Rigid Body Motion Test for Nonlinear Analysis with Beam Elements
Publication: Journal of Engineering Mechanics
Volume 113, Issue 9
Abstract
A rigid body motion test is proposed for verifying the legitimacy of a finite element to be used in a geometrically nonlinear analysis. The test requires that the initial forces acting on an element rotate or translate with the rigid body motion while the magnitudes of the initial forces remain unchanged, so as to preserve the equilibrium of the element during the rigid body motion. Such a test is consistent with basic physical laws, and is, therefore, more rational than previous considerations on rigid body motions. This paper also demonstrates the significance of using a consistent procedure for calculating the member forces in an incremental nonlinear, solution process. When a consistent element is used along with a consistent force calculation procedure, convergent and accurate solutions can be obtained for various nonlinear problems.
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References
1.
Bathe, K.‐J., and Bolourchi, S. (1979). “Large displacement analysis of three‐dimensional beam structures.” Int. J. Num. Meth. Engrg., 14(7), Jul., 961–986.
2.
Bathe, K.‐J., Ramm, E., and Wilson, E. L. (1975). “Finite element formulation for large displacement dynamic analysis.” Int. J. Num. Meth. Engrg., 9(2), Feb., 353–386.
3.
Belytschko, T., and Hsieh, B. J. (1973). “Non‐linear transient finite element analysis with convected coordinates.” Int. J. Num. Meth. Engrg., 7(3), Mar., 255–271.
4.
Cook, R. D. (1981). Concepts and applications of finite element analysis, 2nd ed. John Wiley & Sons, Inc., New York, N.Y.
5.
Gattass, M. (1982). “Large displacement, interactive‐adaptive dynamic analysis of frames,” thesis presented to Cornell University, in Ithaca, N.Y., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
6.
Irons, B., and Ahmad, S. (1980). Techniques of finite elements. John Wiley & Sons, Inc., New York, N.Y.
7.
Jagannathan, D. S., Epstein, H. I., and Christiano, P. (1975). “Fictitious strains due to rigid body rotation.” J. Struct. Div., ASCE, 101(11), Nov., 2472–2476.
8.
Mattiasson, K. (1981). “Numerical results from large deflection beam and frame problems analyzed by means of elliptic integrals.” Int. J. Num. Meth. Engrg., 17(1), Jan., 145–153.
9.
Papadrakakis, M. (1981). “Post‐buckling analysis of spatial structures by vector iteration methods.” Comput. and Structs., 14(5–6), 393–402.
10.
Porter, F. L., and Powell, G. H. (1971). “Static and dynamic analysis of inelastic frame structures.” Report No. EERC 71‐3, Earthquake Engineering Research Center, Univ. of California, Berkeley, Calif.
11.
Williams, F. W. (1964). “An approach to the nonlinear behavior of the members of a rigid jointed plane framework with finite deflections.” Quart. J. Mech. and Appl. Math., 17(4), 451–469.
12.
Wood, R. D., and Zienkiewicz, O. C. (1977). “Geometrically nonlinear finite element analysis of beams, frames, arches, and axisymmetric shells.” Comput. and Structs., 7(6), Dec., 725–735.
13.
Yang, Y. B., and McGuire, W. (1985). “A work control method for geometrically nonlinear analysis.” Proc. Int. Conf. on Advances in Num. Meth. in Engrg., Swansea, U.K. 913–921.
14.
Yang, Y. B., and McGuire, W. (1986a). “Stiffness matrix for geometric nonlinear analysis.” J. Struct. Engrg., ASCE, 112(4), Apr., 853–877.
15.
Yang, Y. B., and McGuire, W. (1986b). “Joint rotation and geometric nonlinear analysis.” J. Struct. Engrg., ASCE, 112(4), Apr., 879–905.
16.
Zienkiewicz, O. C. (1977). The finite element method, 3rd ed. McGraw‐Hill Book Co., Inc., New York, N.Y.
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Copyright © 1987 ASCE.
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Published online: Sep 1, 1987
Published in print: Sep 1987
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