Finite deformation of slender beams

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 81, Issue 7, 2001, Pages 481-488

  Reismann, H ^a,b  

^a State University of New York ^*  (United States)

^b NONE   (United States)

Author keywords

Beam; Coupled flexure torsion extension (contraction); Finite (non linear) deformation; Oblique bending

Indexed keywords

EID: 33747898344     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/1521-4001(200107)81:7<481::AID-ZAMM481>3.0.CO;2-1     Document Type: Article

References (20)

1. KIRCHHOFF, G.: Über das Gleichgewicht und die Bewegung eines unendlich dünnen elastischen Stabes. J. Math. (Grelle) 56 (1859), 381.
2. KIRCHHOFF, G.: Vorlesungen über Mathematische Physik. I: Mechanik. 3. Aufl. B. G. Teubner, Leipzig 1883, 28. Vorl., pp. 406-427.
3. THOMSON, Sir William (Lord KELVIN); TAIT, P. G.: Principles of mechanics and dynamics. 2. Dover Publications, Inc., New York 1962, pp. 144-145.
4. FRISCH-FAY, R.: Flexible bars. Butterworth, London 1962, Ch. 6.
5. POPOV, E. P.: Non-linear problems in the statics of thin bars. Gostekhizdat, Leningrad-Moscow 1948 (Russian).
6. SIMO, J. C.; VU-QUOC, L.: A geometrically-exact rod model incorporating shear and torsion-warping deformation. Int. J. Solids Structures 27 (1991) 3, 371-393.
7. WUNDERLICH, W.; OBRECHT, H.: Large spacial deformation of rods using generalized variational principles. In: WUNDERLICH, W.; STEIN, E.; BATHE, K.-J.: Nonlinear finite element analysis in structural mechanics. Springer Verlag, Berlin 1981, pp. 185-216.
8. KAPPUS, R.: Zur Elastizitätstheorie endlicher Verschiebungen. I, II. ZAMM 19 (1939) 5, 271-285,
9. KAPPUS, R.: ZAMM 19 (1939) 6, 344-361.
10. RENTON, J. D.: Applied elasticity. John Wiley and Sons, New York 1987, pp. 158-162.
11. LOVE, A. E. H.: A Treatise on the mathematical theory of elasticity. 4th ed. Cambridge University Press, London 1927, Ch. XVIII.
12. SOMMERFELD, A.: Mechanics. Lectures on theoretical physics, 1. Academic Press, New York 1952, 197.
13. LANDAU, L. D.; LIFSHITZ, E. M.: Theory of elasticity. 3rd English ed. (Course on Theoretical Physics, 7) Pergamon Press, Oxford 1986, 68.
14. WASHIZU, K.: Variational methods in elasticity and plasticity. 3rd. ed. Pergamon Press, Oxford 1982, pp. 91-93.
15. LANCZOS, C.: The variational principles of mechanics. 4th ed. University of Toronto Press, Toronto 1974, pp. 69-71.
16. VETTERLING, W. T.; TEUKOLSKY, S. A.; PRESS, W. H.; FLANNERY, B. P.: Numerical recipies in Fortran. 2nd ed. Cambridge University Press, Cambridge 1994, pp. 749-751.
17. PRESS, W. H.; TEUKOLSKY, S. A.; VETTERLING, W. T.; FLANNERY, B. P.: Numerical recipies example book (Fortran). 2nd ed. Cambridge University Press, Cambridge 1994, pp. 221-223.
18. Mathcad 2000 Professional. Users guide. Mathsoft, Inc., Cambridge, Mass. 1999, Program sbval, pp. 183-185.
19. Mathcad 2000 Reference Manual. Mathsoft Inc., Cambridge, Mass. 1999, Program sbval, pp. 108-109.
20. ZIEGLER, H.: Mechanics, I. Addison-Wesley Publishing Co., Inc., Reading, Mass. 1965, pp. 190-192.