Virtual Large Displacement Theorem for Framed Structures
Publication: Journal of Engineering Mechanics
Volume 116, Issue 2
Abstract
This paper formulates a new theorem of virtual work for finite deformation with the following qualities: (1) Any actual large displacement in a body may be adopted as the virtual displacement; and (2) the internal virtual work is composed in terms of the physical components of stresses and their conjugate finite virtual strains in the Lagrangian description plus the additional terms; these terms become the rigid‐body rotations for axial strains and the corrections due to elongations for shear strains. Fundamental matrix equations are derived for the finite deformation analyses of pin‐jointed trusses and rigid‐jointed frames on the basis of the present theorem. These formulations are simpler than previous approaches and lead to the exact solutions of nonlinear analyses, particularly for plane and space pin‐jointed trusses. Further, when using these equations, the larger increments of load and displacement can be accommodated in the numerical computations. This theorem unifies the principle of virtual work and the principle of complementary virtual work for finite deformation.
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References
1.
Dym, C. I., and Shames, I. H. (1973). Solid mechanics—A variational approach. McGraw‐Hill Inc., New York, N.Y.
2.
Fraeijs de Veubeke, B. (1972). “A new variational principle for finite elastic displacements.” Int. J. Engrs. Sci., 10, 745–763.
3.
Fung, Y. C. (1965). Foundations of solid mechanics. Prentice‐Hall, Inc., Englewood Cliffs, N.J.
4.
Jagannathan, D. S., Epstein, H. I., and Christiano, P. (1975). “Nonlinear analysis of reticulated space trusses.” J. Struct. Div., ASCE, 101(12), 2641–2658.
5.
Livesley, R. K. (1964). Matrix methods of structural analysis. Pergamon Press, Ltd., Oxford, England.
6.
Miike, R. (1981). “Incremental energy theorems for finite deformations.” Proc. Japan Soc. Civ. Engrs., 309(5), 41–50 (in Japanese).
7.
Murakawa, H., and Atluri, S. N. (1978). “Finite elasticity solutions using hybrid finite elements based on a complementary energy principle.” J. Appl. Mech., ASME, 45(9), 539–547.
8.
Nishino, F., et al. (1984). “A total Lagrangian nonlinear analysis of elastic trusses.” Struct. Engrg./Earthquake Engrg. Proc. Japan Soc. Civ. Engrs., 344(I‐1), 39–53.
9.
Oden, J. T. (1973). “Variational principles in nonlinear continuum mechanics.” Variational methods in engineering, I, Southampton University Press, Southampton, England, 2/1–2/20.
10.
Reissner, E. (1984). “Formulation of variational theorems in geometrically nonlinear elasticity.” J. Engrg. Mech., ASCE, 110(9), 1377–1390.
11.
Stricklin, J. A., et al. (1972). “Static geometric and material nonlinear analysis.” Advances in computational structural mechanics and design, J. T. Oden, R. W. Clough, and Y. Yamamoto, eds., UAH Press, Huntsvill, Ala., 301–324.
12.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability. 2nd Ed., McGraw‐Hill, New York, N.Y.
13.
Washizu, K. (1975). Variational methods in elasticity and plasticity. 2nd Ed., Pergamon Press Ltd., Oxford, England.
14.
Wempner, G. (1980). “Complementary theorems of solid mechanics.” Variational methods in mechanics of solids, S. Nemat‐Nasser, ed., Pergamon Press Inc., Evanston, Ill., 127–135.
15.
Yoshida, Y., et al. (1980). “An incremental formulation for computer analysis of space framed structures.” Proc. Japan Soc. Civ. Engrs., 300(8), 21–31 (in Japanese).
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 116 • Issue 2 • February 1990
Pages: 411 - 428
Copyright
Copyright © 1990 ASCE.
History
Published online: Feb 1, 1990
Published in print: Feb 1990
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