, protective layers used in the armour of tanks, combat vehicles and aeroplanes. A task of ceramic panels is reduction and dispersion of localized kinetic energy before a projectile or its fragment approaches the interior of protected object. The numerical investigations have been performed to determine the ballistic resistance of ceramic/metal panels subjected to projectile impact. The impact of the 7.62mm armour-piercing projectile on the ceramic elements backed by a metal plate was analyzed. The tested panels were composed of a ceramic layer (Al2O3, SiC or B4C) and a metal layer (7017 aluminium alloy, Armox 500T steel or Ti6Al-4 titanium alloy). Different shapes of ceramic elements were analyzed, including hemispheres and pyramids, with respect to standard flat tiles. The influence of the impact point location was also taken into considerations. The computer simulations were performed with the Finite Element Method implemented in LS-DYNA code. Full 3D models of the projectile and targets were developed with strain rate and temperature dependent material constitutive relations. The conclusions presented in the paper can be applied to develop modern impact protection panels in which the appropriate balance between the mass and protection level must be accomplished.