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Application of simplified curved boundary elements to the plate analysis. Part 1

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Static analysis of Kirchhoff plate by the Boundary Element Method is presented in the paper. The Bettie theorem is used to derive the boundary integral equation. Simplified curved elements are introduced. Modified approach of boundary integral equation formulation is adopted in which there is no need to introduce the equivalent shear forces at the boundary and concentrated forces at the plate corners. The collocation version of boundary element method with singular and non-singular approach is presented.
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Bibliografia
  • [1] Burczyński T., The Boundary Element Method in Mechanics, Scientific - Technical Publishing House, Warszawa 1995 (in Polish).
  • [2] Wrobel L.C., Aliabadi M.H., The Boundary Element Methods in Engineering, McGraw-Hill College 2002.
  • [3] Bèzine G., Gamby D.A., A new integral equations formulation for plate bending problems, Advances in Boundary Element Method, Pentech Press, London 1978.
  • [4] Stern M., A general boundary integral formulation for the numerical solution of plate bending problems, International Journal of Solids and Structures 1978, 15, 769-782.
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  • [6] Okupniak B., Sygulski R., Non-singular BEM analysis of Reissner plates, CMM-2003 15th International Conference on Computer Methods in Mechanics, Gliwice/Wisła 2003, June 3-6, Short Papers, 265-266, [w:] CD-ROM, red.: T. Burczyński, P. Fedeliński, E. Majchrzak.
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  • [8] Altiero N.J., Sikarskie D.L., A boundary integral method applied to plates of arbitrary plane form, Computers and Structures 1978, 9, 163-168.
  • [9] Debbih M., Boundary element method versus finite element method for the stress analysis of plates in bending, MSc Thesis, Cranfield Institute of Technology, Bedford 1987.
  • [10] Debbih M., Boundary element stress analysis of thin and thick plates, PhD Thesis, Cranfield Institute of Technology, Bedford 1989.
  • [11] Beskos D.E., Dynamic analysis of plates by boundary elements, Applied Mechanics Review 1999, 26, 7, 213-236.
  • [12] Wen P.H., Aliabadi M.H., Young A., A boundary element method for dynamic plate bending problems, International Journal of Solids and Structures 2000, 37, 5177-5188.
  • [13] El-Zafrany A., Debbih M., Fadhil S., A modified Kirchhoff theory for boundary element bending analysis of thin plates, International Journal of Solids Structures 1994, 31, 21, 2885-2899.
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  • [15] Guminiak M., Okupniak B., Sygulski R., Analysis of plate bending by boundary element method, Proceedings of European Conference on Computational Mechanics ECCM-2001, June 26- 29, Cracow 2001, Poland, Book of Abstract 176-177.
  • [16] 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 2004.
  • [17] Rashed Y.F., A coupled BEM-flexibility force method for bending analysis of internally supported plates, International Journal of Numerical Method in Engineering 2002, 54, 1431-1457.
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bwmeta1.element.baztech-article-BPC6-0003-0029
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