Buckling of Skew Plates and Corner Condition for Simply Supported Edges
Publication: Journal of Engineering Mechanics
Volume 118, Issue 4
Abstract
The paper considers the elastic buckling of skew plates subjected to in‐plane loadings. The buckling analysis is performed using the Rayleigh‐Ritz method with the newly proposed pb‐2 Ritz functions, which consist of the product of a two‐dimensional polynomial function and a basic function. The basic function is formed from taking the product of the equations of the boundaries, with each equation raised to the power of 0,1, or 2 corresponding to free, simply supported, or clamped edges; thus satisfying the kinematic boundary conditions at the outset. With pb‐2 Ritz functions, the analyst avoids the difficulty of searching for the appropriate function for any arbitrarily shaped plates with various combinations of supporting‐edge conditions. Using this efficient and accurate pb‐2 Rayleigh‐Ritz method, buckling solutions are obtained and presented in the form of design charts for skew plates with different edge conditions, angles, and aspect ratios. In addition, the differing viewpoints on the kinematic condition for a corner formed by two simply supported edges are discussed.
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References
1.
Argyris, J. H. (1966). “Continua and discontinua (An apergu of recent developments of the matrix displacement method). “Proc. Matrix Methods in Struct. Mech., Wright Air Development Center, Ohio Oct. 26‐28, 11–190.
2.
Ashton, J. E. (1969). “Stability of clamped skew plates under combined loads.” J. Appl. Mech., 36, Trans. ASME, 91, Series E., March, 139–140.
3.
Durvasula, S. (1970). “Buckling of clamped skew plates.” AIAA J., 8(1), 178–181.
4.
Durvasula, S. (1971). “Buckling of simply supported skew plates.” J. Engrg. Mech. Div.,ASCE, 97(3), 967–979.
5.
Edwardes, R. J., and Kabaila, A. P. (1978). “Buckling of simply supported skew plates.” Int. J. Numer. Methods Engrg., 12(5), 779–785.
6.
Fried, I., and Schmitt, K. H. (1972). “Numerical results from the application of gradient iterative techniques to the finite element vibration and stability analysis of skew plates.” Aeronaut. J., 76, 166–169.
7.
Guest, J. (1951). “The buckling of uniformly compressed parallelogram plates having all edges clamped.” Rep. SM 172Aeronaut. Res. Labs., Melbourne, Australia.
8.
Gustafson, W. C., and Wright, R. N. (1968). “Analysis of skewed composite girder bridges.” J. Struct. Div., ASCE, 94, 919–942.
9.
Hegedus, T. (1988). “Finite strip buckling analysis of skew plates under combined loading.” Stability of steel structures, M. Ivanyi, ed., Akademiai Kiado, Budapest, Hungary, 633–641.
10.
Kennedy, J. B., and Prabhakara, M. K. (1978). “Buckling of simply supported orthotropic skew plates.” Aeronaut. Q., 29, 161–174.
11.
Kennedy, J. B., and Prabhakara, M. K. (1979). “Combined‐load buckling of ortho‐tropic skew plates.” J. Engrg. Mech. Div., ASCE, 105(1), 71–79.
12.
Klein, B. (1957). “Buckling of simply supported rhombic plates under externally applied shear,” Journal of the Royal Aeronautical Society, London, U.K., 61(557), 357–358.
13.
Laura, P. A., and Grosson, J. (1971). “Buckling of rhombic plates.” J. Engrg. Mech. Div., ASCE, 97(1), 145–148.
14.
Levy, S. (1942). “Buckling of rectangular plates with built‐in edges.” J. Appl. Mech., 9(4), A171‐A174.
15.
Liew, K. M., and Lam, K. Y. (1990). “Application of two‐dimensional orthogonal plate function to flexural vibration of skew plates.” J. Sound Vib., 139(2), 241–252.
16.
Mahabaliraja, and Durvasula, S. (1972). “Stability of simply supported skew plates under combined loading.” J. Appl. Mech., 39(1), 310–311.
17.
Mizusawa, T., Kajita, T., and Naruoka, M. (1980). “Analysis of skew plate problems with various constraints.” J. Sound Vib., 73(4), 575–584.
18.
Morley, L. S. D. (1963). “Skew plates and structures”. Pergamon Press, Oxford, U.K.
19.
Prabhu, M. S. S., and Durvasula, S. (1972). “Stability of clamped skew plates.” Appl. Sci. Res., 26, 255–271.
20.
Rozvany, G. I. N. (1974). “Optimal flexure fields for corners.” J. Engrg. Mech. Div., ASCE, 100(4), 828–831.
21.
Salvadori, M. G. (1949). “Numerical computation of buckling loads by finite differences.” Proc. ASCE, 75(10), 1,441‐1,475.
22.
Thangam Babu, P. V., and Reddy, D. V. (1978). “Stability analysis of skew ortho‐tropic plates by the finite strip method.” Comput. Struct, 8(5), 599–607.
23.
Timoshenko, S. P., and Woinowsky‐Krieger, S. (1970). Theory of plates and shells, 2 Ed., McGraw‐Hill, Singapore.
24.
Wittrick, W. H. (1953). “Buckling of oblique plates with clamped edges under uniform compression.” Aeronaut. Q., 4, 151–163.
25.
Wittrick, W. H. (1954). “Buckling of oblique plates with clamped edges under uniform shear.” Aeronaut. Q., 5, May, 39–51.
26.
Wittrick, W. H. (1956). “On the buckling of oblique plates in shear.” Aircraft Engrg., 28(323), 25–27.
27.
Yoshimura, Y., and Iwata, K. (1963). “Buckling of simply supported oblique plates.” J. Appl. Mech., 30(2), 363–366.
28.
Zienkiewicz, O. C., and Taylor, R. L. (1989). The finite element method. 4 Ed., Vol. 1, McGraw‐Hill, Singapore.
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Copyright © 1992 ASCE.
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Published online: Apr 1, 1992
Published in print: Apr 1992
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