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1
Content available remote Shear buckling of steel foam sandwich panel resting on Pasternak foundation
Nazarimofrad Ebrahim, Barang Mehdi
Mechanics and Mechanical Engineering
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2019
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Vol. 23, nr 1
192--197
EN
The objective of this paper is to assess the inplane shear buckling of a steel foam sandwich panel that relies on elastic Pasternak foundation. The panel is a combination of solid steel face sheets and foamed steel cores. Foamed steel, that is steel with internal voids, provides enhanced bending rigidity and energy dissipation, and also, the potential to reduce local buckling. The Classic plate theory is employed where their governing equations are solved by the Rayleigh-Ritz method. Uniformly distributed in-plane shear loads are applied to the two opposite edges of the panel and all the four edges of the panel are simply supported. Finally, the effects of the panel parameters, such as the existence of a Pasternak foundation, aspect ratios, and central fraction of the steel foam core, are presented. The results showed that the optimum central fraction of the steel foam core would be 65%, so that the maximum critical shear buckling load has taken place.
2
Content available Free Vibration Analysis of Mindlin Plates Resting on Pasternak Foundation Using Coupled Displacement Method
Rajesh K., Saheb K. M.
Archive of Mechanical Engineering
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2018
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Vol. LXV, nr 1
107--128
EN
The authors developed a simple and efficient method, called the Coupled Displacement method, to study the linear free vibration behavior of the moderately thick rectangular plates in which a single-term trigonometric/algebraic admissible displacement, such as total rotations, are assumed for one of the variables (in both X,Y directions), and the other displacement field, such as transverse displacement, is derived by making use of the coupling equations. The coupled displacement method makes the energy formulation to contain half the number of unknown independent coefficients in the case of a moderately thick plate, contrary to the conventional Rayleigh-Ritz method. The smaller number of undetermined coefficients significantly simplifies the vibration problem. The closed form expression in the form of fundamental frequency parameter is derived for all edges of simply supported moderately thick rectangular plate resting on Pasternak foundation. The results obtained by the present coupled displacement method are compared with existing open literature values wherever possible for various plate boundary conditions such as all edges simply supported, clamped and two opposite edges simply supported and clamped and the agreement found is good.
3
Content available Free Vibrations of Uniform Timoshenko Beams on Pasternak Foundation Using Coupled Displacement Field Method
Rajesh K., Saheb K. M.
Archive of Mechanical Engineering
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2017
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Vol. LXIV, nr 3
359--373
EN
Complex structures used in various engineering applications are made up of simple structural members like beams, plates and shells. The fundamental frequency is absolutely essential in determining the response of these structural elements subjected to the dynamic loads. However, for short beams, one has to consider the effect of shear deformation and rotary inertia in order to evaluate their fundamental linear frequencies. In this paper, the authors developed a Coupled Displacement Field method where the number of undetermined coefficients 2n existing in the classical Rayleigh-Ritz method are reduced to n, which significantly simplifies the procedure to obtain the analytical solution. This is accomplished by using a coupling equation derived from the static equilibrium of the shear flexible structural element. In this paper, the free vibration behaviour in terms of slenderness ratio and foundation parameters have been derived for the most practically used shear flexible uniform Timoshenko Hinged-Hinged, Clamped-Clamped beams resting on Pasternak foundation. The findings obtained by the present Coupled Displacement Field Method are compared with the existing literature wherever possible and the agreement is good.
4
Duże siły osiowe w belkach na dwuparamrtrowym podłożu o zmiennych współczynnikach
Ataman M., Szcześniak W.
Logistyka
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2014
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nr 6
1523-1528
PL
W pracy przeanalizowano sprężystą belkę Bernoulliego-Eulera o swobodnych końcach spoczywającą na dwuparametrowym, jednokierunkowym podłożu Pasternaka. Na belkę działa w środku rozpiętości siła skupiona lub równomiernie rozłożone obciążenie ciągłe. Dodatkowo belka jest obciążona dużą ściskającą siłą osiową. Belkę przeanalizowano przy różnych wartościach siły osiowej. W pierwszej części pracy rozważano podłoże o stałych współczynnikach, natomiast w drugiej części rozwiązano zadanie przy współczynnikach zmieniających się na długości belki. Równania równowagi belki rozwiązano bezpośrednio i numerycznie. Wyniki rozwiązania przedstawiono na rysunkach. W opracowaniu zamieszczono wykaz literatury dotyczącej podłoży i belek na podłożach jedno i wieloparametrowych o stałych i zmiennych współczynnikach. Wyniki opracowania mogą być wykorzystane przez projektantów fundamentów i ław fundamentowych oraz projektantów nawierzchni drogowych i kolejowych.
EN
In the paper the elastic Bernoulli-Euler beam of free ends resting on two-parameter, unidirectional Pasternak foundation is analyzed. Two cases of loading are considered: concentrated force applied to the middle point of the beam and uniformly distributed load. In addition, the beam is subject to large compressive axial force. The beam was analyzed at various values of axial force. In the first part of the paper foundation with constant coefficients was considered, while the second part of the paper is devoted to the foundation with coefficients changing along the beam. The equations of the beam equilibrium were solved directly and numerically. Results of solution are shown in the figures. The article presents a numerous items of literature concerning elastic foundations and beams resting on one or multi-parameter foundations with constant or variable coefficients.
5
Content available Buckling of heated temperature dependent FGM cylindrical shell surrounded by elastic medium
Sabzikar Boroujerdy M, Naj R, Kiani Y
Journal of Theoretical and Applied Mechanics
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2014
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Vol. 52 nr 4
869--881
EN
Based on the Donnell theory of shells combined with the von-Karman type of geometrical nonlinearity, three coupled equilibrium equations for a through-the-thickness functionally graded cylindrical shell embedded in a two parameter Pasternak elastic foundation are ob- tained. Equivalent properties of the shell are obtained based on the Voigt rule of mixture in terms of a power law volume fraction for the constituents. Properties of the constituents are considered to be temperature dependent. The temperature profile through the shell thick- ness is obtained by means of the central finite difference method. Linear prebuckling analysis is performed to obtain the prebuckling forces of the cylindrical shell. Stability equations are derived based on the well-known adjacent equilibrium criterion. Three coupled partial dif- ferential stability equations are solved with the aid of a hybrid Fourier-GDQ method. After validating the numerical results, some parametric studies are conducted to investigate the influence of various parameters, especially foundation interaction. It is shown that elastic foundation enhances the critical buckling temperature difference of the shell and violates the buckled pattern.
6
Content available remote Effects of hygrothermal conditions on cross-ply laminated plates resting on elastic foundations
Zenkour A. M., Allam M. N. M., Radwan A. F.
Archives of Civil and Mechanical Engineering
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2014
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Vol. 14, no. 1
144--159
EN
The influence of temperature and moisture on the hygrothermal behavior of laminated composite plates resting on elastic foundations is investigated using a refined plate theory. The material properties of the composite are affected by the variation of temperature and moisture. The present plate theory enables the trial and testing of different through-the-thickness transverse shear-deformation distributions and, among them, strain distributions that do not involve the undesirable implications of the transverse shear correction factors. The governing equations are derived based on the present theory, including hygrothermal effects and elastic foundation parameters. The effects of Winkler and Pasternak foundation parameters, temperature, moisture concentration, transverse shear deformation, plate aspect ratio, side-to-thickness ratio on deflections and stresses are investigated.
7
Stochastyczna dynamika belki na podłożu Pasternaka
Rystwej A.
Zeszyty Naukowe. Budownictwo / Politechnika Śląska
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2004
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z. 102
425-432
PL
W pracy rozpatruje się drgania belki nieskończenie długiej spoczywającej na podłożu Pasternaka obciążonej ciągiem sił skupionych poruszających się w jednym kierunku ze stałą prędkością. Przyjęto, że wartości sił, jak również ich rozmieszczenie na długości belki są zmiennymi losowymi. Podano rozwiązanie na kumulantę dla ogólnego i maksymalnego ugięcia belki.
EN
The paper presents an infinite beam resting on a Pasternak foundation is subject to vibration under a series of concentrated forces moving at a constant velocity. The force values and their spacing along the beam are assumed to be random variables. The solution for the n-th order cumulant of the general and maximum beam deflection is given.
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