Direct approach-based analysis of plates composed of functionally graded materials

Archive of Applied Mechanics

Volumn 78, Issue 10, 2008, Pages 775-794

  Altenbach, Holm ^a   Eremeyev, Victor A ^b  

^a MARTIN LUTHER UNIVERSITY HALLE WITTENBERG   (Germany)

^b SOUTHERN FEDERAL UNIVERSITY   (Russian Federation)

Author keywords

Direct approach; Effective stiffness; Functionally graded materials; Plate theories; Transverse shear stiffness

Indexed keywords

BEAMS AND GIRDERS; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; CRACK INITIATION; TECHNOLOGY;

BOUNDARY CONDITIONING; CLASSICAL PLATE THEORY; DIRECT APPROACH; EFFECTIVE STIFFNESS; GOVERNING EQUATIONS; INTEGRATION TECHNIQUES; KIRCHHOFF; MATE RIAL PROPERTIES; MATHEMATICAL APPROACHES; PLATE THEORIES; PLATE THEORY; POWER-SERIES EXPANSIONS; THICKNESS DIRECTION; THIN PLATES; TRANSVERSE SHEAR STIFFNESS;

FUNCTIONALLY GRADED MATERIALS;

EID: 50149100167     PISSN: 09391533     EISSN: 14320681     Source Type: Journal    
DOI: 10.1007/s00419-007-0192-3     Document Type: Article

References (33)

1. Abramowitz, M., Stegun, I.: (eds.) (1972). Handbook of Mathematical Functions. Dover, New York
2. Altenbach H. (1988). Eine direkt formulierte lineare Theorie für viskoelastische Platten und Schalen. Ingenieur Archiv 58: 215-228
3. Altenbach H. (2000). An alternative determination of transverse shear stiffnesses for sandwich and laminated plates. Int. J. Solids Struct. 37(25): 3503-3520
4. Altenbach H. (2000). On the determination of transverse shear stiffnesses of orthotropic plates. ZAMP 51: 629-649
5. Altenbach H. and Zhilin P. (1988). A general theory of elastic simple shells (in Russian). Uspekhi Mekhaniki 11(4): 107-148
6. Altenbach, H., Zhilin, P.A.: The theory of simple elastic shells. In: Kienzler, R., Altenbach, H., Ott, I. (eds.) Critical Review of the Theories of Plates and Shells and New Applications. Lect. Notes Appl. Comp. Mech, vol. 16, pp. 1-12. Springer, Berlin (2004)
7. Altenbach H., Altenbach J. and Naumenko K. (1998). Ebene Flächentragwerke. Grundlagen der Modellierung und Berechnung von Scheiben und Platten. Springer, Berlin
8. Altenbach H., Altenbach J. and Kissing W. (2004). Mechanics of Composite Structural Elements. Springer, Berlin
9. Ashby M.F., Evans A.G., Fleck N.A., Gibson L.J., Hutchinson J.W. and Wadley H.N.G. (2000). Metal Foams: A Design Guid. Butterworth-Heinemann, Boston
10. Banhart J. (2000). Manufacturing routes for metallic foams. J. Miner. 52(12): 22-27
11. Chróścielewski J., Makowski J. and Pietraszkiewicz W. (2004). Statics and dynamics of multifold shells. Non-linear theory and finite element method (in Polish). Wydawnictwo IPPT PAN, Warszawa
12. Gibson L.J. and Ashby M.F. (1997). Cellular Solids: Structure and Properties, 2nd edn. Cambridge Solid State Science Series. Cambridge University Press, Cambridge
13. Grigolyuk, E.I., Seleznev, I.T.: Nonclassical theories of vibration of beams, plates and shelles (in Russian). In: Itogi nauki i tekhniki, Mekhanika tverdogo deformiruemogo tela, vol. 5, VINITI, Moskva (1973)
14. Gupta N. and Ricci W. (2006). Comparison of compressive properties of layered syntactic foams having gradient in microballoon volume fraction and wall thickness. Mater. Sci. Eng. A 427: 331-342
15. El Hadek M.A. and Tippur H.V. (2003). Dynamic fracture parameters and constraint effects in functionally graded syntactic epoxy foams. Int. J. Solids struc. 40: 1885-1906
16. Kienzler R. (2002). On the consistent plate theories. Arch. Appl. Mech. 72: 229-247
17. Kienzler, R., Altenbach, H., Ott, I.: (eds.) Critical review of the theories of plates and shells, new applications. Lect. Notes Appl. Comp. Mech. vol. 16, Springer, Berlin (2004)
18. Kirchhoff G.R. (1850). Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. Crelles Journal für die reine und angewandte Mathematik 40: 51-88
19. Libai A. and Simmonds J.G. (1998). The Nonlinear Theory of Elastic Shells, 2nd edn. Cambridge University Press, Cambridge
20. Lurie A.I. (2005). Theory of Elasticity. Foundations of Engineering Mechanics. Springer, Berlin
21. Mindlin R.D. (1951). Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. Trans. ASME J. Appl. Mech. 18: 31-38
22. Naghdi, P.: The theory of plates and shells. In: Flügge, S. (ed.) Handbuch der Physik, vol. VIa/2, pp. 425-640. Springer, Heidelberg (1972)
23. Nye J.F. (2000). Physical Properties of Crystals. Oxford Science Publications, Clarendon, Oxford
24. Reissner E. (1944). On the theory of bending of elastic plates. J. Math. Phys. 23: 184-194
25. Reissner E. (1945). The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. 12(11): A69-A77
26. Reissner E. (1947). On bending of elastic plates. Q. Appl. Math. 5: 55-68
27. Reissner E. (1985). Reflection on the theory of elastic plates. Appl. Mech. Rev. 38(11): 1453-1464
28. Rothert, H.: Direkte Theorie von Linien- und Flächentragwerken bei viskoelastischen Werkstoffverhalten. Techn.-Wiss. Mitteilungen des Instituts für Konstruktiven Ingenieurbaus 73-2, Ruhr-Universität, Bochum (1973)
29. Stoer J. and Bulirsch R. (1980). Introduction to Numerical Analysis. Springer, New York
30. Timoshenko S.P. and Woinowsky-Krieger S. (1985). Theory of Plates and Shells. McGraw Hill, New York
31. Truesdell C. (1964). Die Entwicklung des Drallsatzes. ZAMM 44(4/5): 149-158
32. Zhilin P.A. (1976). Mechanics of deformable directed surfaces. Int. J. Solids Struc. 12: 635-648
33. Zhilin, P.A.: Applied mechanics. Foundations of the theory of shells (in Russian). St Petersburg State Polytechnical University (2007)