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Analysis Methods for Spatial Structures

  • M. Papadrakakis
Conference paper
Part of the Lecture Notes in Engineering book series (LNENG, volume 26)

Abstract

A state-of-the-art survey of all trends and applications developed for the static analysis of spatial structures is presented. Emphasis is given to the numerical matrix structural analysis approach for treating geometric and material nonlinearities. The behavior of members considered either pin-jointed or end-restrained in the inelastic post-buckling range is described and the response of a 3-D beam element in a large displacement environment is discussed. Numerical techniques for the solution of the resulting linear and nonlinear systems of equations as well as for tracing the nonlinear response near limit points are also discussed.

Keywords

Beam Element Space Structure Space Frame Apply Science Publisher Nonlinear Finite Element Analysis 
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. 1.
    Dean, D.L., “Discrete Field Analysis of Structural System” CISM Courses and Lectures, No 203, Udine, Italy, Springer-Verlag, Wien, 1976.Google Scholar
  2. 2.
    Dean, D.L., and Avent, R.R., “State of the Art Discrete Field Analysis of Space Structures, “Proc. of the 2nd Int. Conf. on Space Structures, Guilford, England, 1975, pp. 7–16.Google Scholar
  3. 3.
    Heki, K., and Fujitani, Y., “The Stress Analysis of Grids under the Action of Bending and Shear”, Space Structures, Blackwell Publ., Oxford, 1967, pp. 33–43.Google Scholar
  4. 4.
    Renton, J.D., “On the Gridword Analogy for Plates”, J. of the Mech. and Phys. of Solids, Vol. 13, 1965, pp. 413–420.ADSCrossRefGoogle Scholar
  5. 5.
    Fluge, W., “Stresses in Shells”, Springer-Verlag, Berlin, 1962, pp. 293–307.Google Scholar
  6. 6.
    Heki, K., “The Effect of Shear Deformation on Double Layer Lattice plates and Shells, Proc. of the 2nd Int. Conf. on Space Structures, Guilford, England, 1975, pp. 189–198.Google Scholar
  7. 7.
    Saka, T., and Heki, K., “The Effect of Joint on the Strength of Space Trusses”, Third Int. Conf. on Space Structures, Guilford, England, H. Nooshin ed., Applied Science Publishers Ltd., London, 1984, pp. 417–422.Google Scholar
  8. 8.
    Wright, D.T., “Membrane Forces and Buckling in Reticulated Shells” J. of the Str. Div., ASCE, Vol. 21, No. ST1, 1965, pp. 173–201.Google Scholar
  9. 9.
    Forman, S.E., and Hutchinson, J.W., “Buckling of Reticulated Shell Structures”, Int.J.of Solids and Str. Vol. 6, 1970, pp. 909–932.CrossRefGoogle Scholar
  10. 10.
    Cohn, M.Z., Ghosh, S.K., and Parimi, S.R., “Unified Approach to Theory of Plastic Structures”, J. of the Eng. Mech. Div. ASCE, Vol. 98, No. EM5, 1972, pp. 1133–1158.Google Scholar
  11. 11.
    Grierson. D.E., and Abdel-Baset, S.B., “Plastic Analysis under Combined Stresses”, J. of the Eng. Mech. Div., ASCE, Vol.103, No.EM5 1977,pp.837–854.Google Scholar
  12. 12.
    Watwood, V.B., “Mechanism Generation for Limit Analysis of Frames”, J. of the Str. Div., ASCE, Vol. 109, ST1, 1978, pp. 1–15.Google Scholar
  13. 13.
    Higginbotham, A.B., and Hanson, R.D., “Axial Hysteretic Behavior of Steel Members”, J. of the Str. Div. ASCE, Vol. 102, No. ST7, 1975, pp. 1365–1381.Google Scholar
  14. 14.
    Nonaka, T., “An Elastic-Plastic Analysis of a Bar under Repeated Axial Loading”, Int. J. of Solids and Str., Vol. 9, 1973, pp. 569–580.MATHGoogle Scholar
  15. 15.
    Papadrakakis, M., and Loukakis, K., “Inelastic Cyclic Analysis of Imperfet Columns with End Restraints”, Submitted for Publication.Google Scholar
  16. 16.
    Prathuangsit, D., Goel, S.C., and Hanson, R.D., “Axial Hysteresis Behavior with End Restraints”, J. of the Str. Div., ASCE, Vol. 104, No. ST6, 1978, pp.883–898.Google Scholar
  17. 17.
    Supple, W.J., and Collins, I., “Post-Critical Behaviour of Tubular Struts”, Engineering Structures, Vol. 2, Oct. 1980, pp. 225–229.CrossRefGoogle Scholar
  18. 18.
    Toma, S., and Chen, W.F., “Inelastic Cyclic Analysis of Pin-Ended Tubes”, J. of Str. Div. ASCE, Vol. 108, No. ST10, 1982, pp. 2279–2293.Google Scholar
  19. 19.
    Wakabayashi, M., Matsui, C., and Mitani, I., “Cyclic Behavior of a Restrained Steel Brace under Axial Loading”, Proc. of the 6th, World Conference on Earthquake Enging. New Delhi, 1977, pp. 3181–3187.Google Scholar
  20. 20.
    Argyris, J.H., et al., “Finite Element Analysis to Two-and Three-Dimensional Elastro-Plastic Frames”. -The Natural Approach”, Comp. Meth.in Appl. Mech. and Enging. Vol. 35, 1982, pp. 221–248.ADSMATHCrossRefGoogle Scholar
  21. 21.
    Cichon, C., “Large Displacements in-Plane Analysis of Elastic-Plastic Frames”, Comp, and Str., Vol. 19, No. 5/6, 1984, pp. 737–745.MATHCrossRefGoogle Scholar
  22. 22.
    El-Zanaty, M.H., and Murray, D.W., “Nonlinear Finite Element Analysis of Steel Frames”, Journal of Structural Engineering, ASCE, Vol. 109, No. 2 1983, pp. 353–368.CrossRefGoogle Scholar
  23. 23.
    Fujimoto, et al., “Nonlinear Analysis for K-Type Braced Steel Frames”, Transactions, Architectural Institute of Japan, No. 209, July, 1973, pp. 41–51, (in Japanese).Google Scholar
  24. 24.
    Kassimali, A., “Large Deformation Analysis of Elastic Plastic Frames”, J. of Str., ASŒ, Vol. 109, No. 8, 1983, pp. 1869–1886.CrossRefGoogle Scholar
  25. 25.
    Madi, U.R., and Smith, D.L., “A Finite Element Model for Determining the Constitutive Relation of a Compression Member”, Third Int. Conf. on Space Structures, Guilford, England, H. Nooshin ed., Applied Science Publishers Ltd., 24. London, 1984, pp. 625–629.Google Scholar
  26. 26.
    Wakabayashi, M., and Shibata, M., “Studies on the Post-Buckling Behavior of Braces”, Part 4, Abstracts Annual Meeting Kinki Branch, Architectural Institute of Japan, 1976, p. 201.Google Scholar
  27. 27.
    Chen, W.F., and Sugimoto, H., “Inelastic Cyclic Behavior of Tubular Members in Offshore Structures”, Proc. of the 8th World Conf. on Earthquake Engng., San Francisco, 1984.Google Scholar
  28. 28.
    Shibata, M., “Analysis of Elastic-Plastic Behavior of a Steel Brace subjected to Repeated Axial Force”, Int. J. of Solids and Str. Vol. 18, No. 3, 1982, pp. 217–228.MATHCrossRefGoogle Scholar
  29. 29.
    Toma, S., and Chem, W.F., “Cyclic Analysis of Fixed-Ended Steel Beam-Columns”, J. of Str. Div. ASCE, Vol. 108, No. ST6, 1982, pp. 1385–1399.Google Scholar
  30. 30.
    Nonaka, T., “An Analysis of Large Deformation of an Elastic-Plastic Bar under Repeated Axial Loading”, Int.J.of Mech. Sci.,Vol. 19, 1977, pp. 619–638.MATHCrossRefGoogle Scholar
  31. 31.
    Papadrakakis, M., and Chrysos, L., “Inelastic Cyclic Analysis of Imperfect Columns”, J. of Str. Engng., ASCE, Vol. 111, No. 6, 1985.Google Scholar
  32. 32.
    Smith, E.A., and Epstein, H.I., “Hartford Coliseum Roof Collapse: Structural Collapse Sequence and Lessons Learned”, Civil Engng. ASCE, April. 1980,pp.59–62.Google Scholar
  33. 33.
    Toma, S., and Chem. W.F., “Post-Buckling Behavior of Tubular Beam-Columns”, J. of Str. Engng., Vol. 109, No. 8, 1983, pp. 1918–1932.CrossRefGoogle Scholar
  34. 34.
    Schmidt, L.C., Morgan, P.R., and Clarkson, J.A., “Space Trusses with Brittle-Type Strut Buckling”, J. of Str. Engng. ASCE, Vol. 102, No.ST7, 1976,pp.1479–1492.Google Scholar
  35. 35.
    Suzuki, T., Kubodera, I., and Ogawa, T., “An Experimental Study on Load-Bearing Capacity”, Third Int. Conf. on Space Structures, Guilford, England, H. Nooshin, ed., Applied Science Publishers, Ltd., London, 1984, pp. 571–576.Google Scholar
  36. 36.
    Schmidt L.C., Gregg, B.M., “A Method for Space Truss Analysis in the Post-Buckling Range”, Int. J. for Num. Methods in Engng. Vol. 15, 1980, pp. 237–247.MATHCrossRefGoogle Scholar
  37. 37.
    Singh, P., and Goel, S.C., “Hysteresis Model of Bracing Members for Earthquake Response of Braced Frames”, Proc. of the 6th World Conf. on Earthquake Engng., New Delhi, Vol. 11, Jan. 1977, pp. 43–48.Google Scholar
  38. 38.
    Wakabayashi, M., et al., “Hysteretic Behavior of Steel Braces Subjected to Horizontal Load due to Earthquake”, Proc. of the 6th, World Conf. on Earthquake Engng., New Delhi, 1977, pp. 3188–3194.Google Scholar
  39. 39.
    Maison, B.F., and Popov, E., “Cyclic Response Prediction for Braced Steel Frames”, J. of the Str. Div., ASCE, Vol. 106, No. ST7, 1980, pp. 1401–1416.Google Scholar
  40. 40.
    Roeder, C., and Popov, E., “Inelastic Behavior of Eccentrically Braced Steel Frames under Cyclic Loadings”, Report No. UCB/EERC-77/18, Univ. of California, Berkeley, Aug. 1977.Google Scholar
  41. 41.
    Bathe, K.-J., “Finite Element Procedures in Engineering Analysis”, Prentice-Hall, Inc., New Jersey, 1982.Google Scholar
  42. 42.
    Bathe, K.-J., and Bolourchi, S., “Large Displacement Analysis of Three-Dimensional Beam Structures”, Int. J. for Num. Methods in Engng., Vol. 14, 1979, pp.961–986.MATHCrossRefGoogle Scholar
  43. 43.
    Argyris, J.H., et al. “Finite Element Method -The Natural Approach” Comp. Meth. in Appl. Msch. and Engng., Vol. 17/18, 1979, pp. 1–106.ADSCrossRefGoogle Scholar
  44. 44.
    Oran, C, “Tangent Stiffness in Space Frames”, J. of the Str. Div., ASCE, Vol. 99, No. ST6, 1973, pp. 987–1001.Google Scholar
  45. 45.
    Bathe, K.-J., and Ozdemir, H., “Elastic-Plastic Large Deformation Static and Dynamic Analysis”, Comp. and Str., Vol. 6, 1976, pp. 81–92.MATHCrossRefGoogle Scholar
  46. 46.
    Wen, R.K., and Rahimzadeh, J., “Nonlinear Elastic Frame Analysis by Finite Element”, J. of Str. Engng., ASCE, Vol. 109, No. 8, 1983, pp. 1952–1971.CrossRefGoogle Scholar
  47. 47.
    Wood, R.D., and Zienkiewicz O.C., “Geometrically Nonlinear Finite Element Analysis of Beams, Frames, Arches and Axisymmetric Shells”, Comp. and Str. Vol. 7, 1977, pp. 725–735.MathSciNetMATHCrossRefGoogle Scholar
  48. 48.
    Remseth, S.N., “Nonlinear Static and Dynamic Analysis of Framed Structures”, Comp. and Str., Vol. 10, 1979, pp. 879–897.MATHCrossRefGoogle Scholar
  49. 49.
    Boswell, L.F., “A Small Strain Large Rotation Theory and Finite Element Formulation of Thin Curved Lattice Members”, Third Int. Conf. on Space Structures, Guilford, England, H. Nooshin, ed., Applied Science Publishers Ltd., London, 1984, pp. 375–380.Google Scholar
  50. 50.
    Tang, S.C., Yeung, K.S., and Chon, C.T., “On the Tangent Stiffness Matrix in a Convected Coordinate System”, Comp, and Str.,Vol. 12, 1980, pp. 849–856.MATHCrossRefGoogle Scholar
  51. 51.
    Kani, I.M., McConnel, R.E., and See, T., “The Analysis and Testing of a Single Layer, Shallow Braced Dome”, Third Int. Conf. on Space Structures, Guilford, England, H. Nooshin ed., Applied Science Publishers, London, 1984, pp. 613–618.Google Scholar
  52. 52.
    Jain, A.K., Goel, S.C., and Hanson, R.D., “Inelastic Response of Restrained Steel Tubes”, J. of the Str. Div., ASCE, Vol. 104, No. ST6, 1978, pp. 897–910.Google Scholar
  53. 53.
    Papadrakakis, M., “A Family of Methods with Three-Term Recursion Formulae”, Int. J. for Num. Methods in Engng.,Vol. 18, 1982, pp. 1785–1799.MathSciNetMATHCrossRefGoogle Scholar
  54. 54.
    Engeli, M., et al., “Refined Iterative Methods for Computation of the Solution and the Eigenvalues of Self-Adjoint Boundary Value Problems”, Birkhauser Verlag, Basel/Stuttgart, 1959.Google Scholar
  55. 55.
    Matthies, H., and Strang, G., “The Solution of Nonlinear Finite Element Equations”, Int. J. for Num. Methods in Engng. Vol. 14, 1979, pp. 1613–1626.MathSciNetMATHCrossRefGoogle Scholar
  56. 56.
    Crisfield, M.A., “A Faster Modified Newton-Raphson Iteration” Comp. Meth. in Appl. Mech. and Engng., Vol. 20, 1979, pp. 267–278.MathSciNetADSMATHCrossRefGoogle Scholar
  57. 57.
    Crisfield, M.A., “Incremental/Iterative Solution Procedures for Non-Linear Structural Analysis”, Numerical Methods for Nonlinear Problems, C. Taylor, E. Hinton, and D.R.J. Owen, eds., Pineridge Press, Swansea U.K., 1980, pp.261–290.Google Scholar
  58. 58.
    Irons, B., and Elsawaf, A., The Conjugate-Newton Algorithm for Solving Finite Element Equations”, Proc. U.S. -German Symposium on Formulations and Algorithms in Finite Element Analysis, K.-J. Bathe, J.T. Oden, and W. Wunderlich, eds., MIT press, 1977, pp. 656–672.Google Scholar
  59. 59.
    Gambolati, G., “Fast Solution to Finite Element Flow Equations by Newton Iteration and Modified Conjugate Gradient Method”, Int. J. for Num. Meth. in Engng., Vol. 15, 1980. pp. 661–675.ADSMATHCrossRefGoogle Scholar
  60. 60.
    Buckley, A.G., “A Combined Conjugate-Gradient Quasi-Newton Minimization Algorithm”, Math. Progr., Vol. 15, 1978, pp. 200–210.MathSciNetMATHCrossRefGoogle Scholar
  61. 61.
    Jennings, A., and Malik, G.M., “The Solution of Sparse Linear Equations by the Conjugate Gradient Method”, Int. J. for Num. Meth. in Engng., Vol. 12, 1978, pp. 141–158.MathSciNetMATHCrossRefGoogle Scholar
  62. 62.
    Papadrakakis, M., “Accelerating Vector Iteration Methods”, J. of Appl. Mech., ASME, Vol. 53, 1986, pp. 291–297.MathSciNetADSMATHCrossRefGoogle Scholar
  63. 63.
    Bathe, K.-J., and Dvorkin, E., “On the Automatic Solution of Nonlinear Finite Element Equations”, Comp. and Str., Vol. 17, No. 5–6, 1983, pp. 871–879.CrossRefGoogle Scholar
  64. 64.
    Geradin, M., Idelsohn, S., and Hogge, M., “Computational Strategies for the Solution of Large Nonlinear Problems via Quasi-Newton Methods”, Computers and Structures”, Vol. 13, 1981, pp. 73–81.MathSciNetMATHCrossRefGoogle Scholar
  65. 65.
    Crisfield, M.A., “An Arc-Length Method Including Line Searches and Accelerations”, Int. J. for Num. Meth.in Engng., Vol. 19, 1983, pp. 1269–1289.MATHCrossRefGoogle Scholar
  66. 66.
    Wright, E.W., Gaylord, E.H., “Analysis of Unbraced Multi-Story Steel Rigid Frames”, J. of the Str. Div., ASCE, Vol. 94, 1968, pp. 1143–1163.Google Scholar
  67. 67.
    Bergan, P.G., “Solution Algorithms for Nonlinear Structural Problems”, Proc. of the Conf. on Engng. Applies, of the Finite Element Method”, Høvik, Norway 1979, published by A.S. Computas.Google Scholar
  68. 68.
    Argyris, J.H., “Continua and Discontinua, Matrix Methods in Structural Mechanics”, Proc. of the Conf. on Matrix Methods, Wright-Patters on Air Force Base, Ohio 1965.Google Scholar
  69. 69.
    Riks, E., “The Application of Newton’s Method to the Problem of Elastic Stability”, J. of Appl. Mech., Vol. 39, 1972, pp. 1060–1066.ADSMATHCrossRefGoogle Scholar
  70. 70.
    Wempner, G.A., “Discrete Approximations Related to Nonlinear Theories of Solids”, Int. J. of Solids and Str., Vol. 7, 1971, pp. 1581–1599.MATHCrossRefGoogle Scholar
  71. 71.
    Crisfield, M.A. “A Fast Increamental/Iterative Solution Procedure that handles “Snap-Through”, Comp. and Str., Vol. 13, 1981, pp. 55–62.MATHCrossRefGoogle Scholar
  72. 72.
    Park, K.C., “A Family of Solution Algorithms for Nonlinear Structural Analysis Based on Relaxation Equations”, Int. J. for Num. Methods in Engng., Vol. 18, 1982, pp. 1337–1347.MATHCrossRefGoogle Scholar
  73. 73.
    Bergan, P.G., “Solution Algorithms for Nonlinear Structural Problems”, Comp, and Str., Vol. 12, 1980, pp. 497–509.MathSciNetMATHCrossRefGoogle Scholar
  74. 74.
    Fried, I., Orthogonal Trajectory Accession to the Nonlinear Equilibrium Curve”, “Comp. Meth. in Appl. Mech. and Engng., Vol. 47, 1984, pp. 283–297.MathSciNetADSCrossRefGoogle Scholar
  75. 75.
    Noor, A.K., and Peters, J.M., “Tracing Post-Limit-Point Paths with Reducedn Basis Technique”, Comp. Meth. in Appl. Mech. and Engng., Vol. 28, 1981, pp.217–240.ADSMATHCrossRefGoogle Scholar
  76. 76.
    Powell, G., and Simons, J., “Improved Iteration Strategy for Nonlinear Structures”, Int. J. for Num. Meth. in Engng., Vol. 17, 1981, pp. 1455–1467.MATHCrossRefGoogle Scholar
  77. 77.
    Riks, E., “An Incremental Approach to the Solution of Snapping and Buckling Problems”, Computers and Structures, Vol. 15, 1979, pp. 259–551.MathSciNetGoogle Scholar
  78. 78.
    Waszczyszyn, Z., “Numerical Problems of Nonlinear Stability Analysis of Elastic Structures”, Comp. and Str., Vol. 17, No. 1, 1983, pp. 13–24.MathSciNetMATHCrossRefGoogle Scholar
  79. 79.
    Klimke, H., and Posch, J., “A Modified Fictitius Force Method for the Ultimate Load Analysis of Space Trusses”, Third Int. Conf. on Space Structures, Guilford, England, H. Nooshin, ed., Applied Science Publishers, London, 1984, pp. 589–593.Google Scholar
  80. 80.
    Papadrakakis, M., “Inelastic Post-Buckling Analysis of Trusses”, Journal of Structural Engineering, ASCE, Vol. 109, No. 9, 1983, pp. 2129–2147.CrossRefGoogle Scholar
  81. 81.
    Smith, E.A., “Space Truss Nonlinear Analysis”, J. of Str. Engng., ASCE, Vol. 110, No. 4, 1984, pp. 688–705.CrossRefGoogle Scholar
  82. 82.
    Cichon, C., “Stability Analysis of Elastic Space Trusses”, Third Int. Conf. on Space Structures, Guilford, England, H. Nooshin ed., Applied Science Publishers Ltd, London, 1984, pp. 567–570.Google Scholar
  83. 83.
    McConnel, R.E., and Klimke, H., “Geometrically Nonlinear Pin-Jointed Space Frames”, Numerical Methods for Nonlinear Problems,Vol. 1, C. Taylor, E. Hinton, and D.R.J. Owen, eds., Pineridge Press, Swansea, 1980, pp. 333–342.Google Scholar
  84. 84.
    Bathe, K.-J., Ramm, E., and Wilson, E.L., “Finite Element Formulations for Large Deformation Dynamic Analysis”, Int. J. for Num. Meth. in Enging., Vol. 9, pp. 353–386, 1975.MATHCrossRefGoogle Scholar
  85. 85.
    Ramm, E., “Strategies for tracing nonlinear responses near limit points” in Nonlinear Finite Element Analysis in Structural Mechanics, Wunderlich, Stein, Bathe, eds, Springer -Verlag, 1981.Google Scholar
  86. 86.
    Hangai, Y., and Kawamata, S., Nonlinear Analysis of Space Frames and Snap -Through Buckling of Reticulated Shell Structures”, Proceedings, 1971 IASS Pacific Symposium on Tension Structures and Space Frames, Architectural Institute of Japan, Tokyo, 1972, pp. 803–816.Google Scholar
  87. 87.
    Bergan, P.G., and Søreide, T., “A Comparative Study of Different Numerical Solution Techniques as Applied to a Nonlinear Structural Problem”, Computer Methods in Applied Mechanics and Engineering, Vol. 2, 1973, pp. 185–201.ADSMATHCrossRefGoogle Scholar
  88. 88.
    Papadrakakis, M., “Post-Buckling Analysis of Spatial Structures by Vector Iteration Methods” Computers and Structures, Vol. 14, No. 5–6, 1981,pp. 393–402.MATHCrossRefGoogle Scholar
  89. 89.
    Jagannathan, D., Epstein, H.I., and Christiano, P., “Nonlinear Analysis of Reticulated Space Trusses”, Journal of the Structural Division, ASCE, Vol. 101, No. ST12, pp. 2641–2658.Google Scholar
  90. 90.
    Rothert, H., Dickel, T., and Renner D., “Snap-’Ihrough Bucklingof Reticulated Space Trusses”, Journal of the Structural Division, ASCE, Vol. 107, 1981, pp. 129–143.Google Scholar
  91. 91.
    Paradiso, M., and Tempesta, G., “Member Buckling Effects in Nonlinear Analysis of Space Trusses”, Numerical Methods for Nonlinear Problems, Vol. 1, C. Taylor, E. Hilton, and D.R.J. Owen eds., Pineridge Press, Swansea, 1980, pp. 395–405.Google Scholar
  92. 92.
    Watson, L.T., and Holzer, S.M., “Quadratic Convergence of Crisfielďs Method”, Computers and Structures, Vol. 17, No. 1, 1983, pp. 69–72.MATHCrossRefGoogle Scholar
  93. 93.
    Meek, J.L., and Tan, H.S., “Geometrically Nonlinear Analysis of Space Frames by an Incremental Iterative Technique”, Computer Methods in Applied Mechanics and Engineering, Vol. 47, 1984, pp. 261–282.ADSMATHCrossRefGoogle Scholar
  94. 94.
    Schmidt, L.C., Morgan P.R., and Hanaor, A., “Ultimate Load Testing on Space Trusses”, Journal of the Structural Division, ASCE, Vol. 108, No. ST6, 1982, 1324–1335.Google Scholar
  95. 95.
    Griggs, H.P., “Experimental Study of Instability in Elements of Shallow Space Frames”, Research Report, Department of Civil Engineering, MIT, Cambridge, MA, 1966.Google Scholar
  96. 96.
    Chu, K.H., and Rampetsreiter, R.H., “Large Deflection Buckling of Space Frames”, Journal of the Structural Division, ASCE, Vol. 98, No. ST12, 1972, pp.2701–2722.Google Scholar
  97. 97.
    Connor, J.J., Logcher, D., and Chan, S.C., “Nonlinear Analysis of Elastic Framed Structures”, Journal of the Structural Division, ASCE ,Vol. 94, No. ST6, 1968, pp. 1525–1547.Google Scholar
  98. 98.
    Brendel, B., and Ramm, E., “Stabilitätsuntersuchungen Weitgespannter Tragwerke mit der Methode der Finiten Elemente”, Proceedings of the International Symposium on Wide Span Surface Structures, Universität Stuttgart, 1976.Google Scholar
  99. 99.
    Papadrakakis, M., and Ghionis, P., “Conjugate Gradient Algorithms in Nonlinear Structural Analysis Problems”, Computer Methods in Applied Mechanics and Engineering, to be Published.Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1987

Authors and Affiliations

  • M. Papadrakakis
    • 1
  1. 1.Institute of Structural AnalysisNational Technical UniversityAthensGreece

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