Numerical convergence of simple and orthogonal polynomials for the unilateral plate buckling problem using the Rayleigh-Ritz method

International Journal for Numerical Methods in Engineering

Volumn 44, Issue 11, 1999, Pages 1685-1707

  Smith, S T ^a   Bradford, M A ^a   Oehlers, D J ^b  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b UNIVERSITY OF ADELAIDE   (Australia)

Author keywords

Bilateral buckling; Contact problems; Elasticity; Polynomials; Rayleigh Ritz method; Unilateral buckling; Unilateral restraint

Indexed keywords

BOUNDARY CONDITIONS; BUCKLING; CONVERGENCE OF NUMERICAL METHODS; ELASTICITY; POLYNOMIALS; SHEAR STRESS; STRUCTURAL ANALYSIS;

RAYLEIGH-RITZ METHOD; UNILATERAL BUCKLING;

PLATES (STRUCTURAL COMPONENTS);

EID: 0040288816     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19990420)44:11<1685::AID-NME562>3.0.CO;2-9     Document Type: Article

References (25)

1. N. M. Hamdan and L. Abdel Latif, 'On the numerical convergence of discretization methods for free vibrations of beams with attached inertia elements', J. Sound Vibr., 169(4), 527-545 (1994).
2. L. Meirovitch and M. K. Kwak, 'Convergence of the classical Rayleigh-Ritz method and the Finite Element method', A.I.A.A. J., 28(8), 1509-1516 (1990).
3. W. H. Wittrick, 'Buckling of oblique plates with clamped edges under uniform shear', Aeronaut. Quart., 5, 39-51 (1954).
4. J. E. Ashton, 'Stability of clamped skew plates under combined loads', J. Appl. Mech. Ser. E, 36, 139-140 (1969).
5. W. H. Wittrick, 'Buckling of oblique plates with clamped edges under uniform compression', The Aeronautical Quart., 4, 151-163 (1953).
6. T. Mizusawa, T. Kajita and M. Naruoka, 'Analysis of skew plate problems with various constraints', J. Sound Vibr., 73(4), 575-584 (1980).
7. R. B. Bhat, 'Natural frequencies of rectangular plates using characteristic orthogonal polynomials in Rayleigh-Ritz method', J. Sound Vibr., 102(4), 493-499 (1985).
8. R. B. Bhat 'Flexural vibration of polygonal plates using characteristic orthogonal polynomials in two variables', J. Sound Vibr., 114(1), 65-71 (1987).
9. S. M. Dickinson and A. Di Blasio, 'On the use of orthogonal polynomials in the Rayleigh-Ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates', J. Sound Vibr., 108(1), 51-62 (1986).
10. K. M. Liew and K. Y. Lam, 'Application of two dimensional orthogonal plate function to flexural vibration of skew plates', J. Sound Vibr., 139(2), 241-252 (1990).
11. R. L. Burden, J. D. Faires and A. C. Reynolds. Numerical Analysis, 2nd edn, Prindle, Webber and Schmidt, Boston, MA, 1981.
12. K M. Liew and C. M. Wang, 'Elastic buckling of regular polygonal plates', Thin-Walled Structures, 21, 163-173 (1995).
13. S. Singhvi and R. K. Kapania, 'Comparison of simple and Chebyshev polynomials in Rayleigh-Ritz analysis', J. Engng. Mech. ASCE, 120(10), 2126-2135 (1994).
14. P. D. Panagiotopoulos, Inequality Problems in Mechanics and Applications - Convex and Nonconvex Energy Functions, Birkhauser, New York, 1985.
15. K. M. Liew, K. Y. Lam and S. T. Chow, 'Free vibration analysis of rectangular plates using orthogonal plate functions', Comput. Struct., 34, 79-85 (1990).
16. K. M. Liew and C. M. Wang, 'pb-2 Rayleigh-Ritz method for general plate analysis', Engng Struct., 15, 55-60 (1993).
17. C. M. Wang and K. M. Liew, 'Buckling of triangular plates under uniform compression', Engng. Struct., 16(1), 43-50 (1994).
18. M. R. Spiegel, Mathematical Handbook of Formulas and Tables, McGraw-Hill, New York, 1968.
19. S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability, McGraw Hill, New York, 1961.
20. S. E. Swartz and R. J. O'Neill, 'Linear elastic buckling of plates subjected to combined loads', Thin-Walled Struct., 21, 1-15 (1995).
21. S. T. Smith, M. A. Bradford and D. J. Oehlers, 'Local buckling of side plated reinforced concrete beams', submitted for publication.
22. R. W. Hornbeck, Numerical Methods, Prentice-Hall, Englewood Cliffs, N.J., 1975.
23. G. Bezine, A. Cimetiere and J. P. Gelbert, 'Unilateral buckling of thin elastic plates by the boundary integral equation method', Int. J. Numer. Meth. Engng., 21, 2189-2199 (1985).
24. S. F. Bassily and M. Dickinson, 'On the use of beam functions for problems of plates involving free edges', J. Appl. Mech., 42, 858-864 (1975).
25. M. Ahmed, D. J. Oehlers, N. T. Nguyen and M. A. Bradford, 'Reinforced concrete beams with steel plates bolted to their sides', Proc ICSF-97 5th Int. Conf. on Structural Failure, Durability and Retrofitting, Singapore, November 1997.