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Simplified approach of free vibration analysis of plates supported in vicinity of the corners by BEM

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Języki publikacji
EN
Abstrakty
EN
Free vibration analysis of Kirchhoff plate by the Boundary Element Method is presented in the paper. The boundary integral equation are derived according to the Bettie theorem. The collocation version of BEM with non-singular approach with one and double collocation points is used. The constant type of element is introduced. Boundary suport at selected point is modelled as support in vicinity of point along single boundary element.
Rocznik
Strony
45--54
Opis fizyczny
Bibliogr. 28 poz., rys., tab.
Twórcy
autor
  • Institute of Structural Engineering, Poznan University of Technology, Poland
Bibliografia
  • [1] Nadai A., Uber die Biegung durchlaufender Platten und der rechteckigen Platte mit freien Radern, Zeitschritt fuer angewandte Mathematik und Mechanik 1922, 2.
  • [2] Iguchi S., Die Eigenschwingungen und Klangfiguren der vierseitig freien rechteckigen Platte, Ingenieur-Archiv 1953, 21, 5-6.
  • [3] Kączkowski Z., Orthotropic rectangular plates with free edges, Archives of Applied Mechanics 1955, 7(4), (in Polish).
  • [4] Timoshenko S., Woinowsky-Krieger S., Theory of plates and shells, Arkady, Warszawa 1962.
  • [5] Woźnica K., Vibration and bending of rectangular plates supported punctually (in Polish), PhD Thesis, Warsaw University of Technology, Faculty of Civil Engineering, 1978.
  • [6] Guminiak M., Sygulski R., The analysis of internally supported thin plates by the Boundary Element Method. Part 2 - Free vibration analysis, Foundations of Civil and Environmental Engineering, 9, Poznan University of Technology, 2007, 43-74.
  • [7] 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.
  • [8] Burczyński T., The Boundary Element Method in Mechanics, Technical-Scientific Publishing House, Warszawa 1995 (in Polish).
  • [9] Bezine G., Boundary integral formulation for plate flexure with arbitrary boundary condition, Mechanics Research Communications 1978, 5(4), 197-206.
  • [10] Stern M., A general boundary integral formulation for the numerical solution of plate bending problems, Int. J. Solids Structures 1979, 15, 169-782.
  • [11] Vander Weeen F., Application of the boundary integral equation method to Reissner's plate model, Int. J. Num. Meth. Engng. 1982, 18, 1-10.
  • [12] Litewka B., Sygulski R., Application of the fundamental solutions by Ganowicz in a static analysis of Reissner's plates by the boundary element method, Engineering Analysis with Boundary Elements 2010, 34, 1072-1081.
  • [13] Ganowicz R., Selected problems of theory of Reissner and three layer plates, Theoretical and Applied Mechanics 1966, 3-4, 55-95, (in Polish).
  • [14] Myślecki K., Approximate fundamental solutions of equilibrium equations for thin plates on an elastic foundation, Arch. Civ. Mech. Eng. 2004, 4, 1.
  • [15] Myślecki K., Metoda elementów brzegowych w statyce dźwigarów powierzchniowych, Oficyna Wydawnicza Politechniki Wrocławskiej, Wrocław, 2004.
  • [16] Myślecki K., Oleńkiewicz J., Analiza częstotliwości drgań własnych płyty cienkiej Metodą Elementów brzegowych, Problemy naukowo-badawcze budownictwa, Wydawnictwo Politechniki Białostockiej, Białystok 2007, 2, 511-516.
  • [17] Oleńkiewicz J., Analiza drgań wybranych dźwigarów powierzchniowych metodą elementów brzegowych, Rzoprawa doktorska, Politechnika Wrocławska, Instytut Inżynierii Lądowej, 2011.
  • [18] Bezine G., A boundary integral equation method for plate flexure with condition inside the domain, Int. J. Num. Meth. Engng. 1981, 15, 1647-1657.
  • [19] de Paiva J.B., Venturini W.S., Boundary element algorithm for building floor slab analysis, International Conference of BETECH 85, Adelaide, Australia, Brebbia C.A., Noye B.J. (eds.), Computational Mechanics Publications 1985, 201-209.
  • [20] de Paiva J.B., Venturini W.S., Analysis of building structures considering plate-beam-column interactions, International Conference of BETECH 87, Rio de Janeiro, Brazil, Brebbia C.A., Venturini W.S. (eds.), Computational Mechanics Publications 1987, 209-219.
  • [21] Hartmann F., Zotemantel R., The direct boundary element method in plate bending, Int. J. Num. Meth. Engng. 1986, 23, 2049-2069.
  • [22] Abdel-Akher A., Hartley G.A., Evaluation of boundary integrals for plate bending. Int. J. Num. Meth. Engng. 1989, 28, 75-93.
  • [23] 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.
  • [24] Providakis C.P., Toungelis G., A D/BEM approach to the transient response analysis of elastoplastic plates, Engineering Computations, 1998, 5(4), 501-511.
  • [25] Katsikadelis J.T., Synoriaka Stoiheia, Tomoz P: Analysi Plakon, EMP 2010, 2i Ekdosi.
  • [26] Guminiak M., Litewka B., Selected problems of thin and thick plates theory in therms of BEM. Theoretical foundations and numerical comparison, Foundations of Civil and Environmental Engineering, 15, Poznan University of Technology, 2012, 41-90.
  • [27] Katsikadelis J.T., The analog equation method. A powerful BEM-based solution technique for solving linear and nonlinear engineering problems, [in:] C.A. Brebbia (ed.), Boundary Element Method XVI : Computational Mechanics Publications, Southampton 1994, 167-182.
  • [28] Nerantzaki M.S., Katsikadelis J.T., An analog equation solution to dynamic analysis of plates with variable thickness, Engineering Analysis with Boundary Elements, 1996, 17(2 Special Issue), 145-152.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-caca13a7-505c-47b6-9294-e9f530bde256
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