A singular and non-singular BEM analysis of thin plates considering modified boundary conditions

• Autorzy: Guminiak M.
• Języki publikacji: EN

Abstrakty

EN

A static analysis of Kirchhoff plates using the boundary element method is presented in the paper. In this approach, physical boundary conditions are imposed. The Bettie theorem is used to derive the boundary integral equation. The collocation version of the boundary element method is presented. Typical and simplified, curved constant boundary elements are introduced.

Słowa kluczowe

EN

boundary element method; thin plates; fundamental solution; singular integrals

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Foundations of Civil and Environmental Engineering
• Rocznik: 2011
• Tom: No. 14
• Strony: 5--45
• Opis fizyczny: Bibliogr. 21 poz., rys., tab.

Twórcy

autor

Guminiak M.

• Institute of Structural Engineering, Piotrowo 5, 61-138 Poznan

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. ISBN 0-07-707769-5, 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, No. 15, pp. 769-782, 1978.
• 5. Vander Weeën F.: Application of the boundary integral equation method to Reissner’s plate model, International Journal for Numerical Methods in Engineering, 18, pp. 1-10, 1982.
• 6. 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, Vol. 32, Issue 12, pp. 1072-1081,2010.
• 7. Ganowicz R.: Choosen problems of Reissner and three layers plates, Applied and Theoretical Mechanics, 1966 (in Polish).
• 8. Altiero N. J., Sikarskie D. L.: A boundary integral method applied to plates of arbitrary plane form, Computers and Structures No. 9, pp. 163-168, 1978.
• 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, Vol. 26., No. 7, pp. 213-236, 1999.
• 12. Wen P. H., Aliabadi M. H., Young A.: A boundary element method for dynamic plate bending problems, International Journal of Solids and Structures, No. 37, pp. 5177-5188, 2000.
• 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, Vol. 31, No. 21, pp. 2885-2899, 1994.
• 14. Abdel-Akher A., Hartley G. A.: Domain integration for plate bending analysis by the boundary element method, Applied Numerical Method, Vol. 5, pp. 23-28, 1989.
• 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 2001, Cracow, Poland, Book of Abstract pp. 176-177.
• 16. Katsikadelis J.T.: ΣΥΝΟΡΙΑΚΑ ΣΤΟΙΧΕΙΑ (BOUNDARY ELEMENTS), Τομος II: Ανάλυση Πλακών, ΕΜΠ 2010, 2η Εκδοση.
• 17. Timoshenko S., Woinowsky-Krieger S.: Theory of plates and shells, Arkady Publishing House, Warszawa, 1962.
• 18. Schleicher C., Müller Κ.: Schiefe Eindfeldplatten, Transpress VEB Verlag für Verkehrswesen, Berlin, 1962.
• 19. 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.
• 20. Rashed Y. F.: A coupled BEM-flexibility force method for bending analysis of internally supported plates. International Journal of Numerical Method in Engineering, 54, pp. 1431-1457, 2002.
• 21. Guminiak M., Sumelka W.: The free vibrations analysis of plates resting on continuous internal supports by the Boundary Element Method, Foundation of Civil and Environmental Engineering, No. 10, pp. 69-97, 2007.