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Free vibrations analysis of thin plates by the boundary element method in non-singular approach

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Języki publikacji
EN
Abstrakty
EN
A free vibration analysis of Kirchhoff plates is presented in the paper. Using proposed approach, there is no need to introduce Kirchhoff forces at the plate corner and equivalent shear forces at a plate boundary. Two unknown and independent variables are considered at the boundary element node. The Bettie theorem is used to derive the boundary integral equation. The collocation version of boundary element method with "constant" type of elements is presented. The source points are located slightly outside a plate boundary, hence the quasi-diagonal integrals of fundamental functions are non-singular.
Rocznik
Strony
75--90
Opis fizyczny
Bibliogr. 19 poz., rys., tab.
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autor
Bibliografia
  • [1] Brebbia C.A., Telles J.C.F., Wrobel L.C., Boundary Element Techniques, Theory and Applications in Engineering, Springer-Verlag, Berlin Heidelberg, New York, Tokyo 1984.
  • [2] Burczyński T., The Boundary Element Method in Mechanics, Technical-Scientific Publishing House, Warszawa 1995 (in Polish).
  • [3] Bèzine G., Boundary integral formulation for plate flexure with arbitrary boundary condition, Mechanics Research Communications 1978, 5(4), 197-206.
  • [4] Stern M., A general boundary integral formulation for the numerical solution of plate bending problems, Int. J. Solids Structures 1979, 15, 169-782.
  • [5] Vander Weeën F., Application of the boundary integral equation method to Reissner’s plate model, Int. J. Num. Meth. Engng. 1982, 18, 1-10.
  • [6] Okupniak B., Sygulski R., Non-singular BEM analysis of Reissner plates, Proceedings of 15th International Conference on Computer Methods in Mechanics CMM-2003, 3-6 June 2003, Gliwice/ Beskidy Mountains, Poland 265-266.
  • [7] Ganowicz R., Some questions of theory Reissner and three-layers plates, Theoretical and Applied Mechanics 1966 (in Polish).
  • [8] El-Zafrany A., Debbih M., Fadhil S., A modified Kirchhoff theory for boundary element bending analysis of thin plates, Int. J. Solids Structures 1994, 21(31), 2885-2889.
  • [9] Hartley G.A., Development of plate bending elements for frame analysis, Engineering Analysis with Boundary Element 1997, 17, 2, 93-104.
  • [10] Guminiak M., Application of the boundary element method in static analysis of thin plates (in Polish), 3nd Scientific Conference of PhD Students of Civil Engineering, Gliwice-Wisła, 21-22 November, 2002, Silesian University of Technology, Poland 223-232.
  • [11] Guminiak M., Thin plates analysis by the boundary element method using new formulation of a boundary condition (in Polish), PhD Thesis, Poznan University of Technology, Poznan, Poland 2004.
  • [12] Guminiak M., Sygulski R., Vibration of plate immersed in fluid by BEM, CMM-2003, 15th International Conference on Computer Methods in Mechanics, June 3-6, Gliwice-Wisła, Poland, 143-144, 2003.
  • [13] Katsikadelis J.T., Sapountzakis E.J., Zorba E.G., A BEM approach to static and dynamic analysis of plates, Computational Mechanics 1990, 7(1), 31-42.
  • [14] Providakis C.P., Toungelis G., A D/BEM approach to the transient response analysis of elastoplastic plates, Engineering Computations 1998, 5(4), 501-511.
  • [15] Shi G., Flexural vibration and buckling analysis of orthotropic plates by the boundary element method, International Journal of Solids Structures 1990, 12(26), 1351-1370.
  • [16] Rashed Y.F., A coupled BEM-flexibility force method for bending analysis of internally supported plates. Int. J. Num. Meth. Engng. 2002, 54, 1431-1457.
  • [17] Nowacki W., Dynamic of the structures, Arkady, Warszawa 1961 (in Polish).
  • [18] Gawroński W., Kruszewski J., Ostachowicz W., Tarnowski J., Wittbrodt E., The finie element metod in dynamic of the structures, Arkady, Warszawa, 1984 (in Polish).
  • [19] Liang C-C., Liao C-C., Tai Y-S., Lai W-H., The free vibration analysis of submerged cantilever plates, Ocean Engineering 2001, 28, 1225-1245.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPC6-0019-0012
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