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Nonlinear Dynamic Analysis of Reticulated Space Truss Structures

Published online by Cambridge University Press:  05 May 2011

C.-Y. Wang ,
R.-Z. Wang ,
C.-C. Chuang  and
T.-Y. Wu
C.-Y. Wang*
Affiliation:
Department of Civil Engineering, National Central University, Chungli, Taiwan 32001, R.O.C.
R.-Z. Wang*
Affiliation:
National Center for Research on Earthquake Engineering, Taipei, Taiwan 10668, R.O.C.
C.-C. Chuang*
Affiliation:
Department of Civil Engineering, Chung Yuan Christian University, Chungli, Taiwan 32023, R.O.C.
T.-Y. Wu*
Affiliation:
Department of Civil Engineering, National Central University, Chungli, Taiwan 32001, R.O.C.
*
*Professor
**Associate Research Fellow
***Associate Professor
****Adjunct Assistant Professor
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Abstract

In this paper, a simpler formulation for the nonlinear motion analysis of reticulated space truss structures is developed by applying a new concept of computational mechanics, named the vector form intrinsic finite element (VFIFE or V-5) method. The V-5 method models the analyzed domain to be composed by finite particles and the Newton's second law is applied to describe each particle's motion. By tracing the motions of all the mass particles in the space, it can simulate the large geometrical and material nonlinear changes during the motion of structure without using geometrical stiffness matrix and iterations. The analysis procedure is vastly simple, accurate, and versatile. The formulation of VFIFE type space truss element includes a new description of the kinematics that can handle large rotation and large deformation, and includes a set of deformation coordinates for each time increment used to describe the shape functions and internal nodal forces. A convected material frame and an explicit time integration scheme for the solution procedures are also adopted. Numerical examples are presented to demonstrate capabilities and accuracy of the V-5 method on the nonlinear dynamic stability analysis of space truss structures.

Keywords

Space trussNonlinearDynamicStabilityParticleConvected material frameDeformation coordinates
Type
Articles
Information
Journal of Mechanics , Volume 22 , Issue 3 , September 2006 , pp. 199 - 212
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2006

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References

1.Epstein, M. and Tene, Y., “Nonlinear Analysis of Pin-Jointed Space Trusses,” J. Struct. Div., ASCE, 97(9), pp. 2189–2202(1971).Google Scholar
2.Baron, F. and Venkatesan, M. S., “Nonlinear Analysis of Cable and Truss Structures,” J. Struct. Div., ASCE 97(2), pp. 679–710 (1971).CrossRefGoogle Scholar
3.Noor, A. K., “Nonlinear Analysis of Space Trusses,” J. Struct. Div., ASCE, 100(3), pp. 533–546 (1974).CrossRefGoogle Scholar
4.Wright, D. J., “Membrane Forces and Buckling in Re- Ticulated Shells,” J. Struct. Div., ASCE 91(1), pp. 173–201 (1965).CrossRefGoogle Scholar
5.Cooker, J. O., “Buchert KP. Reticulated Space Structures,” J. Struct. Div., ASCE, 96(3), pp. 687–700 (1970).Google Scholar
6.Noor, A. K. and Peters, M., “Instability Analysis of Space Trusses,” Comp. Meth. Appl. Mech. Eng., 40, pp. 199–218 (1983).CrossRefGoogle Scholar
7.Jagannathan, D. S., Epstein, H. I. and Christiano, P., “Fictitious Strains Due to Rigid Body Rotation,” J. Struct. Div., ASCE, 101(11), pp. 2472–2476 (1975).CrossRefGoogle Scholar
8.Jagannathan, D. S., Epstein, H. I. and Christiano, P., “Nonlinear Analysis of Reticulated Space Trusses,” J. Struct. Div., ASCE, 101(12), pp. 2641–2658 (1975).CrossRefGoogle Scholar
9.Rothert, H., Dickel, T. and Renner, D., “Snap-Through Buckling of Reticulated Space Trusses,” J. Struct. Div., ASCE 107(1), pp. 129–143 (1981).CrossRefGoogle Scholar
10.Papadrakakis, M., “Post-Buckling Analysis of Spatial Structures by Vector Interaction Methods,” Comput. Struct., 14(5–6), pp. 759–768 (1981).Google Scholar
11.Meek, J. L. and Tan, H. S., “Geometrically Nonlinear Analysis of Space Frames by an Incremental Iterative Technique,” Comp. Meth. Appl. Mech. Eng., 47, pp. 261–282 (1984).CrossRefGoogle Scholar
12.Hill, C. D., Blandford, G. E. and Wang, S. T., “Post-Buckling Analysis of Steel Space Trusses,” J. Struct. Eng., ASCE 115(4), pp. 900–919 (1989).Google Scholar
13.Freitas, J. A. T. and Ribeiro, A. C. B. S., “Large Displacement Elastoplastic Analysis of Space Trusses,” Comput. Struct., 44(5), pp. 1007–1016 (1992).CrossRefGoogle Scholar
14.Ramesh, G. and Krishnamoorthy, C. S., “Post-Buckling Analysis of Structures by Dynamic Relaxation,” Int. J. Num. Meth. Eng., 36, pp. 1339–1364 (1993).Google Scholar
15.Ramesh, G. and Krishnamoorthy, C. S., “Inelastic Post-Buckling Analysis of Truss Structures by Dynamic Relaxation Method,” Int. J. Num. Meth. Eng., 37, pp. 3633–3657 (1994).CrossRefGoogle Scholar
16.Blandford, G. E., “Progressive Failure Analysis of Inelastic Space Truss Structures,” Comput Struct., 58(5), pp. 981–990 (1996).Google Scholar
17.Holzer, S. M., Plaut, R. H., Somers, A. E. and White, S. W., “Stability of Lattice Structures Under Combined Loads,” J. Eng. Mech. Div., ASCE 106(2), pp. 289–305 (1980).Google Scholar
18.Leu, L. J. and Yang, Y. B., “Effects of Rigid Body and Stretching on Nonlinear Analysis of Trusses,” J. Struct. Eng., ASCE, 116(10), pp. 2582–2598 (1990).CrossRefGoogle Scholar
19.Levy, R., Vilany, O. and Acheampong, K. B., “Exact Geometry Considerations in Buckling Analysis of Trusses,” Comput. Struct., 41(6), pp. 1241–1248 (1991).Google Scholar
20.Krishnamoorthy, C. S., Ramesh, G. and Dinesh, K. U., “Post-Buckling Analysis of Structures by Three-Parameter Constrained Solution Techniques,” Finite. Elem. Anal. Des., 22, pp. 109–142 (1996).Google Scholar
21.Goldberg, J. E. and Richard, R. M., “Analysis of Nonlinear Structures,” J. Struct. Div., ASCE, 89(4), pp. 333–351 (1963).CrossRefGoogle Scholar
22.Richard, R. M. and Goldberg, J. E., “Analysis of Nonlinear Structures: Force Method,” J. Struct. Div., ASCE, 91(9), pp. 33–48(1965).Google Scholar
23.Hensley, R. C. and Azar, J. J., “Computer Analysis of Nonlinear Truss Structures,” J. Struct. Div., ASCE 94(9), pp. 1427–1439 (1968).CrossRefGoogle Scholar
24.Wood, R. D. and Zienkiewicz, O. C., “Geometrically Nonlinear Finite Element Analysis of Beam, Frames, Arches and Axisymmetric Shell,” Comput. Struct., 7, pp. 725–735 (1977).CrossRefGoogle Scholar
25.Watson, L. T. and Holzer, S. M., “Quadratic Convergence of Crisfield's Method,” Comput. Struct., 17(1), pp. 69–72 (1983).CrossRefGoogle Scholar
26.Leu, L. J. and Yang, Y. B., Discussion of “Post-Buckling Analysis of Steel Space Trusses,” by Hill, C. D., Blandford, G. E. and Wang, S. T. (Proc. No. 23407), J. Struct. Eng., ASCE, 117(12), pp. 3824–3828 (1991).Google Scholar
27.Mallett, R. H. and Marcal, P. V., “Finite Element Analysis of Nonlinear Structures,” J. Struct. Eng., ASCE 94(9), pp. 2081–2105 (1968).Google Scholar
28.Rajasekaran, S. and Murray, D. W., “Incremental Finite Element Matrices,” J. Struct. Eng., ASCE 99(12), pp. 2423–2438 (1973).Google Scholar
29.Hallquist, J. O., LLS-DYNA Theoretical Manual, Livermore Software Technology Corporation (1998).Google Scholar
30.Ting, E. C., Shih, C. and Wang, Y. K., “Fundamentals of a Vector Form Intrinsic Finite Element: Part I. Basic Procedure and a Plane Frame Element,” J. Mech., 20(2), pp. 113–122(2004).Google Scholar
31.Ting, E. C., Shih, C. and Wang, Y. K., “Fundamentals of a Vector Form Intrinsic Finite Element: Part II. Plane Solid Elements,” J. Mech., 20(2), pp. 123–132 (2004).Google Scholar
32.Shih, C., Wang, Y. K. and Ting, E. C., “Fundamentals of a Vector Form Intrinsic Finite Element: Part III. Convected Material Frame and Examples,” J. Mech., 20(2), pp. 133–143 (2004).CrossRefGoogle Scholar
33.Goldstein, H., Classical Mechanics, MA, Addison-Wesley Publishing (1959).Google Scholar
34.Rice, D. L. and Ting, E. C., “Large Displacement Transient Analysis of Flexible Structures,” Int. J. Num. Meth. Eng., 36, pp. 1541–1562 (1993).Google Scholar
35.Crisfield, M. A., Non-Linear Finite Element Analysis of Solids and Structures, 0John Wiley & Sons, England (1991).Google Scholar
36.Yang, Y. B., Yang, C. T., Chang, T. P. and Chang, P. K., “Effect of Member Buckling and Yielding on Ultimate Strengths of Space Trusses,” Eng. Struct., 19(2), pp. 179–191 (1997).CrossRefGoogle Scholar
37.Yang, Y. B. and Chiou, H. T., “Rigid Body Motion Test for Nonlinear Analysis with Beam Elements,” J. Engrg. Mech., ASCE, 113(9), pp. 1404–1419 (1987).Google Scholar
38.Abrate, S. and Sun, C. T., “Dynamic Analysis of Geometrically Nonlinear Truss Structures,” Comput. Struct., 17(4), pp. 491–497(1983).CrossRefGoogle Scholar
39.Noor, A. K. and Peters, J. M., “Nonlinear Dynamic Analysis of Space Trusses,” Comput. Meth. Appl. Mech. Engng. 21, pp. 131–151 (1980).CrossRefGoogle Scholar
40.Coan, C. H. and Plaut, R. H., “Dynamic Stability of a Lattice Dome,’ Earthquake. Engng. Struct. Dynam., 11, pp. 269–274 (1983).CrossRefGoogle Scholar
41.Kassimali, A. and Bidhendi, E., “Stability of Trusses Under Dynamic Loads,” Comput. Struct., 29(3), pp. 381–392 (1988).Google Scholar
42.Sllaats, P. M., de Jough, J. and Sauren, A. A. H., “Model Reduction Tools for Nonlinear Structural Dynamics,” Comput. Struct., 54(6), pp. 1155–1171 (1995).CrossRefGoogle Scholar
43.Zhu, K., Al-Bermani, F. G. A. and Kitipornchai, S. “Nonlinear Dynamic Analysis of Lattice Structures,” Comput. Struct., 52(1), pp. 9–15 (1994).Google Scholar
44.Tada, M. and Suito, A., “Static and Dynamic Post-Buckling Behavior of Truss Structures,” Eng. Struct., 20(4–6), pp. 384–389(1998).CrossRefGoogle Scholar
45.Walker, A. C. and Hall, D. G., “An Analysis of Large Deflections of Beams Using the Rayleigh-Ritz Finite Element Method,” Aeronautical Quarterly, pp. 357–367 (1968).CrossRefGoogle Scholar
46.Walker, A. C., “A Nonlinear Finite Element Analysis of Shallow Circular Arches,” Int. J. Solids Struct., 5, pp. 97–107(1969).CrossRefGoogle Scholar