Effects of Rigid Body and Stretching on Nonlinear Analysis of Trusses
Publication: Journal of Structural Engineering
Volume 116, Issue 10
Abstract
According to the law of rigid body motion, a body initially acted upon by a set of forces in equilibrium will experience no additional straining when subjected to a rigid body motion, and will remain in equilibrium after the rigid body motion. When such a law is not strictly followed in an incremental‐iterative nonlinear analysis, especially in the element force recovery procedure, fictitious forces may occur at each intermediate step, which eventually may result in the deviation of the calculated behavior of a structure from its true response. From the point of view of solution accuracy, the rigid body effect plays a more important role than the stretching effect in determining which higher‐order terms should be included in a force‐recovery procedure. In this paper, both of these effects are considered in the derivation of the nonlinear stiffness matrices for a truss element. Each term involved in the formulation is examined with clear physical meanings given. Comparisons are made with previous results in the numerical examples.
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References
1.
Chajes, A., and Churchill, J. E. (1987). “Nonlinear frame analysis by finite element method.” J. Struct. Engrg., ASCE, 113(6), 1221–1235.
2.
Hangai, Y., and Kawamata, S. (1971). “Nonlinear analysis of space frames and snap‐through buckling of reticulated shell structures.” Proc. Int. Assoc. for Shell and Spatial Struct. (IASS) Pacific Symp., Part II on Tension Structs., and Space Frames, Tokyo and Kyoto, Japan, Sept.
3.
Holzer, S. M., Plaut, R. H., Somers, A. E., Jr. (1980). “Stability of lattice structures under combined loads.” J. Engrg. Mech. Div., ASCE, 106(2), 289–305.
4.
Jagannathan, D. S., Epstein, H. I., and Christiano, P. (1975). “Snap‐through buckling of reticulated shells.” Proc. Inst. of Civ. Engrs., Part 2, 59, London, U.K., 727–742.
5.
Mallett, R. H., and Marcal, P. V. (1968). “Finite element analysis of nonlinear structures.” J. Struct. Div., ASCE, 94(9), 2081–2105.
6.
Papadrakakis, M., (1981). “Post‐buckling analysis of spatial structures by vector iteration methods.” Computers & Struct., 14 (5–6), 393–402.
7.
Rajasekaran, S., and Murray, D. W. (1973). “Incremental finite element matrices.” J. Struct. Div., ASCE, 99(12), 2423–2438.
8.
Wen, R. K., and Rahimzadeh, J. (1983). “Nonlinear elastic frame analysis by finite element.” J. Struct. Engrg., ASCE, 109(8), 1952–1971.
9.
Yang, Y. B., and Chiou, H. T. (1987). “Rigid body motion test for nonlinear analysis with beam elements.” J. Engrg. Mech., ASCE, 113(9), 1404–1419.
10.
Yang, Y. B., and McGuire, W. (1985). “A work control method for geometrically nonlinear analysis.” Proc. Int. Conf. on Advances in Numerical Methods in Engrg., Univ. Coll., Swansea, U.K., 913–921.
11.
Yang, Y. B., and McGuire, W. (1986). “Joint rotation and geometric nonlinear analysis.” J. Struct. Engrg., ASCE, 112(4), 879–905.
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Copyright © 1990 ASCE.
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Published online: Oct 1, 1990
Published in print: Oct 1990
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