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1
Content available Zastosowanie metody różnic skończonych w dynamice cienkich płyt mostowych poddanych działaniu obciążeń ruchomych
Zakęś F.
Czasopismo Inżynierii Lądowej, Środowiska i Architektury / Journal of Civil Engineering, Environment and Architecture
|
2017
|
z. 64, nr 2/I
7--16
PL
Praca przedstawia rozwiązanie zagadnienia drgań nietłumionych cienkiej prostokątnej płyty mostowej poddanej działaniu obciążenia nieinercyjnego poruszającego się ze stałą prędkością. Zastosowane zostały znane procedury numeryczne Metody Różnic Skończonych, mające na celu dyskretyzację przestrzenną obszaru płyty, a także algorytmy metody Newmarka przy dyskretyzacji czasu przejazdu obciążenia przez płytę. Podano formuły pozwalające zbudować i rozwiązać macierzowe równanie ruchu w tym budowę wektorów obciążeń dla przypadku ruchomej siły skupionej oraz ruchomego obciążenia rozłożonego. Praca uzupełniona jest przykładem numerycznym płyty mostowej podpartej 4 słupami obciążonej dwoma rodzajami obciążenia ruchomego.
EN
This paper presents solution of problem of undamped vibrations of thin rectangular bridge plate subjected to a non-inertial load moving with constant velocity. In order to spatial discretization of the plate numerical procedures have been applied as well as formulas of Newmark method applied to discretize time of the load movement. Formulas required to build and solve matrix equation of motion have been given as well as formulas for load vectors corresponding with two cases of moving load namely the case of moving constant force and the case of moving distributed load. A numerical example of a bridge plate with 4 point supports subjected to 2 types of moving load has been presented in order to show the efficiency of the method.
2
Content available remote Flexural stability analysis of stiffened plates using the finite element method
Panda S., Barik M.
Computer Assisted Methods in Engineering and Science
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2017
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Vol. 24, no. 3
181--198
EN
A four-noded stiffened plate element has been developed which has all the advantages and efficiency of an isoparametric element to model arbitrary shaped plates, but without the disadvantage of the shear-locking problem inherent in the isoparametric element. Another unique feature is that the arbitrary placement of the stiffener inside the plate element is without any restriction of its orientation. The boundary conditions have been incorporated in a general manner so as to accommodate the curved as well as the straight-edged boundaries. The element has been used for stability analysis of arbitrary shaped stiffened plates.
3
Content available remote Effect of post-weld heat treatment on thermal diffusivity in UNS S32304 duplex stainless steel welds
Betini E. G., Mucsi C. S., Luz T. S., Orlando M. T. D., Avettand-Fènoël M.-N., Rossi J. L.
Archives of Materials Science and Engineering
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2017
|
Vol. 88, nr 2
49--58
EN
Purpose: The thermal diffusivity variation of UNS S32304 duplex stainless steel welds was studied after pulsed GTA welding autogenous process without filler addition. This property was measured in the transverse section of thin plates after welding process and post-heat treated at 750°C for 8 h followed by air-cooling. Design/methodology/approach: The present work reports measurements of thermal diffusivity using the laser-flash method. The thermal cycles of welding were acquired during welding by means of k-type thermocouples in regions near the weld joint. The used shielding gas was pure argon and 98% argon plus 2% of nitrogen. The temperature profiles were obtained using a digital data acquisition system. Findings: It was found an increase of thermal diffusivity after welding process and a decrease of these values after the heat treatment regarding the solidified weld pool zone, irrespective of the welding protection atmosphere. The microstructure was characterized and an increase of austenite phase in the solidified and heat-affected zones was observed for post-weld heat-treated samples. Research limitations/implications: It suggests more investigation and new measurements about the influence of the shielding gas variation on thermal diffusivity in the heat-affected zone. Practical implications: The nuclear industry, especially, requests alloys with high thermal stability in pipes for power generation systems and safe transportation equipment’s for radioactive material. Thus, the duplex stainless steel grades have improved this stability over standard grades and potentially increase the upper service temperature reliability of the equipment. Originality/value: After heat treatment, the welded plate with 98%Ar plus 2%N2 as shielding gas presented a thermal diffusivity closer to the as received sample. By means of 2%-nitrogen addition in shielding gas during GTAW welding of duplex stainless steel may facilitate austenite phase reformation, and then promotes stability on the thermal diffusivity of duplex stainless steels alloys.
4
Content available Application of anisotropic thin plate theory for development of displacements for silicon <111> crystals plates in cylindrical systems
Javidinejad A.
International Journal of Applied Mechanics and Engineering
|
2016
|
Vol. 21, no. 4
879--890
EN
Silicon <111> crystal is one of the crystal orientations, which shows potential for application in micro device developments of pressure diaphragms for measurement purposes. To date, no theoretical basis has been examined to develop the deflections for computational analysis purposes [1]. This paper presents the development of the diaphragm deflections for Silicon <111> Crystal in Cylindrical coordinates system. The Silicon <111> crystal possesses transverse isotropic properties. Thus, an anisotropic thin plate theory is used here to develop the plate deflection. A numerical example is given to compare the theoretical results with Finite Element Analysis (FEA) results.
5
Content available remote Vibrations of point-supported rectangular thin plate subjected to a moving force
Zakęś F.
Engineering Transactions
|
2016
|
Vol. 64, iss. 4
409--415
EN
In this paper, the dynamic behaviour of a rectangular thin plate simply supported on all edges and point supported within its region is investigated. The problem is solved by replacing this type of structure with a simply supported plate subjected to a given moving load and redundant forces situated in positions of intermediate point supports. Redundant forces are obtained by solving Volterra integral equations of the first order, which are compatibility equations corresponding to each redundant. Solutions for a simply supported plate loaded with a moving point force and concentrated time-varying force are given. Difficulties of solving Volterra integral equations analytically are bypassed by applying a simple numerical procedure. Finally, a numerical example of a plate with two point supports is presented in order to show the effectiveness of the presented method.
6
Content available remote Sequential stochastic identification of elastic constants using Lamb waves and particle filters
Słoński M.
Computer Assisted Methods in Engineering and Science
|
2014
|
Vol. 21, no. 1
15--26
EN
Sequential stochastic identification of elastic parameters of thin aluminum plates using Lamb waves is proposed. The identification process is formulated as a Bayesian state estimation problem in which the elastic constants are the unknown state variables. The comparison of a sequence of numerical and pseudoexperimental fundamental dispersion curves is used for an inverse analysis based on particle filter to obtain sequentially the elastic constants. The proposed identification procedure is illustrated by numerical experiments in which the elastic parameters of an aluminum thin plate are estimated. The results show that the proposed approach is able to identify the unknown elastic constants sequentially and that this approach can be also useful for the quantification of uncertainty with respect to the identified parameters.
7
On the modelling of vibrations of functionally graded plates
Kaźmierczak M., Jędrysiak J.
Zeszyty Naukowe. Budownictwo / Politechnika Łódzka
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2012
|
Z. 64
61-68
EN
In this paper there are considered functionally graded plates. To describe vibrations of these plates and take into account the effect of the microstructure it is applied the tolerance method, cf. [10, 11]. There are formulated governing equations of three presented models: the tolerance model, the asymptotic model and the combined asymptotic-tolerance model.
PL
W pracy rozpatrywane są płyty o funkcyjnej gradacji własności. Aby opisać drgania tych płyt, wykorzystano technikę tolerancyjnego modelowania [10, 11]. Równania zostały wyprowadzone w ramach trzech zaproponowanych modeli: modelu tolerancyjnego, modelu asymptotycznego oraz modelu asymptotyczno-tolerancyjnego.
8
On a certain nonlinear model of thin periodic plates
Domagalski Ł., Gajdzicki M., Jędrysiak J.
Zeszyty Naukowe. Budownictwo / Politechnika Łódzka
|
2012
|
Z. 64
49-59
EN
The object under consideration are thin plates, which structure is periodic in planes parallel to the midplane. Plates of this kind consist of many small, repetitive elements, called periodicity cells, that can be treated as thin plates. The microstructure size is characterized by the diameter of the cell, which is called the microstructure parameter l. It is assumed that mechanical properties (bending and membrane stiffness tensors' components) of such plates are periodic, highly-oscillating, non-continuous functions. The main aim is to propose a mathematical model describing moderately large static deflections problem of considered plates, which is based on the tolerance modelling technique. A calculational example for a specific problem is included. The results are compared with results obtained within the linear model and with Finite Element Method.
PL
Rozważane są cienkie płyty o strukturze periodycznej w płaszczyznach równoległych do płaszczyzny środkowej. Płyty tego rodzaju składają się z wielu małych, powtarzalnych elementów, zwanych komórkami periodyczności, z których każda może być traktowana jak cienka płyta. Wielkość mikrostruktury jest charakteryzowana poprzez średnice (największy liniowy wymiar) komórki. Wymiar ten jest nazywany parametrem mikrostruktury i oznaczany przez /. Przyjęto, że własności mechaniczne płyty, reprezentowane przez składowe tensorów sztywności płytowych i tarczowych, są periodycznymi, nieciągłymi, silnie oscylującymi funkcjami. Głównym celem opracowania jest zaproponowanie matematycznego modelu opisującego zagadnienie umiarkowanie dużych ugięć rozważanych płyt, opartego na tzw. technice modelowania tolerancyjnego. Praca zawiera przykład obliczeniowy dla pewnego przypadku szczególnego. Dokonano porównania wyników uzyskanych w ramach proponowanego modelu nieliniowego, modelu liniowego oraz Metody Elementów Skończonych.
9
Dynamic modelling of thin plates made of longitudinally functionally graded material
Wirowski A.
Zeszyty Naukowe. Budownictwo / Politechnika Łódzka
|
2012
|
Z. 64
69-78
EN
Subject of this paper are thin plates with characteristic geometry: periodic in one direction and smoothly varying along another. The aim of the contribution is to formulate and investigate an averaged model describing the vibrations of this plate. Modelling procedure is based on the tolerance averaging technique. We are to analyze the plate in rectangular and polar coordinate systems.
PL
Przedmiotem pracy są płyty cienkie o określonej geometrii: periodyczne w jednym kierunku i wolnozmienne w drugim. Celem opracowania jest sformułowanie uśrednionego modelu opisującego drgania takiej płyty. Procedura modelowania jest oparta na technice tolerancyjnego uśrednienia. Analizowane płyty są w biegunowym i kartezjańskim układzie współrzędnych.
10
Content available remote Vibrations of Thin Plates Reinforced by a Periodic System of Stiffeners
Nagórko W.
Vibrations in Physical Systems
|
2004
|
Vol. 21
275--278
11
Zastosowanie metody elementów brzegowych w analizie statyki płyt cienkich
Guminiak M.
Zeszyty Naukowe. Budownictwo / Politechnika Śląska
|
2002
|
z. 95
223-232
PL
W pracy rozwiązuje się zadanie zginania płyty cienkiej przy zastosowaniu metody elementów brzegowych. Na brzegu płyty występują trzy zmienne statyczne i trzy geometryczne. W podanym sformułowaniu nie wprowadza się zastępczej siły poprzecznej na brzegu płyty oraz sił skupionych w narożach. W węźle elementu brzegowego występują dwie niezależne niewiadome. Uwzględnia się również występowanie podpór słupowych w obrębie płyty. Do zapisu całkowych równań brzegowych zastosowano podejście kolokacyjne z punktami kolokacji umieszczonymi na zewnątrz płyty. Pozwoliło to wyeliminować obliczanie całek osobliwych.
EN
The boundary element analysis of thin plates is presented in the paper. In this formulation there are considered three geometric and three static variables at the plate boundary. This approach avoids the development of Kirchhoff forces at plate comers and equivalent shear force at plate boundary. The present formulation is based upon two degrees-of-freedom per boundary node. The case of column supports is considered, too. The collocation version of boundary element method with constant element is adopted. To avoid the calculation of singular integrals, the source points are located slightly outside the plate boundary.
12
Badanie numeryczne wpływu imperfekcji technologicznych na obciążenia krytyczne i pracę zakrytyczną cienkich płyt i powłok
Gołoś K., Jachimowicz J., Ruszkowski P., Techmański T.
Systems : journal of transdisciplinary systems science
|
2002
|
Vol. 7, No. 1 sp.
225-234
EN
In this scientific description are introduced chosen kinds of initial technological imperfections which occur in thin board's coats and also in bent coats. Using the MSC.Nastran system, presented imperfections are described and their influence on a form of the stability's loss and an overcritical work of boards nad coats are analysed.
13
Content available remote Thin plate bending analysis using an indirect Trefftz collocation method
Tiago C. M., Leitao V. M. A., Vasarhelyi A.
Computer Assisted Mechanics and Engineering Sciences
|
2001
|
Vol. 8, No. 1
1--16
EN
In this work, the application of an indirect Trefftz collocation method to the analysis of bending of thin plates (Kirchhoff's theory) is described. The deflection field approximation is obtained with the use of a set of functions satisfying a priori the homogeneous part of the differential equation of the problem. Each of the approximating functions is derived from a known thick plate solution. The boundary conditions are imposed by means of continuous (integral) and discrete (collocation) least squares methods. Numerical examples are presented and the accuracy of the proposed technique is assessed.
14
Content available remote Asymptotic theory of dynamics of thin plates on the asymmetrical theory of elasticity
Sargsyan S.
Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika
|
1999
|
z. 52 [174]
345-350
EN
In the work it is constructed asymptotical theory of dynamics of thin plates on asymmetrical theory of elasticity. Two-dimensional applied theory of dynamics of thin plates, which is asymptotically substantiated, is created in the area of plate, on the basis ot integration of equations of asymmetrical theory of elasticity by asymtotic method.
15
Content available remote Analysis of rectangular thin plates and plate structures basing on the Vlasov's variational procedure
Altenbach J., Naumenko K., Naumenko V. K.
Computer Assisted Mechanics and Engineering Sciences
|
1998
|
Vol. 5, nr 2
115-128
EN
The solution procedure proposed by Vlasov based on the reduction of the basic two-dimensional boundary value problems into ordinary differential equations provides a good accuracy in the case of rectangular domains with small size ratios. The paper presents an extension of this method applied to rectangular Kirchhoffs plates in connection with the iterational scheme. The results are compared with analytical solutions available for rectangular plates with simplified boundary conditions and loading. The possibilities of application of the solutions for simple plate geometry to complex plate problems (e. g. complex geometry, boundary conditions) are discussed and illustrated by numerical examples.
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