Consistent theories of isotropic and anisotropic plates

• Autorzy: Kienzler R. , Schneider P.

Warianty tytułu

PL

Spójne teorie izotropowych i anizotropowych płyt

• Języki publikacji: EN

Abstrakty

EN

In this paper, the uniform-approximation technique in combination with the pseudoreduction technique is applied in order to derive consistent theories for isotropic and anisotropic plates. The approach is used to assess and validate the plate theories already established in the literature. Further lines of research are indicated.

PL

W pracy omówiono metodę jednorodnej aproksymacji połączonej z techniką pseudo-redukcji zastosowaną do sformułowania spójnych teorii płyt izotropowych i anizotropowych. Zaprezentowaną metodologię wykorzystano do oceny i weryfikacji teorii już istniejących i dobrze znanych z literatury. Wskazano także dalsze kierunki badań.

Słowa kluczowe

EN

linear elasticity; consistent plate theories; uniform-approximation technique; pseudo-reduction technique

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2012
• Tom: Vol. 50 nr 3
• Strony: 755--768
• Opis fizyczny: Bibliogr. 25 poz., rys.

Twórcy

autor

Kienzler R.

autor

Schneider P.

• Bremen Institute of Mechanical Engineering (BIME), University of Bremen, Bremen, Germany,

Bibliografia

• 1. Altenbach H., Altenbach J., Naumenko K., 1998, Ebene Fl¨achentragwerke: Grundlagen der Berechnung von Scheiben und Platten, Springer, Berlin
• 2. Altenbach J., Altenbach H., Eremeyev V.A., 2010, On generalized Cosserat-type theories of plates and shells: a short review and bibliography, Archive of Applied Mechanics, 80, 73-92
• 3. Ambartsumyan S.A., 1970, Theory of Anisotropic Plates, Progress in Material Science Series II, Technonic, Stamford, Conn.
• 4. Bose D.K., Kienzler R., 2006, On material conservation laws for a consistent plate theory, Archive of Applied Mechanics, 75, 606-617
• 5. Goldenveizer, A.L., Kaplunov J.D., Nolde E.V., 1993, On Timoshenko-Reissner type theories of plates and shells, International Journal of Solids and Structures, 30, 675-694
• 6. Huber M.T., 1929, Probleme der Statik technisch wichtiger orthotroper Platten, Gebetner and Wolff, Warsaw
• 7. Kienzler R., 1982, Eine Erweiterung der klassischen Schalentheorie; der Einfluss von Dickenverzerrungen und Verw¨olbungen, Ingenieur Archiv, 52, 311-322; Extended version in: Phd-Thesis, Technische Hochschule Darmstadt, Darmstadt (1980)
• 8. Kienzler R., 2002, On consistent plate theories, Archive of Applied Mechanics, 72, 229-247
• 9. Kienzler R., 2004, On consistent second-order plate theories, [In:] Kienzler R., Altenbach H., Ott I. (Eds.), Theories of Plates and Shells. Critical Review and New Applications, Lecture Notes in Applied and Computational Mechanics, 16, Springer, Berlin, 85-96
• 10. Kienzler R., Altenbach H., Ott I. (Eds.), 2004, Theories of Plates and Shells; Critical Review and New Applications, Lecture Notes in Applied and Computational Mechanics, 16, Springer, Berlin
• 11. Koiter W.T., Simmonds J.G., 1973, Foundation in shell theories, [In:] Becker E., Mikhailov G.K. (Eds.), Theoretical and Applied Mechanics, Proc. 13th Int. Congr. Theor. Appl. Mech., 150-176
• 12. Kr¨atzig W.B., 1989, On the structure of consistent plate theories, [In:] Koiter W.T., Mikhailov G.K. (Eds.), Proc. 3rd IUTAM Symp. on Shell Theory, North-Holland, Amsterdam, 353-368
• 13. Lo K.H., Christensen R.M., Wu E.M., 1977, A higher-order theory of plate deformation, Part 1: Homogeneous plates, Journal of Applied Mechanics, 44, 663-668
• 14. Naghdi P.M., 1972, The theory of plates and shells, [In:] Fl¨ugge S. (Ed.), Handbuch der Physik, Springer, Berlin, VI, A2, 425-646
• 15. Reissner E., 1945, The effect of transverse shear deformation on the bending of elastic plates, Journal of Applied Mechanics, 12, A69-A77
• 16. Rodionova V.A., Titaev V.F, Chernykh K.F., 1996, Applied Theory of Anisotropic Plates and Shells, St. Petersburg University Press, St. Petersburg [in Russian]
• 17. Schneider P., 2010, Eine konsistente Plattentheorie zweiter Ordnung f¨ur monotropes Material, Diploma Thesis, University of Bremen, Bremen
• 18. Schneider P., Kienzler, R., 2011, An algorithm for the automatization of pseudo reductions of PDE systems arising from the uniform-approximation technique, [In:] Altenbach H., Eremeyev V.A. (Eds.), Shell-like Structures; Non-classical Theories and Applications, Advanced Structured Materials, 15, Springer, Berlin, 377-390
• 19. Schneider P., Kienzler, R., B¨ohm M., 2012, A consistent second-order plate theory for monotropic material, Zeitschrift f¨ur Angewandte Mathematik und Mechanik, submitted
• 20. Szabó I., 1987, Geschichte der mechanischen Prinzipien, Birkh¨auser, Basel
• 21. Timoshenko S.P., 1983, History of Strength of Materials, Dover, New York
• 22. Todhunter I., Pearson K., 1960, A History of the Theory of Elasticity and of the Strength of Materials, Dover, New York
• 23. Vekua I.N., 1982, Shell Theory: General Methods of Construction, Pitman, Boston
• 24. Wang C.M., Reddy J.N., Lee K.H., 2000, Shear Deformable Beams and Plates; Relationships with Classical Solutions, Elsevier, Amsterdam
• 25. Zhilin P.A., 1992, On the Poisson and Kirchhoff plate theories from the point of view of the modern plate theory, Izvesta Akademii Nauk Rossii, Mekhanica Averdogotela, Moscow, 3, 48-64 [in Russian]