Beams and plates on elastic foundations: a review

Wang, Y H; Tham, L.G.; Cheung, Y.K.

doi:10.1002/pse.202

Cited by 170 publications

(76 citation statements)

References 87 publications

(101 reference statements)

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“…Amongst the prevailing models, the most diffused one considers the train vehicle as a single load traveling at constant velocity on a beam supported by an elastic foundation (see Kerr [13]). Comprehensive literature reviews about the problem of moving loads acting on beams may be found in Beskou and Theodorakopoulos [2], Frýba [11], Kerr [13] and Wang et al [20].…”

Section: Introductionmentioning

confidence: 99%

Numerical Dynamic Analysis of Beams on Nonlinear Elastic Foundations Under Harmonic Moving Load

Froio¹,

Moioli²,

Rizzi³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Section: Introductionmentioning

confidence: 99%

Numerical Dynamic Analysis of Beams on Nonlinear Elastic Foundations Under Harmonic Moving Load

Froio¹,

Moioli²,

Rizzi³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…Following a different approach, Cheung and Nag (1968;Wang et al, 2005) substituted piecewise constant tractions into Equation 7a and 7b and directly used those equations to obtain horizontal and vertical displacements of the substrate boundary, respectively. Such an approach assumes the presence of a finite number of equally spaced links between the foundation beam and the substrate.…”

Section: Finite Element Modelmentioning

confidence: 99%

“…However, in order to ensure null displacements at the boundaries, the substrate mesh must be extended far away from the loaded area, often involving a huge number of FEs and a discouraging computional effort. To improve the numerical efficiency, infinite elements were proposed (Wang et al, 2005). The use, in the FE Method (FEM), of classical beam models for the foundation and of two-dimensional FEs for the soil makes to lose the continuity of rotations at the substrate boundary.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Analysis of RC Box Culverts Resting on a Linear Elastic Soil

Baraldi¹,

Minghini²,

Tezzon³

et al. 2018

International Journal of Structural Glass and Advanced Material

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In the analyses presented, the soil-structure interaction is accounted for by means of a FE-BIE approach, in which the structure is modelled with displacement-based beam finite elements, whereas the boundary between structure and substrate is described in terms of surface tractions by means of a boundary integral equation incorporating a suitable Green's function. This mixed formulation ensures full continuity between structure and substrate in terms of displacements and rotations. To take account of structural nonlinearities, potential plastic hinges are defined at the end sections of the beam elements in the form of semi-rigid connections characterized by a rigidplastic moment-rotation relationship. The incremental analyses carried out emphasize the effectiveness of the model in reproducing collapse mechanisms and stiffness loss of the structure for increasing loads. Moreover, the adopted formulation is able to capture both interfacial shear tractions and vertical normal tractions which develop along the substrate boundary under a variety of loading conditions.

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“…For example, the review [1], devoted to this subject matter, considers the items of elastic foundations development models, as well as various approaches to analytical and numerical investigation of beams and plates with elastic foundations interaction. Reference [2] studies free and forced oscillations of a circular plate, the plate resting on Winkler foundation.…”

Section: Introductionmentioning

confidence: 99%

Hydroelastic Oscillations of a Circular Plate, Resting on Winkler Foundation

Kondratov

Mogilevich

Popov

et al. 2018

J. Phys.: Conf. Ser.

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Abstract. The forced hydroelastic oscillations of a circular plate resting on elastic foundation are investigated. The oscillations are caused by a stamp vibration under interaction with a plate through a thin layer of viscous incompressible liquid. The axis-symmetric problem for the regime of the steady-state harmonic oscillations is considered. On the basis of hydroelasticity problem solution the laws of plate deflection and pressure in the liquid are found. The functions of the amplitudes deflection distribution and liquid pressure along the plate are constructed. The presented mathematical model provides for investigating viscous liquid layer interaction dynamics with a circular plate resting on an elastic foundation. The above-mentioned model makes it possible to define the plate oscillations resonance frequencies and the corresponding amplitudes of deflection and liquid pressure, as well. Keywords -circular plate; hydroelastic oscillations; vibration stamp; viscous liquid; Winkler foundation IntroductionThe investigations of the plates and supporting elastic foundations interaction are of theoretical, as well as of practical interest. For example, the review [1], devoted to this subject matter, considers the items of elastic foundations development models, as well as various approaches to analytical and numerical investigation of beams and plates with elastic foundations interaction. Reference [2] studies free and forced oscillations of a circular plate, the plate resting on Winkler foundation. The investigation is carried out in axis-symmetric setting for the cases of a simply supported edge and a clamped one. Reference [3] studies stability and oscillations of circular polar orthotropic plates of variable thickness resting on Winkler foundation. The cases of the simply supported and clamped edge of the plates are considered. Reference [4] deals with investigation of oscillations of a thin circular plate with elastic fixation along the contour, the plate resting on Winkler elastic foundation. Reference [5] studies free oscillations of thin circular plate on Winkler foundation. The axis-symmetric problem under the condition of foundation rigidity change in radial direction is investigated in the above-mentioned reference. References [6,7] consider oscillations and stability of multi-layered circular plates on elastic foundation under the impact of local and distributed loadings of various nature. The Winkler and Pasternak models are used for foundation reactions modelling. On the other hand, the investigations of hydroelastic interaction of circular plates with an ideal liquid are of

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Beams and plates on elastic foundations: a review

Cited by 170 publications

References 87 publications

Numerical Dynamic Analysis of Beams on Nonlinear Elastic Foundations Under Harmonic Moving Load

Numerical Dynamic Analysis of Beams on Nonlinear Elastic Foundations Under Harmonic Moving Load

Nonlinear Analysis of RC Box Culverts Resting on a Linear Elastic Soil

Hydroelastic Oscillations of a Circular Plate, Resting on Winkler Foundation

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