On the bending of viscoelastic plates made of polymer foams

Acta Mechanica

Volumn 204, Issue 3-4, 2009, Pages 137-154

  Altenbach, Holm ^a   Eremeyev, Victor A ^b  

^a MARTIN LUTHER UNIVERSITY HALLE WITTENBERG   (Germany)

^b SOUTHERN FEDERAL UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

DEFORMABLE SURFACES; DIRECT APPROACHES; KIRCHHOFF; MATERIAL PROPERTIES; PLATE THEORIES; POLYMER FOAMS; STIFFNESS PARAMETERS; THICKNESS DIRECTIONS; TWO-DIMENSIONAL EQUATIONS; TYPE THEORIES; VISCO-ELASTIC MATERIALS; VISCOELASTIC BEHAVIORS; VISCOELASTIC PLATES;

BEAMS AND GIRDERS; FUNCTIONAL POLYMERS; PLATES (STRUCTURAL COMPONENTS); STRUCTURAL ANALYSIS; TWO DIMENSIONAL;

FUNCTIONALLY GRADED MATERIALS;

EID: 67349153055     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00707-008-0053-3     Document Type: Article

References (39)

1. H. Altenbach P. Zhilin 1988 A general theory of elastic simple shells (in Russian) Usp. Mek. 11 107 14
2. H. Altenbach 1988 Eine direkt formulierte lineare Theorie für viskoelastische Platten und Schalen Ing. Arch. 58 215 228 (Pubitemid 18633836)
3. Altenbach H., Zhilin P.: 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)
4. H. Altenbach 1987 Determination of elastic moduli of anisotropic plates with nonhomogeneous material in thickness direction (in Russian) Mech. Solids 22 135 141 (Pubitemid 18505038)
5. H. Altenbach 2000 An alternative determination of transverse shear stiffnesses for sandwich and laminated plates Int. J. Solids Struct. 37 3503 3520 (Pubitemid 30565680)
6. H. Altenbach 2000 On the determination of transverse shear stiffnesses of orthotropic plates ZAMP 51 629 649
7. Altenbach, H., Eremeyev, V.A.: Direct approach based analysis of plates composed of functionally graded materials. Arch. Appl. Mech. doi: 10.1007/s00419-007-0192-3
8. H. Altenbach V.A. Eremeyev 2008 Analysis of the viscoelastic behavior of plates made of functionally graded materials ZAMM 88 332 341
9. Ashby M.F., Evans A.G., Fleck N.A., Gibson L.J., Hutchinson J.W., Wadley H.N.G.: Metal Foams: a Design Guide. Butterworth-Heinemann, Boston (2000)
10. Banhart J., Ashby M.F., Fleck N.A. (eds): Metal Foams and Porous Metal Structures. Verlag MIT Publishing, Bremen (1999)
11. Brinson H.F., Brinson C.L.: Polymer Engineering Science and Viscoelasticity. An Introduction. Springer, New York (2008)
12. Christensen R.M.: Theory of Viscoelasticity. An Introduction. Academic Press, New York (1971)
13. Collatz L.: Eigenwertaufgaben mit Technischen Anwendungen. Akademische Verlagsgesellschaft, Leipzig (1963)
14. Degischer, H.P., Kriszt B. (eds): Handbook of Cellular Metals. Wiley-VCH, Weinheim (2002)
15. Drozdov A.D.: Finite Elasticity and Viscoelasticity. World Scientific, Singapore (1996)
16. Gibson L.J., Ashby M.F.: Cellular Solids: Structure and Properties, 2nd edn. Cambridge Solid State Science Series. Cambridge University Press, Cambridge (1997)
17. Hartman Ph.: Ordinary Differential Equations. Wiley, New York (1964)
18. Haupt P.: Continuum Mechanics and Theory of Materials, 2nd edn. Springer, Berlin (2002)
19. Kraatz, A.: Berechnung des mechanischen Verhaltens von geschlossenzelligen Schaumstoffen unter Einbeziehung der Mikrostruktur. Diss., Zentrum für Ingenieurwissenschaften, Martin-Luther-Universität Halle-Wittenberg (2007)
20. R.S. Lakes 1987 Foam structures with a negative Poisson's ratio Science 235 1038 1040
21. R.S. Lakes 1992 The time-dependent Poisson's ratio of viscoelastic materials can increase or decrease Cell. Polym. 11 466 469
22. R.S. Lakes A. Wineman 2006 On Poisson's ratio in linearly viscoelastic solids J. Elast. 85 45 63 (Pubitemid 44259543)
23. Landrock, A.H. (eds): Handbook of Plastic Foams. Types, Properties, Manufacture and Applications. Noes Publications,Park Ridge (1995)
24. Lee S.T., Ramesh N.S. (eds): Polymeric Foams. Mechanisms and Materials. CRC Press, Boca Raton (2004)
25. Mills N.: Polymer Foams Handbook. Engineering and Biomechanics Applications and Design Guide. Butterworth-Heinemann, Amsterdam (2007)
26. R.D. Mindlin 1951 Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates Trans. ASME J. Appl. Mech. 18 31 38
27. Naghdi P.M.: The theory of plates and shells. In: Flügge, S.(eds) Handbuch der Physik, Bd. VIa/2, pp. 425-640. Springer, Berlin (1972)
28. Rabotnov Yu N.: Elements of Hereditary Solid Mechanics. Mir Publishers, Moscow (1980)
29. E. Reissner 1944 On the theory of bending of elastic plates J. Math. Phys. 23 184 194
30. E. Reissner 1945 The effect of transverse shear deformation on the bending of elastic plates J. Appl. Mech. 12 A69 A77 (Pubitemid 28161596)
31. E. Reissner 1985 Reflection on the theory of elastic plates Appl. Mech. Rev. 38 1453 1464
32. Riande, E. (eds) et al.: Polymer Viscoelasticity: Stress and Strain in Practice. Marcel Dekker, New York (2000)
33. Rothert, H.: Direkte Theorie von Linien- und Flächentragwerken bei viskoelastischem Werkstoffverhalten. Techn.-Wiss. Mitteilungen des Instituts für Konstruktiven Ingenieurbau 73-2. Ruhr-Universität, Bochum (1973)
34. Shaw M.T., MacKnight W.J.: Introduction to Polymer Viscoelasticity, 3rd edn. Wiley, Hoboken (2005)
35. Stoer J., Bulirsch R.: Introduction to Numerical Analysis. Springer, New York (1980)
36. S.P. Timoshenko 1921 On the correnction for shear of the differential equation for transverse vibrations of prismatic bars Philos. Mag. Ser. 6 41 744 746
37. Tschoegl N.W.: The Phenomenological Theory of Linear Viscoelastic Behavior. An Introduction. Springer, Berlin (1989)
38. Zhilin P.A.: Applied Mechanics. Foundations of the Theory of Shells (in Russian). Petersburg State Polytechnical University, Saint Petersburg (2006)
39. P.A. Zhilin 1976 Mechanics of deformable directed surfaces Int. J. Solids Struct. 12 635 648