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Stress distribution in an elastic layer resting on a Winkler foundation with an emptiness

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper deals with the plane problem of an elastic layer resting on a Winkler foundation with an emptiness. The stresses in the layer are caused by a given normal loading on its upper boundary plane. The mathematical formulation of the problem leads to a mixed boundary value problem and it is solved using Fourier transform methods and Fredholm integral equation of the second kind. The detailed analysis is derived analytically and numerically for an elliptic distribution of boundary loadings. The results for the normal displacement and the stresses on the lower boundary of the layer are presented in figures.
Rocznik
Strony
721--727
Opis fizyczny
Bibliogr. 20 poz., rys., wykr.
Twórcy
  • nstitute of Hydrogeology and Engineering Geology, Faculty of Geology, University of Warsaw, 93 Żwirki i Wigury Ave., 02-089 Warsaw, Poland
  • Faculty of Mechanical Engineering, Białystok University of Technology, 45 C Wiejska St., 15-351 Białystok, Poland
  • Faculty of Mechanical Engineering, Białystok University of Technology, 45 C Wiejska St., 15-351 Białystok, Poland
Bibliografia
  • [1] A. Birinci and R. Erdol, “A frictionless contact problem for two elastic layers supported by a Winkler foundation”, Structural Engineering and Mechanics, 15, 331‒344 (2003).
  • [2] J. Marzęda, V. Pauk, and M. Woźniak, “Contact of a rigid flat punch with a wedge supported by the Winkler foundation”, Journal of Theoretical and Applied Mechanics 39, 563‒575 (2001).
  • [3] J.P. Dempsey, Z.G. Zhao, and H. Li, “Axisymmetric indentation of an elastic layer supported by a Winkler foundation”, International Journal of Solids and Structures, 27, 73‒87 (1991).
  • [4] J.P. Dempsey, Z.G. Zhao, L. Minnetyan, and H.Li, “Plane contact of an elastic layer supported by a Winkler foundation”, Journal of Applied Mechanics, 57, 974‒980 (1991).
  • [5] M. Woźniak, A. Hummel, and V.J. Pauk, “Axisymmetric contact problems for an elastic layer resting on a rigid base with a Winkler type excavitation”, International Journal of Solids and Structures, 39, 4117‒4131 (2002).
  • [6] S.J. Matysiak and V.J. Pauk, “Edge crack in an elastic layer resting on Winkler foundation”, Engineering Fracture Mechanics 70, 2353‒2361 (2003).
  • [7] F.L. Liu, “Rectangular thick plates on Winkler foundation: differential quadrature element solution”, International Journal of Solids and Structures, 37, 1743‒1763 (2000).
  • [8] A. Karasin and G. Alitas, “An approximate solution for plates resting on Winkler foundation”, International Journal of Civil Engineering and Technology 5, 114‒124 (2014).
  • [9] H. Kobayashi and K. Sonoda, “Rectangular Midlin plates on elastic foundations”, International Journal of Mechanical Sciences, 31, 679‒692 (1989).
  • [10] Y. Kumar and R. Lai, “Vibrations of nonhomogenous orthotropic rectangular plates with bilinear thickness variation resting on Winkler foundation”, Meccanica, 47, 893‒915 (2012).
  • [11] A. Daloglu and C. Vallabhan, “Values of k for slab on Winkler foundation”, Journal of Geotechnical and Geoenvironmental Engineering, 126, 463‒471 (2000).
  • [12] S.Ch. Datta and R. Roy, “A critical review on idealization and modelling for interaction among soil-foundation structure system”, Computers and Structures, 80, 1579‒1594 (2002).
  • [13] A.P.S. Selvadurai, “Elastic Analysis of Soil-Foundation Interaction”, Developments in Geotechnical Engineering, Vol. 17, Elsevier, Amsterdam (1979).
  • [14] E. Tsudik, Analysis of Structures on Elastic Foundation, J. Ross Publ., Plantation, FL. (2013).
  • [15] I. Cömez, “Contact problem of a functionally graded layer resting on a Winkler foundation”, Acta Mechanica, 224, 2833‒2843 (2013).
  • [16] S.J. Matysiak and V.J. Pauk, “Some problems of stress distribution in a periodic stratified elastic stratum”, Journal of Theoretical and Applied Mechanics, 21, 795‒811 (1993).
  • [17] S.J. Matysiak and C. Woźniak, “Micromorphic effects in a modelling of periodic multilayered elastic composites”, International Journal of Engineering Science, 25, 549‒559 (1987).
  • [18] S.J. Matysiak and V.J. Pauk, “On crack problem in an elastic ponderable layer”, International Journal of Fracture, 96, 371‒380 (1999).
  • [19] I.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals, Series, and Products, Academic Press, New York, 1980.
  • [20] M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, Dover Publications, New York, 1965.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b1ae249f-2640-45bd-9f66-a4f934356736
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