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Nonlinearities in the Dynamics and Control of Space Structures: Some Issues for Computational Mechanics

  • S. N. Atluri
  • M. Iura
Part of the Springer Series in Computational Mechanics book series (SSCMECH)

Abstract

This article deals with nonlinearities that arise in the study of dynamics and control of highly flexible large-space-structures. Broadly speaking, these nonlinearities have various origins: (i) geometrical: due to large deformations and large rotations of these structures and their members; (ii) inertia: depending on the coordinate systems used in characterizing the overall dynamic motion as well as elastic deformations; (iii) damping: due to nonlinear hysterisis in flexible joints; viscoelastic coatings etc. , and (iv) material: due to the nonlinear behavior of the structural material. The geometrical and material nonlinearities affect the “tangent stiffness operator” of the structure; the inertia nonlinearities affect the “tangent inertia operator”.

Keywords

Axial Force Trial Function Tangent Stiffness Local Buckling Shallow Shell 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Atluri, S. N., and Murakawa, H. (1977) “On Hybrid Finite Element Models in Nonlinear Solid Mechanics” in Finite Elements in Nonlinear Mechanics (Eds. P. G. Bergan, et al) Tapir Press, Norway, Vol. 1, pp. 3–41.Google Scholar
  2. Atluri, S. N., and Grannel, J. J. (1978): Boundary Element Methods (BEM) and Combination BEM-FEM, Report GIT-ESM-SNA-78-16, Georgia Tech, 78 pp.Google Scholar
  3. Atluri, S. N., Gallagher, R. H., and Zienkiewicz, O. C. (Eds.) (1983) Hybrid and Mixed Finite Element Methods, J. Wiley & Sons.Google Scholar
  4. Atluri, S. N. (1984): “Alternate Stress and Conjugate Strain Measures, and Mixed Variational Formulations Involving Rigid Rotations, for Computational Analyses of Finitely Deformed Solids, with Application to Plate and Shell Theory” Computers & Structures, Vol. 18, No. 1, pp. 93–116.MathSciNetMATHCrossRefGoogle Scholar
  5. Atluri, S. N., Zhang, J-D., and O’Donoghue, P. E., (1986) “Analysis and Control of Finite Deformations of Plates and Shells: Formulations and Interior/Boundary Element Algorithms” in Finite Element Methods For Plate & Shell Structures, Vol. 2 Formulations & Algorithms (Eds. T. J. R. Hughes & E. Hinton), Pineridge Press, pp. 127-153.Google Scholar
  6. Bryson, A. E., and Ho, Y. (1975) Applied Optimal Control, Hemisphere Publishing Co. Washington.Google Scholar
  7. Crawley, E. F., and de Luis, J. (1984) “Use of Piezo-Ceramics as Distributed Acuators in Large Space Structures” Proc. 22nd AIAA Structures, Structural Dynamics, and Materials Conference, Lake Tahoe, Nevada.Google Scholar
  8. Crisfield, M. A. (1981) “A Fast Incremental/Iterative Solution Procedure That Handles Snap-Through”, Computers & Structures, Vol. 13, pp. 55–62.MATHCrossRefGoogle Scholar
  9. Fraeijis de Veubeke, B. (1972): “A New Variational Principle for Finite Elastic Displacements” Int. J. Engrg. Science, Vol. 10, pp. 745–763.CrossRefGoogle Scholar
  10. Im, S., and Atluri, S. N. (1987) “Force Transfer To a Beam-Column by a Piezo-Actuator in Conjunction with Nonlinear Control of Slender Structures”, Computers & Structures (In Press).Google Scholar
  11. Iura, M., and Atluri, S. N. (1986) “On a Consistent Theory, and Variational Formulation of Finitely Stretched and Rotated 3-D Space Curved Beams” Computational Mechanics (In Press).Google Scholar
  12. Iura, M., and Atluri, S. N. (1987): “Dynamic Analysis of Finitely Stretched and Rotated 3-D Space-Curved Beams” Computers & Structures (In Press).Google Scholar
  13. Kondoh, K., Tanaka, K., and Atluri, S. N. (1985) “A Method for Simplified Nonlinear Analysis of Large Space-Tresses and Frames, Using Explicitly Derived Tangent Stiffnesses, and Accounting for Local Buckling” U. S. Air Force Wright Aero Labs, AFFDL-TR-85-3079, 171 pp.Google Scholar
  14. Kondoh, K., and Atluri, S. N. (1985a) “Influence of Local Buckling on Global Instability: Simplified, Large Deformation, Post-Buckling Analysis of Plane Trusses” Computers & Structures, Vol. 21, No. 4, pp. 613–627.MATHCrossRefGoogle Scholar
  15. Kondoh, K., and Atluri, S. N. (1985b) “A Simplified Finite Element Method for Large Deformation, Post-Buckling Analyses of Large Frame Structures, Using Explicitly Derived Tangent Stiffness Matrices” Int. Jnl. for Num. Meth. in Engg., Vol. 23, pp. 69–90.MathSciNetCrossRefGoogle Scholar
  16. Kondoh, K., Tanaka, K., and Atluri, S. N. (1986) “An Explicit Expression for Tangent Stiffnesses of a Finitely Deformed 3-D Beam and its Use in the Analysis of Space Frames” Computers & Structures, Vol. 24, No. 2, pp. 253–272.MATHCrossRefGoogle Scholar
  17. Kondoh, K., and Atluri, S. N. (1987) “Large-Deformation, Elasto-Plastic Analysis of Frames Under Non-Conservative Loading, Using Explicitly Derived Tangent Stiffness Based on Assumed Stresses” Computational Mechanics, Vol. 2, No. 1, pp. 1–25.MATHCrossRefGoogle Scholar
  18. Laub, A. J. (1979) “A Shur Method for Solving Algebraic Riccati Equations” IEEE Transactions on Automatic Control. Vol. AC-24, pp. 913–921.MathSciNetCrossRefGoogle Scholar
  19. Noor, A. K., and Mikulas, M. M. (1987) “Continuum Modeling of Large Lattice Structures-Status and Projections” in Large Space Structures: Dynamics & Control (Eds: S. N. Atluri and A. K. Amos), Springer-Verlag (this volume).Google Scholar
  20. O’Donoghue, P. E. (1985) “Boundary Integral Equation Approach to Nonlinear Response Control of Large Space Structures: Alternating Technique Applied to Multiple Flaws in Three-Dimensional Bodies” Ph. D. Thesis, Georgia Tech, 232 pages.Google Scholar
  21. O’Donoghue, P. E., and Atluri, S. N. (1986) “Control of Dynamic Response of a Continuum Model of a Large Space Structure” Computers & Structures, Vol. 23, pp. 199–211.MATHCrossRefGoogle Scholar
  22. O’Donoghue, P. E., and Atluri, S. N. (1987) “Field/Boundary Element Approach to the Large Deflection of Thin Plates” Computers & Structures, Vol. 27, No. 3, pp. 427–435.MATHCrossRefGoogle Scholar
  23. Punch, E. F., and Atluri, S. N. (1985) “Large Displacement Analysis of Plates by a Stress-Based Finite Element Approach” Computers & Structures, Vol. 24, No. 1, pp. 107–117.CrossRefGoogle Scholar
  24. Reissner, E. (1973) “On a One-Dimensional Large-Displacement Finite-Beam Theory” Studies in Applied Math., Vol. 52, pp. 87–95.MATHGoogle Scholar
  25. Reissner, E. (1981) “On Finite Deformations of Space-Curved Beams” J. Appl. Math. Physics (ZAMP), Vol. 32, pp. 734–744.MATHCrossRefGoogle Scholar
  26. Riks, E. (1972) “The Application of Newton’s Method to the Problem of Elastic Stability” J. Applied Mech., Vol. 39, pp. 1060–1066.MATHCrossRefGoogle Scholar
  27. Shi, G. Y., and Atluri, S. N. (1987) “Elasto-Plastic Large Deformation Analysis of Space-Frames: A Plastic-Hinge and Stress-Based Explicit Derivation of Tangent Stiffness” Int. Jrl. for Num. Meth. in Engg. (In Press).Google Scholar
  28. Simo, J. C., and Vu-Quoc, L. (1986) “A Three-Dimensional Finite-Strain Rod Model. Part II: Computational Aspects” Comp. Meth. Appl. Mech. & Engg., Vol. 58, pp. 79–116.MATHCrossRefGoogle Scholar
  29. Tanaka, K., Kondoh, K., and Atluri, S. N. (1985) “Instability Analysis of Space Trusses Using Exact Tangent Stiffness Matrices” Finite Elements in Analysis & Design, Vol. 1, pp. 291–311.MATHCrossRefGoogle Scholar
  30. Timoshenko, S. P., and Gere, J. M. (1961) Theory of Elastic Stability 2nd ed., McGraw-Hill, N. Y., pp. 76–82.Google Scholar
  31. Zhang, J-D., and Atluri, S. N. (1986a) “A Boundary/Interior Element Method for Quasi-static and Transient Response Analyses of Shallow Shells” Computers & Structures, Vol. 24, pp. 213–224.MATHCrossRefGoogle Scholar
  32. Zhang, J-D., and Atluri, S. N. (1986b) “Nonlinear Quasi-static and Transient Response Analyses of Shallow Shells: Formulations and Interior/Boundary Element Algorithms” in Boundary Elements (Ed: Q. Du) Pergamon Press, Oxford, pp. 87–110.Google Scholar
  33. Zhang, J-D. (1987) “Nonlinear Dynamic Analysis and Optimal Control of Shallow Shells by the Field-Boundary-Element Approach” Ph. D. Thesis, Georgia Tech, 190 pages.Google Scholar
  34. Zhang, J-D., and Atluri, S. N. (1987) “Post-Buckling Analysis of Shallow Shells by the Field-Boundary-Element Method” Int. Jrl. for Num. Meth. in Engg. (In Press).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • S. N. Atluri
    • 1
  • M. Iura
    • 1
  1. 1.Center for the Advancement of Computational MechanicsGeorgia Institute of TechnologyAtlantaUSA

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