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1

An efficient iteration procedure for form finding of slack cables under concentrated forces

Orynyak Igor, Guarracino Federico, Modano Mariano, Mazuryk Roman

Archives of Civil Engineering

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2022

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Vol. 68, nr 2

645--663

EN

The goal of paper is the development and demonstration of efficiency of algorithm for form finding of a slack cable notwithstanding of the initial position chosen. This algorithm is based on product of two sets of coefficients, which restrict the rate of looking for cable geometry changes at each iteration. The first set restricts the maximum allowable change of absolute values of positions, angles and axial forces. The second set takes into account whether the process is the converging one (the signs of maximal change of parameters remain the same), so that it increases the allowable changes; or it is a diverging one, so that these changes are discarded. The proposed procedure is applied to two different methods of simple slack cable calculation under a number of concentrated forces. The first one is a typical finite element method, with the cable considered as consisting of number of straight elements, with unknown positions of their ends, and it is essentially an absolute coordinate method. The second method is a typical Irvine’s like analytical solution, which presents only two unknowns at the initial point of the cable; due to the peculiarity of implementation it is named here a shooting method. Convergence process is investigated for both solutions for arbitrary chosen, even very illogical initial positions for the ACM, and for angle and force at the left end for SM as well. Even if both methods provide the same correct convergent results, it is found that the ACM requires a much lower number of iterations.

2

Research of maximum stresses zones in circular perforated plates made of S235JR steel loaded with concentrated force

Konieczny Mateusz, Achtelik Henryk, Gasiak Grzegorz

Inżynieria Materiałowa

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2019

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Vol. 40, nr 2

53--60

EN

The paper proposes a numerical approach to determining the internal forces in a circular perforated plate loaded with concentrated force Pi applied in the geometric centre of the plate. The finite element method program Femap was used for numerical calculations. The test plate with diameter D = 300 mm has holes in ten circles. The plate made of S235JR steel has holes with diameter d1 = 3.5 mm on the first inner circle, and holes on the tenth outside circle have a diameter d10 = 20.5 mm. The plate of the above geometry was simply supported and loaded with different values of concentrated force. By means of numerical calculations using the finite element method, the coordinates of concentration zones of reduced stress in the perforated plate were determined. These zones were located on the plate bridges between perforation holes. The most hazardous place in the analysed perforated plate is associated with the 8 zone with the hole radius d3 = 5.0 mm at the circle radius R3 = 33.0 mm, where the highest stress concentration occurs. In this zone, the reduced stress is σred max = 217.20 MPa (point with the coordinates x, y, z [mm], i.e. P2[5.2; 30.6; 4.5]). The results of numerical calculations were verified with experimental results. The differences between the results of numerical calculations of the state of stress and those obtained experimentally did not exceed 10%.

PL

Współczesne konstrukcje inżynierskie charakteryzuje obniżenie współczynnika bezpieczeństwa, dlatego obliczenia wytrzymałości, sztywności i stateczności cienkościennych elementów konstrukcji nabierają coraz większego znaczenia we wszystkich gałęziach techniki, a szczególnie takich jak inżynieria chemiczna. Istnieje wiele zastosowań płyt perforowanych, np. w zbiornikach ciśnieniowych, aparaturze chemicznej (ściany sitowe wymienników ciepła), rafineriach ropy naftowej, budowie samolotów i statków kosmicznych, jednostkach powietrznych, robotach, kontenerach transportowych, taśmociągach skrzynkowych lub jako elementy przesiewaczy materiałów sypkich, które mogą być poddane obciążeniu zmieniającemu się w czasie. Tego typu dźwigary (płyty perforowane) mogą również pełnić rolę płyt montażowych, w których wykonano otwory z różnych względów eksploatacyjnych. Celem pracy jest lokalizacja stref, w których występują maksymalne naprężenia w okrągłej osiowosymetrycznej płycie perforowanej swobodnie podpartej i obciążonej siłą skupioną Pi przyłożoną w środku geometrycznym płyty. Badania obszarów koncentracji naprężeń wykonano numerycznie metodą elementów skończonych.

3

Surface Green’s functions in finite plane elastostatics of harmonic materials

Wang X., Schiavone P.

Archives of Mechanics

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2018

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Vol. 70, nr 2

151--159

EN

The closed-form representations of surface Green’s functions corresponding to the action of a concentrated force applied at the boundary of a region occupied by a particular class of compressible hyperelastic materials of harmonic type, has been derived. In our analysis, we consider both a bounded region in the form of a circular disk and an unbounded region with either an elliptical hole or a parabolic boundary.

4

Numeryczna i doświadczalna analiza naprężeń w kołowych perforowanych płytach swobodnie podpartych obciążonych centralnie siłą skupioną

Ledwoń W.

Logistyka

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2015

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nr 4

9385--9390, CD3

PL

Przedmiotem pracy jest przeprowadzenie doświadczalnej weryfikacji wartości naprężeń w płycie perforowanej obciążonej centralnie siłą skupioną uzyskanych metodą elementów skończonych. Przeprowadzone badania wykazały, że doświadczalna weryfikacja stanu naprężenia w płycie perforowanej w sposób dostateczny potwierdziła wartość naprężeń obliczonych metodą elementów skończonych, maksymalna różnica w wartościach naprężeń redukowanych obliczonych numerycznie i wyznaczonych doświadczalnie nie przekracza 24,8%, wartości naprężeń redukowanych obliczonych numerycznie są zawyżone w stosunku do wartości wyznaczonych doświadczalnie. Sytuacja taka jest bezpieczna dla pracy płyty perforowanej.

EN

The subject of the work is to carry out experimental verification of stresses in the plate perforated centrally loaded with a concentrated force generated by finite element method. The study showed that the experimental verification of the state of stress in the plate perforated in a manner sufficient affirmed the value calculated stress finite element method, the maximum difference in the values of the stress by reduction calculated numerically and experimentally determined does not exceed 24.8%, the stress values calculated numerically reducible are overpriced in comparison the values determined experimentally. Such a situation is safe to run the perforated plate.

5

Numeryczna analiza naprężenia kołowych płyt perforowanych obciążonych siłą skupioną

Ledwoń W.

Logistyka

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2015

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nr 4

9391--9396, CD3

PL

Przedmiotem pracy jest numeryczna analiza stanu naprężenia w swobodnie podpartych kołowych płytach obciążonych centralnie siłą skupioną za pomocą metody elementów skończonych. Wykazano, że metoda elementów skończonych może być bardzo pożyteczna i efektywna przy projektowaniu płyt perforowanych, wykazano, że płyty perforowane o różnej średnicy otworów obciążone centralnie siłą skupioną zawierają obszary o znacznej koncentracji naprężń, tj. w okolicy przyłożenia siły oraz na brzegach perforacji, stosując metody numeryczne inżynier ma możliwość przeanalizować topografię rozkładu naprężeń w płycie perforowanej, szczególnie na brzegach otworów, czego nie można uzyskać metodami analitycznymi, uzyskane mapy naprężeń umożliwiają wykrycie obszarów niebezpiecznych w płytach perforowanych.

EN

The subject of the work is a numerical analysis of stresses in simply supported circular plates loaded centrally concentrated force using the finite element method. It has been shown that the finite element method can be very useful and effective in the design of the perforated plates, it was demonstrated that the perforated plates of different diameter hole centrally loaded with concentrated force comprise areas of significant stress concentration, ie. In the area of application of force and on the edges of the perforations by methods numerical engineer is able to analyze the topography of the distribution of stresses in the plate perforated, especially on the edges of the holes, which can not be obtained by analytical methods, the resulting maps can detect stress in dangerous areas of perforated plates.

6

Modelowanie komputerowe konstrukcji w budownictwie transportowym

Szczecina M.

Logistyka

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2014

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nr 6

10232--10237

PL

W pracy przedstawiono zagadnienia związane z komputerowym modelowaniem konstrukcji poddanych działaniu obciążeniami skupionymi oraz prawidłową interpretacją uzyskanych wyników. Na przykładzie płyty betonowej obciążonej siłą skupioną pokazano wyniki obliczeń teoretycznych oraz uzyskanych komputerowo w metodzie elementów skończonych. Przeprowadzono dyskusję obydwu rozwiązań oraz zaproponowano rozwiązanie problemu gwałtownego wzrostu momentów zginających w pobliżu siły skupionej.

XX

In the paper there are presented some issues related to the computer modeling of structures under concentrated loads and the correct interpretation of gained results. As an example, a concrete slab under concentrated load is calculated and the theoretical and finie element method calculations are presented. Both solutions are discussed and it's proposed a solution to the problem of the rapid growth of bending moments near the concentrated force.

7

Response due to concentrated force in micropolar elastic solid with voids

Singh R., Singh K.

International Journal of Applied Mechanics and Engineering

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2014

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Vol. 19, no. 4

755--769

EN

The eigen value approach, following Laplace and Fourier transforms has been employed to find the general solution of the field equation in a micropolar elastic solid with voids for the plane strain problem. An application of an infinite space with impulsive force has been taken to illustrate the utility of the approach. The integral transformations have been inverted by using a numerical inversion technique to get result in physical domain. The result in the form of normal displacement, volume fraction, normal force stress, tangential force stress and tangential couple stress components has been obtained numerically and illustrated graphically to depict the effect of micropolarity and voids.

8

Analiza numeryczna stanu naprężenia i ugięcia płyt perforowanych obciążonych siłą skupioną

Gasiak G., Ledwoń W.

Górnictwo Odkrywkowe

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2014

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R. 55, nr 4-5

250--253

PL

Przedmiotem artykułu jest numeryczna analiza stanu naprężenia i ugięcia w utwierdzonych oraz swobodnie podpartych, perforowanych płytach prostokątnych obciążonych centralnie siłą skupioną. Obliczenia prowadzono metodą elementów skończonych. Uzyskano rozkłady naprężeń wokół otworów na całej powierzchni płyty perforowanej. Wyniki obliczeń numerycznych w przypadku płyty utwierdzonej na brzegach porównano z rezultatami uzyskanymi dla identycznej płyty swobodnie podpartej.

EN

The work is the numerical analysis of the state of stress and deflection in restrained and simply supported perforated rectangular plates loaded centrally concentrated force. Calculations were carried out by finite element method. Obtained stress distribution around the holes on the entire surface of the perforated plate. The results of numerical calculations for the plate clamped at the edges compared. Results obtained for identical plate simply supported.

9

Response due to mechanical source in second axisymmetric problem of micropolar elastic medium

Singh R.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 4

1249--1261

EN

The second axisymmetric problem in a micropolar elastic medium has been investigated by employing an eigen value approach after applying the Laplace and the Hankel transforms. An example of infinite space with concentrated force at the origin has been presented to illustrate the application of the approach. The integral transforms have been inversed by using a numerical technique to obtain the components of microrotation, displacement, force stress and couple stress in the physical domain. The results for these quantities are given and illustratred graphically.

10

Eigen value approach in micropolar elastic medium with voids

Singh R., Singh K.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 2

521--536

EN

The eigen value approach, following the Laplace and Hankel transformation has been employed to find a general solution of the field equations in a micropolar elastic medium with voids for an axisymmetric problem. An infinite space with the mechanical source has been applied to illustrate the utility of the approach. The integral transformations has been inverted by using a numerical inversion technique to get the result in physical domain. The results in the form of normal displacement, volume fraction, normal force stress, tangential force stress and tangential couple stress components have been obtained numerically and illustrated graphically.

11

Interactions due to mechanical sources in microstretch viscoelastic solid

Singh R., Kumar R.

International Journal of Applied Mechanics and Engineering

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2008

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Vol. 13, no 3

781-796

EN

The eigen value approach, following Laplace and Fourier transforms, has been employed to find the general solution to the field equations in a microstretch viscoelastic medium for the plane strain problem. An application of an infinite space with an impulsive normal point force and influence function has been taken to illustrate the utility of the approach. The integral transforms have been inverted by using a numerical inversion technique to get the results in the physical domain. The results in the form of normal displacement, normal force stress, tangential force stress, tangential couple stress and microstress components have been obtained numerically and illustrated graphically to depict the effects of stretch and viscosity. Special cases of a microstretch elastic solid and micropolar elastic solid have also been deduced.

12

Deformation due to inclined load in monoclinic thermoelastic material

Kumar R., Rani L.

International Journal of Applied Mechanics and Engineering

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2008

|

Vol. 13, no 4

923-938

EN

The two-dimensional deformation of homogeneous, thermally conducting monoclinic material as a result of inclined line load is investigated by applying the fourier transform. the inclined load is assumed to be a linear combination of a normal load and a tangential load. the displacements, stresses and temperature distribution so obtained in the physical domain are computed numerically and illustrated graphically. the variations of these quantities have been depicted graphically for a zinc crystal-like material in the coupled thermoelasticity (ct) and uncoupled thermoelasticity (UCT) for an insulated boundary.

13

Anti-plane strain problem of micropolar viscoelastic medium

Kumar R., Singh R.

International Journal of Applied Mechanics and Engineering

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2008

|

Vol. 13, no 1

175-191

EN

The eigen value approach, following Laplace and Fourier transforms, has been employed to find the general solution to the field equation in a micropolar viscoelasitc medium for the anti- plane strain problem. An infinite space with concentrated force at the origin has been applied to illustrate the application of the approach. The integral transforms have been inverted by using a numerical inversion technique to get the results in the physical domain. The results in the form of normal microrotation, tangential displacement, tangential force stress and normal couple stress components have been obtained numerically and illustrated graphically to depict the effects of viscosity. A particular case of a micropolar elastic solid has also been deduced.

14

Deformation due to moving loads in thermoelastic body with voids

Kumar R., Rani L.

International Journal of Applied Mechanics and Engineering

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2006

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Vol. 11, no 1

37-59

EN

The voids effect of loads which are moving at a constant velocity along one of the coordinate axis in a generalized thermoelastic half-space is studied. The analytical expressions of the displacements, stresses, temperature distribution and change in the volume fraction field for two different theories, i.e., Lord-Shulman (L-S), Green-Lindsay (G-L) are obtained by the use of the Fourier transform technique. The integral transform has been inverted by using a numerical technique and numerical results are illustrated graphically for a magnesium crystal-like material for the insulated boundary and temperature gradient boundary.

15

Elastodynamics of an axisymmetric problem in microstretch viscoelastic solid

Kumar R., Singh R.

International Journal of Applied Mechanics and Engineering

|

2005

|

Vol. 10, no 2

227-244

EN

An eigen value approach, following Laplace and Hankel transforms, has been employed to find the general solution to the field equations in a microstretch viscoelastic medium for an axisymmetric problem. An application of an infinite space with a concentrated force at the origin has been presented to illustrate the application of the approach. The integral transforms have been inverted by using a numerical inversion technique to get the results in the physical domain. The results in the form of normal displacement, normal force stress, tangential force stress, tangential couple stress and microstress components have been obtained numerically and illustrated graphically to depict the effects of stretch and viscosity. Special cases of microstretch elastic solid and micropolar elastic solid have also been deduced.

16

Deformation due to inclined load in thermoelastic half-space with voids

Kumar R., Rani L.

Archives of Mechanics

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2005

|

Vol. 57, nr 1

7-24

EN

The two-dimensional deformation of homogeneous, isotropic, thermoelastic half-space with voids as a result of inclined line load is investigated by applying the Laplace and Fourier transforms. The inclined load is assumed to be a linear combination of a normal load and a tangential load. The displacements, stresses, temperature distribution and change in volume fraction field so obtained in the physical domain are computed numerically. The variations of these quantities have been depicted graphically in the Lord-Shulman (L-S) theory and Green-Lindsay (G-L) theory for an insulated boundary.

17

Antiplane problems for anisotropic layered media with thin elastic inclusions under concentrated forces and screw dislocations

Shevchuk S., Sulym G.

Journal of Theoretical and Applied Mechanics

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1999

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nr 1

47-63

EN

The antiplane problem of elasticity theory for a layered anisotropic medium containing the plane ribbon inhomogenities is solved using the jump function method. The external load is determined by the boundary conditions, concentrated forces and screw dislocations inside layers. The inclusions are modelled by jumps of the stress and displacement vectors on the middle surfaces. Using the Fourier integral transform we obtain the relation between the stress tensor and displacement vector components and the external load is unknown functions of jumps. Taking into account the conditions interaction of between thin inclusion and anisotropic enviroment, the problem is reduced to a system of singular integral equations in the functions of jumps. In a general case the last is solved by means the collocation method. Some example is considered to illustate the method.

PL

W pracy rozwiązano metodą funkcji skoków antypłaskie zagadnienie sprężystości dla pliku anizotropowych warstw, w których są cienkie laminarne inkluzje. Zadane są naprężenia lub przemiszczenia na granice ośrodka, działanie skupionych sił i dyslokacji śrubowych. Inkluzje są modelowane przez skoki wektorów naprężeń i przemiszczeń na powierzchniach środkowych. Przez zastosowanie wykładniczej transformacji całkowitej Fouriera, otrzymujemy zależność współrzędnych tensora naprężeń i pochodnych wektora przemieszczeń od obciążenia zewnętrznego i poszukiwanych funkcji skoków. Z uwzględnieniem warunków oddziaływania cienkiej inkluzji ze środowiskiem anizotropowym zagadnienie jest sprowadzane do układu równań całkowych osobliwych typu Cauchy. W ogólnym przypadku ten układ jest rozwiązany metodą kolokacji. Metodę ilustrują obliczenia dla konkretnego zagadnienia.