Wyniki wyszukiwania - BazTech

1

Numerical and experimental analysis of unevenness of pressure in multidisc brake

Sadowski M., Jachimowicz J., Pietrzakowski M.

Machine Dynamics Research

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2018

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Vol. 42, No. 3

89--105

EN

The paper presents numerical (using Finite Element Method) and experimental (using brake tests) approaches to analyse the problem of unevenness of pressure between brake discs. Influence of surface imperfections on pressure, stress distributions and temperature fields was taken into consideration. The temperature fields were obtained experimentally using thermocouples and an infrared camera. The correlation between the surface imperfections and the temperature fields has been demonstrated in both the numerical and experimental approaches.

2

Study on Possible Replacement of the Aluminum Spar with a Composite Structure Illustrated with the Case of Agricultural Aircraft

Fałek M., Szymczyk E., Jachimowicz J.

Fatigue of Aircraft Structures

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2017

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Iss. 9

85--99

EN

Composite materials are increasingly being used in aviation. Specific stiffness and strength of composite materials (especially CFRP laminate, sandwich structure) are higher compared to metal alloys. They are beneficial features of materials used in aviation. Mass reduction of aircraft structures (e.g. due to the use of composite materials) contributes to an aircraft’s better performance in terms of its range, top speed and ceiling and consequently causes an increase in airplanes capacity. Moreover, the use of high-strength and lightweight materials in aviation contributes to longer life time and lower exploitation costs. The aim of the paper was the study the possibilities of replacing the aluminum spar of an airplane wing with a composite structure. In order to compare the mass and strength of the aluminum with the composite spar, the global shell and local solid models were created and finite elements analysis was performed. The analysis was carried out for the front spar of the wing of the agricultural aircraft PZL-106.

3

Design and Strength Analysis of Curved-Root Concept for Compressor Rotor Blade in Gas Turbine

Wdowiński W., Szymczyk E., Jachimowicz J., Moneta G.

Fatigue of Aircraft Structures

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2017

|

Iss. 9

137--155

EN

The motivation of the article is fatigue and fretting issue of the compressor rotor blades and disks. These phenomena can be caused by high contact pressures leading to fretting occurring on contact faces in the lock (blade-disk connection, attachment of the blade to the disk). Additionally, geometrical notches and high cyclic loading can initiate cracks and lead to engine failures. The paper presents finite element static and modal analyses of the axial compressor 3rd for the original trapezoidal/dovetail lock geometry and its two modifications (new lock concepts) to optimize the stress state of the disk-blade assembly. The cyclic symmetry formulation was used to reduce modelling and computational effort.

4

FEM design of composite - metal joint for bearing failure analysis

Puchała K., Szymczyk E., Jachimowicz J.

Przegląd Mechaniczny

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2015

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nr 2

33--41

PL

Stałe dążenie do uzyskania jak najmniejszej masy samolotu jest powodem stosowania w konstrukcjach lotniczych materiałów o wysokiej wytrzymałości i sztywności właściwej. Wysokowytrzymałe stale, stopy tytanu lub stopy aluminium (np. 2024T3) oraz laminaty kompozytowe (np. CFRP, Glare) są przykładami takich materiałów. Stosowanie różnorodnych materiałów na struktury lotnicze wymusza konieczność łączenia części metalowych z kompozytowymi. Stosuje się różne techniki łączenia pokryć płatowca z elementami usztywniającymi: mechaniczne (połączenia nitowane, śrubowe), adhezyjne (klejenie, okazjonalnie zgrzewanie), hybrydowe (w którym zastosowano kombinacje dwóch różnych metod). W przypadku połączeń mechanicznych konieczne jest wykonywanie otworów, które stanowią miejsca silnych koncentracji naprężeń decydujących o wytrzymałości całej konstrukcji. Połączenia mechaniczne jako stosowane od dziesięcioleci odznaczają się wysokim poziomem niezawodności. Połączenia mechaniczne można wykonywać oraz użytkować w trudnych warunkach środowiskowych. Celem pracy jest projekt mechanicznego połączenia metal-kompozyt oraz analiza niszczenia elementu kompozytowego. Analizowano dwucięte połączenie śrubowe. Przeprowadzono obliczenia analityczne oraz numeryczne.

EN

The constant attempt to obtain as low aircraft mass as possible is the reason for using material of high specific strength (or stiffness) in the aerospace industry. High strength steels, titanium or aluminium alloys (e.g. 2024T3) and composite laminates (e.g. CFRP or Glare) are the examples of such materials. Dissimilar materials in aircraft structures provide a necessity of composite and metallic components joining. Various techniques are used to connect the skin with the stiffening elements: mechanical (riveting, bolting), adhesive (bonding and occasionally welding) and hybrid (where both above mentioned methods are used). Making holes is a necessity for mechanical joints. The holes are the areas of high stress concentrations and they determine load capability of the whole structure. However, mechanical joints used for decades are proved to be reliable. They can be assembled and applied in very rough conditions since they are less sensitive to environmental effects. The goal of the work is development of a mechanical metal-composite joint and failure analysis of the composite part. The double-shear joint is analysed. Both analytical and numerical calculations are performed.

5

Numerical analysis of rod uniaxial tension considering thermo-mechanical coupling effect

Nguyen H. P., Niezgoda T., Derewońko A., Jachimowicz J.

Metallurgy and Foundry Engineering

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2015

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Vol. 41, no. 4

189--199

EN

This paper presents numerical analyses of uniaxial tension tests on rods made of a material with elastic-plastic characteristics with mapping the temperature fields generated in the fields of plastic strains. The use of thermo-mechanical coupling algorithms implemented in CAE programs that enable us to enter the parameters of materials dependent on temperature and used to visualize the damage of the samples is presented. The numerical models were validated with experimental research.

PL

W pracy przedstawiono analizy numeryczne testów jednoosiowego rozciągania prętów wykonanych z materiału o charakterystyce sprężysto-plastycznej z odwzorowaniem pól temperatury generowanych w obszarach odkształceń trwałych. Zaprezentowano wykorzystanie algorytmów sprzężenia termomechanicznego zaimplementowanych w programach CAE, umożliwiających wprowadzenie parametrów materiałów zależnych od temperatury oraz stosowanych do wizualizacji zniszczenia próbek. Wyniki symulacji zwalidowano badaniami eksperymentalnymi.

6

Modelowanie wytrzymałościowe i analiza masowo-materiałowa dźwigara skrzydła samolotu rolniczego

Jachimowicz J., Szymczyk E., Łukasiński Ł., Puchała K.

Logistyka

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2015

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nr 4

3726--3733, CD 2

PL

W artykule przedstawiono metodologię obliczeń wytrzymałościowych mającej na celu zamianę dźwigara metalowego na kompozytowy na przykładzie rolniczego samolotu PZL-106 Kruk. Zilustrowano przypadki obciążeniowe oraz wskazano przypadek wymiarujący z odpowiednim rozkładem obciążeń. Pokazano modele wytrzymałościowe segmentu dźwigara. Wykonano obliczenia analityczne oraz analizy numeryczne. Przedstawiono analizę sztywnościowo-masową przykładowych rozwiązań , z analizy których wynika m.in. , że stosując kompozyt węglowy jako materiał dźwigara można zmniejszyć masę o około 69%.

EN

The paper presents a strength analysis methodology intended for replacing the metallic wing spar with a composite one on the example of PZL-106 Kruk agriculture aircraft. Loading cases are presented and dimensioning case with appropriate load distribution is selected. Static strength models of wing spar are studied. Analytical and numerical calculations are performed. The strength-mass analysis for exemplary configurations is presented. This analysis shows that mass of the spar can be reduced by 69% if the D16TN aluminum alloy is replaced with CFRP composite of appropriate configuration.

7

Analiza dwuzakładkowego połączenia adhezyjnego metal–kompozyt

Szymczyk E., Puchała K., Jachimowicz J.

Mechanik

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2014

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R. 87 nr 11

946--949

PL

Omówiono metody łączenia różnorodnych materiałów. Wskazano ich wady oraz zalety. Przedstawiono mechanizm przenoszenia obciążenia pozwalający na zwiększenie wytrzymałości elementu kompozytowego w miejscach połączeń. W oparciu o analogię do połączenia klejowego, przystąpiono do analizy naprężeń stycznych w połączeniu dwuzakładkowym metal–metal oraz metal– –kompozyt. Przedstawiono dwa podejścia stosowane w modelowaniu kompozytu.

EN

Methods of various materials joining are presented. Their benefits and drawbacks are pointed out and analyzed. The load transfer mechanism resulting in increase of the composite material strength in the joint area is presented. Analysis of the shear stress in double-lap in metal-to-metal and in metal-to-composite adhesive joints was carried out by analogy to the adhesive joint. The paper presents two approaches in the composite material modeling.

8

Influence of Manufacturing Tolerances on Vibration Frequencies of Turbine Blade

Moneta G., Jachimowicz J., Osiński J.

Machine Dynamics Research

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2014

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Vol. 38, No. 1

105-118

EN

High Cycle Fatigue is one of most common mechanism of turbine blade failures. The reason are vibrations, which cause cyclic displacements and though that also variable stresses and strains. The most dangerous are excitation frequencies around resonances - that can cause failure in a very short time. About 70 years of jet engine development and more than one century of steam turbine history, was not enough to fully eliminate that problem. This paper shows an influence of manufacturing tolerances and accuracy of manufacturing technology on blade frequencies. Additionally, few methods for avoiding resonances have been presented and its implementation effort have been compared.

9

Projektowanie i optymalizacja hamulców o napędzie elektrycznym

Grygorcewicz P., Jachimowicz J., Pietrzakowski M.

Logistyka

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2014

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nr 3

2239--2245

PL

Artykuł przedstawia proces projektowania hamulców o napędzie elektrycznym ze szczególnym uwzględnieniem różnych istotnych czynników wpływających na konstrukcję hamulca. Zaakcentowane zostały podstawowe fazy związane ściśle z projektowaniem prototypów: proces projektowania, optymalizacja MES i badania laboratoryjne, które są bardzo istotne i sciśle ze sobą powiązane. Przedstawiona została takze budowa hamulca elektrycznego.

EN

This article presents selected issues related to the design methodology of the electric brakes during the construction process as well as other factors which are important in the design process. The main parts of the design process are: design, FEM (Finite Element Methods) calculation and laboratory tests. Nowadays when new solution of brakes is being designed there is a need to take into account various factors influencing the design. The aim of the paper is to discuss design process from the very beginning. The building of the new prototype electric brakes was shown.

10

Analysis of load transfer into composite structure

Szymczyk E., Jachimowicz J., Puchała K.

Applied Computer Science

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2014

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Vol. 10, no 3

86--94

EN

The paper presents advantages and disadvantages of metal foils insertion between composite layers. Composites are complex materials of aniso-tropic structure leading to various failure mechanisms. Mechanism of compressive load transfer into composite laminates by shear of the matrix is analysed. The method of improvement compressive strength of laminates is presented according to literature and analysed for a sele-cted case. Simplified models of a laminate structure modified using various metal foils configurations are analysed with MSC.Marc code. Axial stress in prepreg layers and shear stress in adhesive layers are studied.

11

Some aspects of dynamic riveting simulations

Szymczyk E., Jachimowicz J., Puchała K.

Journal of KONES

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2012

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Vol. 19, No. 1

423-430

EN

Riveting is a commonly used (especially in aircraft structures) method of joining metal and composite components. The methods of forming solid shank rivets can be classified in two types: static and dynamic. The static method is the most efficient one. Regrettably, its application is limited. A popular upsetting tool used in an aircraft is a pneumatic riveter. The rivet driving requires a few hammer strokes. The total stress in a riveted joint depends on the residual and applied stress. Residual post-riveting stress fields are widely accepted to have a beneficial influence on the fatigue life of aircraft structures. The analysis is carried out for a solid mushroom rivet (made of PA25 alloy) joining two sheets (made of 2024T3 alloy). Nonlinear dynamic simulations of the upsetting process are carried out. Simulation of the riveting process is significantly influenced by a material model. The numerical calculations are performed for three different cases of upsetting described by the formed rivet head diameters 1.4d, 1.5d and 1.6d, respectively. The rivet head diameter and, consequently, the residual stress state depend on hammer stroke energy. It has a significant influence on a plastic region around the rivet hole, whereas the influence of a number of strokes can be neglected. The strain rate in both local and global (average) formulation is analysed in the paper. For one hammer stroke, the global strain rate of the rivet shank is about 1.0 thousand per second. The local strain rate is about two times greater than the global one, so a strain rate factor has an effect on the residual stress state. For a few hammer strokes, the strain rate is lower than for one stroke; however, it increases a little in each stroke. The hole deformation can be treated as a function of the internal energy of the sheet. The lower total energy of the part the greater influence of the strain rate on the internal energy is observed.

12

Friction coefficient determination based on the results of ball – on - flat test

Szymczyk E., Jachimowicz J., Prasek Ł.

Journal of KONES

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2012

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Vol. 19, No. 1

415-422

EN

The interaction of contacting surfaces in relative motion is basic for every engineering design. The transmission of load from one rubbing surface to its mating surface under conditions of dry contact is taken into account. Microlocal or global models of friction are used to describe this phenomenon. In global approach, frictional force is proportional to normal load. A coefficient of external friction depends on the type, shape, and precision of finishing the surfaces of mating elements. The aim of the paper is analysis of a friction coefficient for 2024T3 aluminium alloy during cyclic tangential loading. Experimental tests are carried out on a ball-on-flat wear-testing machine Ducom. Tests of reciprocating friction are carried out using the following friction pairs of specimens: the ball specimen is made of high strength aluminium alloy PA25 and the plane specimen is made of 2024T3 alloy. Finally, graphs of temporary friction coefficients versus time in the form of fluctuated periodical functions are obtained. Two phases of friction are detected. However, during the first stage, the friction coefficient is relatively small while in the second period it rapidly increases and tends to become more irregular. Static and dynamic friction coefficients are estimated. In order to determine the dynamic coefficient the Discrete Fourier Transformation is used. The calculation of the dominant amplitude (corresponding to test frequency) of the studied functions is possible due to this method. An increase of the friction coefficient with an increase of normal load is observed. A cladding layer also causes an increase of friction, especially in the second phase.

13

About mechanical joints design in metal - composite structure

Puchała K., Szymczyk E., Jachimowicz J.

Journal of KONES

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2012

|

Vol. 19, No. 3

381-390

EN

Riveting is still one of the main joining methods of thin-walled aircraft structures. Such features as simplicity of implementation, possibility of two different material connection (e.g. metallic with non-metallic ones) and the fact that is it a well-known (reliable) method causes popularity of riveting. The never-ending attempt to obtain as low mass as possible (mainly to reduce fuel consumption) is the reason for using material of high specific strength in the aerospace industry. High strength titanium or aluminium alloys (e.g. 2024T3) and composite laminates (e.g. CFRP or Glare) are examples of such materials. The article deals with methods of connecting various materials. The paper presents advantages and disadvantages of different/selected connection types. Strength prediction and failure modes of mechanical joints are described for metallic as well as for composite components. Composites are complex materials having an anisotropic structure (and anisotropic mechanical properties) leading to various failure mechanisms. Main principles for appropriate joint design of composite laminate panels (laminate configuration and typical/specific geometrical dimensions) are indicated/specified. The bearing failure mechanism is accepted to be a safe progressive one. Mechanism of bearing (generally compressive) load transfer into composite laminates by shear of the matrix is analysed. Some examples of improvement bearing strength of laminates are presented according to literature. On the base of presented examples and bearing load transfer analysis, some conclusions for an appropriate solution of this problem are drawn.

14

Numerical Analysis of Material and Manufacturing Factors in Riveted Joints Under the Imperja Project

Szymczyk E., Bogusz P., Sławiński G., Jachimowicz J.

Fatigue of Aircraft Structures

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2012

|

Iss. 4

100--113

EN

The aim of the project was to improve fatigue performance of riveted joints in airframes. Fatigue strength of a joint depends on structural, material and manufacturing factors. The project involved numerical and experimental analysis of material factors and manufacturing imperfections. The paper deals with the analysis of material structure and properties by means of the optical and SE methods. Static monotonic tests for sheet and rivet materials were carried out. ARAMIS optical system was used for the study of deformation and strain fields in the material during loading. This tool offers the possibility of a non-contact measurement with 3D image correlation methods (digital image correlation, DIC) using high-resolution digital CCD cameras. In ductile materials (such as aluminium alloy), subjected to appropriate loading conditions, voids may form, which grow and coalesce leading to crack formation and potential failure. A micro crack may be initiated at the inclusion particles and then voids grow around it. Experimental studies showed that these processes are strongly influenced by hydrostatic stress (Gurson’s material model). SEM analysis of material structure was carried out after performing static tests. In the paper, the authors present the influence of a material model on the results of numerical simulation of the tensile loaded samples with open and riveted holes. The application of Gurson’s material model allows observation of crack growth in the sample cross-section and determination of the sheet rupture as the moment when constraint force decreases to zero (material separation occurs).

15

Termograficzne pomiary okładzin ciernych hamulców

Piątkowski T., Polakowski H., Jachimowicz J.

Pomiary Automatyka Kontrola

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2011

|

R. 57, nr 11

1285-1288

PL

Opracowanie nowej generacji hamulców wymaga wykonania pomiarów rozkładów temperatury na powierzchniach jego elementów konstrukcyjnych. W pracy przedstawiono wybrane wyniki takich badań metodami termograficznymi. W rezultacie tych badań określono obszary o podwyższonej temperaturze, temperaturę maksymalną oraz szybkość zmian temperatury. Porównano otrzymane wyniki z pomiarami metodą stykową. Dane otrzymane w wyniku analizy termogramów pozwolą na weryfikację modelu numerycznego hamulca.

EN

Braking process has rather short duration (5s÷15s) and during that time the kinetic energy of a vehicle is transformed into heat. Such amount of heat generates thermal shock to braking pads and discs. Development of a new type of brakes requires measuring temperature distributions on their working surfaces. The paper presents some selected results of such measurements performed on a modified IL-68 test rig by means of thermal imaging (Fig. 2). Two types of composite braking pad materials were tested: C/C and 500/EBC. C/C composite is used for aircraft brakes, whereas 500/EBC type is used for brakes of all-terrain ground vehicles. Due to high dynamics of the thermal signal, the measurements were taken in the range from 200?C to 750?C. The data from the thermal images were processed using IR Control software. As a result there were identified the high temperature areas (hot spots), maximum temperature values for each recorded frame and the rate of temperature changes during braking (Fig. 5) as well as cooling down (Fig. 6) phases. The frame-by-frame analysis of the recorded thermal image sequences made it possible to correlate the temperature distribution non-uniformity with structural defects of the tested brake pads. The results of temperature measurements were compared with those obtained from the contact method (Fig. 7). On that basis, the errors of non-contact temperature measurements were estimated. The analysis of the recorded thermal images allowed calculating several thermal parameters, such as thermal time constants of particular brake elements (1), (2). Those data were used to verify the numerical model of the brake. They also can be the guidelines to optimise the brake design with respect to heat transfer aspects.

16

Badania numeryczne wybranego układu pojazdu specjalnego w aspekcie poprawy bezpieczeństwa

Baranowski P., Damaziak K., Jachimowicz J., Małachowski J., Niezgoda T.

Modelowanie Inżynierskie

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2011

|

T. 11, nr 42

19-26

PL

Jednym z podstawowych podzespołów zapewniających bezpieczne użytkowanie pojazdów jest układ hamulcowy. Niniejsza publikacja przedstawia analizę hamulca tarczowego, mającą na celu wyznaczenie parametrów jego pracy metodami numerycznymi. Stosując metodę elementów skończonych, przeprowadzono dynamiczną analizę pracy hamulca z uwzględnieniem generacji ciepła w wyniku pracy sił tarcia. Prezentowana praca jest etapem wstępnym badań, których efektem ma być przeprowadzenie numerycznej symulacji działania hamulca z uwzględnieniem procesu zużycia okładzin. Na podstawie uzyskanych wyników można stwierdzić, że zastosowane podejście umożliwia odwzorowanie termomechanicznych aspektów pracy hamulca, i wskazać jednocześnie duże wymagania związane z zasobami komputerowymi, niezbędnymi do wykonania tego typu symulacji.

EN

One of the key components ensuring safe use of vehicles is brake system. This publication presents an analysis of a disc brake aimed at the designation of its operating parameters with numerical methods. Dynamic analysis of the brake operation taking account of phenomenon of generation of heat by the work of friction forces was performed using finite element analysis. The presented paper is a preliminary stage of research, which is aimed at carrying out the numerical simulation of the brake including the process of lining wear. The results can be concluded that the approach enables the mapping of thermo-mechanical effects, but also indicate the high demands of computing resources, necessary to perform such simulations.

17

Numeryczny model hamulca tarczowego

Damaziak K., Jachimowicz J., Małachowski J.

Mechanik

|

2011

|

R. 84, nr 1

53-53

PL

Przedstawiono analizę numeryczną procesu hamowania na przykładzie samochodowego hamulca tarczowego. Opisano techniki wykorzystane przy budowie modelu MES hamulca. Szczególną uwagę poświęcono zjawiskom sprzężonym (cieplno-mechanicznym) występującym w procesie hamowania. Zaprezentowano przykładowe wyniki analiz i wskazano na typowe problemy związane z zastosowanym podejściem analitycznym.

EN

The paper presents numerical analysis of a braking process of a disk brake. Various FE techniques used in model generation process are described. Special attention was put on coupling of thermal and mechanical phenomena, taking place during brake process. Sample results are shown, together with indication of most significant problems appearing in presented approach.

18

Proposition for the method of determining the most strenuous piece of rivet seams in shell air panel working under the influence of tension field – calculation example

Jachimowicz J., Mańkowski J., Osiński J., Rumianek P.

Zeszyty Naukowe Instytutu Pojazdów / Politechnika Warszawska

|

2010

|

z. 5/81

53-63

EN

The article presents the results of the analysis of semi-monocoque air panel, exposed of tension field, to determine the most streunous part of the riveted joint. An assessment of the impact of the buckling sheet covering the load state and strain occurring in the surroundings of a single rivet. It has been shown the need for this type of analysis, especially in the design of structures on the sustainability of monitored with a tolerance of failure, in which the method is necessary to know the most vulnerable to the destruction of the structure parts.

PL

W artykule przedstawiono wyniki analiz półskorupowego panelu lotniczego, poddanego działaniu pola ciągnień, mające na celu określenie najbardziej wytężonego fragmentu połączenia nitowego. Dokonano oceny wpływu wyboczenia blach pokrycia na stan obciążeń i odkształceń występujących w otoczeniu pojedynczego nitu. Wykazano potrzebę stosowania tego rodzaju analiz, zwłaszcza przy projektowaniu konstrukcji na trwałość dozorowaną z tolerancją uszkodzenia, w której to metodzie konieczna jest znajomość najbardziej podatnych na zniszczenie fragmentów konstrukcji.

19

Zastosowanie modeli gradientowych w analizach połączeń zgrzewanych

Dalewski R., Jachimowicz J., Pietrzakowski M.

Przegląd Mechaniczny

|

2010

|

nr 7-8

36-44

20

Badanie stateczności powłoki walcowej pod wpływem statycznych i dynamicznych obciążeń ściskających

Miedzińska D., Jachimowicz J., Dziewulski P.

Przegląd Mechaniczny

|

2010

|

nr 7-8

15-21

PL

W artykule przedstawiono wyniki analiz numerycznych dla porównania zachowania się cienkościennych powłok walcowych wykonanych ze stali poddanych ściskającym obciążeniom statycznym i dynamicznym. Porównanie przeprowadzone również dla walców o różnych typach zaburzeń geometrii (imperfekcji). Dodatkowo wykonano analizę modalną buckling dla rozważanych typów walców. Analizę dynamiczną wykonano za pomocą oprogramowania LS Dyna, natomiast statyczną przy użyciu MSC Marc. W procesie dynamicznym przyjęto, że powłoka jest uderzana płytą sztywną o masie 5 kg, której nadawano prędkość 5, 10, 15 i 20 m/s. W analizie statycznej proces obciążania był realizowany przemieszczeniem płyty sztywnej lub odpowiednio przyłożonymi siłami węzłowymi. Porównano otrzymane wartości sił krytycznych oraz deformacje dla różnych typów analiz. Wykazano, iż analiza typu buckling daje zawyżone wartości sił krytycznych. Pokazano wpływ imperfekcji na wartości tych sił.

EN

Results of numerical analysis for comparison of behaviour of thin-walled shell structures made of steel subjected to compressive static and dynamic loads were presented. The comparison concerns cylinders with different types of imperfections. Buckling analysis for considered types of cylinders was performed. Dynamic analysis was made using LS Dyna, while static analysis using MSC Marc. For dynamic process assumed that the shell was struck by rigid plate with the mass 5 kg and velocity: 5, 10, 15 and 20 m/s. In static state load was realized by displacement of rigid plate or appropriately applied nodal forces. Critical forces values were compared as well as deformations for different types of analyses. It was shown that buckling analysis gives inflated values of critical forces. Influence of imperfections on critical forces value was determined.