Buckling of Three‐Dimensional Rigid‐Link Models
Publication: Journal of Engineering Mechanics
Volume 115, Issue 1
Abstract
Two‐dimensional rigid‐link models have been used often in the study of elastic stability to provide insight into the behavior of engineering structures; the buckling modes of such models take only planar shapes. Many engineering structures, however, possess three‐dimensional buckling characteristics, so it is important to have models with three‐dimensional buckling characteristics. A three‐dimensional three‐link model that initially assumes either a straight‐line or a planar zigzag configuration is studied and both in‐plane and out‐of‐plane buckling modes are found in each case. The model is formulated in terms of the total potential energy and differentiation is carried out using the MACSYMA program. This structure may deflect continuously with increasing load, buckle in a plane, or buckle out of plane, depending on the angle between the adjoining links and the relative stiffness between the bending springs and the internal rotation springs. We find that in the case of in‐plane buckling, the buckling load is greater than the lowest buckling load of the perfect structure.
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References
1.
Asada, H., and Slotine, J. J. E. (1986) Robot analysis and control. John Wiley and Sons Inc., New York, N.Y., 29–49.
2.
Budiansky, B. (1974). Theory of buckling and post‐buckling behavior of elastic structure, advances in applied mechanics, Vol. 14, Academic Press Inc., New York, N.Y., 2–11.
3.
Choo, Y., and Casarella, M. J. (1973). “Survey of analytical methods for dynamic simulation of cable‐body system.” J. Hydronaut. 7(4), 137–144.
4.
Craig, J. R. (1986). Introduction to robotics: mechanics & control. Addison‐Wesley Publishing Company, Reading, Mass., 1–96.
5.
Croll, A. G., and Walker, A. C. (1972). Elements of structural stability, John Wiley and Sons, Inc., New York, N.Y., 17–174.
6.
DeTeresa, S. J., Porter, R. S., and Farris, R. J. (1985). “A model for the compressive buckling of extended‐chain polymer.” J. Mater. Sci., 20(5), 1645–1659.
7.
Eyring, H. (1932). “The resultant electric moment of complex molecules.” Physical Review. 39, 745–748.
8.
Huseyin, K. (1974). Nonlinear theory of elastic stability. Noordhoff International Publishing, Leyden, Netherlands, 3–45.
9.
Huston, R. L., and Kamman, J. W. (1981). “A representation of fluid forces in finite segment cable models.” Computer and Structures. 14(3–4), 281–287.
10.
Kamman, J. W., and Huston, R. L. (1985). “Modelling of Submerged Cable Dynamics.” Comput. Struct. 20(1–3), 623–629.
11.
Lee, C. S., and Lardner, T. J. (1988a). “The deformation of helical linked structures.” Proc. Int. Conferences on Composite Materials and Structures, Tata McGraw‐Hill, New Delhi, India, 159–173.
12.
Lee, C. S., and Lardner, T. J. (1988b). “The deformation of linked oriented structures.” Advances in aerospace structures and allied fields, T. K. Varandan, ed., Indian Inst. of Tech., Madras, India, 221–230.
13.
MACSYMA reference manual. (1983). The MathLab Group, Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, Mass.
14.
Mandelkon, L. (1972). An introduction to macromolecules. The English Universities Press Ltd., London, United Kingdom, 25–50.
15.
Roorda, J. (1965). “The buckling behavior of imperfect structural system.” J. Mech. Phys. Solids 13(15), 267–280.
16.
Shimanouchi, T., and Mizushima, S. (1955). “On the helical configuration of a polymer chain.” Journal of Chemical Physics 23(4), 707–711.
17.
Simitses, G. J. (1975). An introduction to the elastic stability of structures. Prentice‐Hall, New York, N.Y., 21–44.
18.
Tashiro, K., Kobayash, M., and Tadoroko, H. (1977). “Elastic moduli and molecular structures of several crystalline polymers, including aromatic polyamides.” Macromolecules 10(2), 413–420.
19.
Thompson, J. M. T. (1965). “Discrete branching points in the general theory of elastic stability.” J. Mech. Phys. Solids 13(5), 295–310.
20.
Thompson, J. M. T. (1982). Instabilities and catastrophes in science and engineering. Pitman Press Limited, Bath, Avon, England, 1–62.
21.
Thompson, J. M. T., and Hunt, G. W. (1969). “A general theory for the equilibrium and stability of discrete conservative system.” Z Angew. Math. Phys. 20(6), 797–846.
22.
Thompson, J. M. T., and Hunt, G. W. (1973). A general theory of elastic stability. John Wiley and Sons, Inc., London, United Kingdom, 1–102.
23.
Thompson, J. M. T., and Hunt, G. W. (1984). Elastic instability phenomena. John Wiley and Sons, Inc., New York, N.Y., 1–26.
24.
Ward, I. M. (1983). Mechanical properties of solid polymers, 2nd Ed., John Wiley and Sons Inc., New York, N.Y., 1–14.
25.
White, J. R., and Lardner, T. J. (1984). “Mechanical models to describe the behavior of polyaramid fibers.” J. Mater. Sci. 19(7), 2387–2395.
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Copyright © 1989 ASCE.
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Published online: Jan 1, 1989
Published in print: Jan 1989
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