Unified finite elements based on the classical and shear deformation theories of beams and axisymmetric circular plates

Communications in Numerical Methods in Engineering

Volumn 13, Issue 6, 1997, Pages 495-510

  Reddy, J N ^a   Wang, C M ^b   Lam, K Y ^b  

^a Texas AandM University   (United States)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Axisymmetric circular plates; Classical deformation; Shear deformation; Unified finite elements

Indexed keywords

BENDING (DEFORMATION); DEFLECTION (STRUCTURES); DEGREES OF FREEDOM (MECHANICS); FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PLATES (STRUCTURAL COMPONENTS); SHEAR DEFORMATION; STIFFNESS MATRIX;

EULER-BERNOULLI BEAM THEORY; TIMOSHENKO BEAM THEORY;

BEAMS AND GIRDERS;

EID: 0031165220     PISSN: 10698299     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-0887(199706)13:6<495::AID-CNM82>3.0.CO;2-9     Document Type: Article

References (19)

1. J. N. Reddy, An Introduction to the Finite Element Method, 2nd edn, McGraw-Hill, New York, 1993.
2. R. C. Averill and J. N. Reddy, 'On the behaviour of plate elements based on the first-order theory', Eng. Comput., 7, 57-74 (1990).
3. R. E. Nickell and G. A. Secor, 'Convergence of consistently derived Timoshenko beam finite elements', Int. j. numer. methods eng., 5, 243-253 (1972).
4. A. Tessler and S. B. Dong, 'On a hierarchy of conforming Timoshenko beam elements', Comput. Struct., 14(3-4), 335-344 (1981).
5. G. Prathap and G. R. Bhashyam, 'Reduced integration and the shear flexible beam element', Int. j. numer. methods eng., 18, 195-210 (1982).
6. S. P. Timoshenko, 'On the correction for shear of the differential equation for transverse vibrations of prismatic bars', Philosophical Magazine, 41, 744-746 (1921).
7. S. P. Timoshenko, 'On the transverse vibrations of bars of uniform cross section', Philos. Mag., 43, 125-131 (1922).
8. G. Jemielita, 'Techniczna teoria plyt srednieej grubbosci' (Technical theory of plates with moderate thickness), Rozprawy Inzynierskie (Engineering Transactions), Polska Akademia Nauk, 23(3), 483-499 (1975).
9. M. Levinson, 'A new rectangular beam theory', J. Sound Vib., 74, 81-87 (1981).
10. W. B. Bickford, 'A consistent higher order beam theory', Dev. Theor. Appl. Mech., 11, 137-150 (1982).
11. J. N. Reddy, 'A simple higher-order theory for laminated composite plates', J. Appl. Mech., 51, 745-752 (1984).
12. J. N. Reddy, Energy and Variational Methods in Applied Mechanics, Wiley, New York, 1984.
13. P. R. Heyliger and J. N. Reddy, 'A higher-order beam finite element for bending and vibration problems', J. Sound Vib., 126(2), 309-326 (1988).
14. N. D. Phan and J. N. Reddy, 'Analysis of laminated composite plates using a higher-order shear deformation theory', Int. J. numer. methods eng., 12, 2201-2219 (1985).
15. J. N. Reddy, Mechanics of Laminated Composite Plates: Theory and Analysis, CRC Press, Boca Raton, Florida, 1997.
16. C. M. Wang, 'Timoshenko beam-bending solutions in terms of Euler-Bernoulli solutions', J. Eng. Mech., ASCE, 121(6), 763-765 (1995).
17. J. N. Reddy et al., 'Exact relationships between the bending solutions of the Euler-Bernoulli beam theory and shear deformable beam theories', Int. J. Solids & Struct. (1997), in press.
18. C. M. Wang and K. H. Lee, 'Deflection and stress-resultants of axisymmetric Mindlin plates in terms of corresponding Kirchoff solutions', Int. J. Mech. Sci. 38(11), 1179-1185 (1996).
19. R. Szilard, Theory and Analysis of Plates, Prentice-Hall, Englewood Cliffs, NJ, 1974.