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Nonlinear Stability of Structures

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 342))

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Abstract

Thermoelastic stability of heated trusses is of technical interest for the design of e.g. space structures. These space structures are in general subjected to high temperature gradients due to intense heating by the sun and cooling in the shadow. When the deformations of such structures are constrained, then buckling may occur which leads to local or global instabilities associated with large undesirable deflections.

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References

  • T. Belytschko, J. S.-.I. Ong, W. K. Liu, J. M. Kennedy, Hourglass control in linear and nonlinear problems, Comp. Meth. Appl. Mech. Eng. 43 (1984), 251–276

    Article  MATH  Google Scholar 

  • B. A. Boley, J. H. Weiner, Theory of thermal stresses, Wiley, New York, 1960

    MATH  Google Scholar 

  • R. de Borst, P. P.J.M. Peeters, Analysis of concrete structures under thermal loading, Comput. Meths. Appl. Mech. Engrg. 77 (1989) 293–310

    Article  MATH  Google Scholar 

  • J. P. Carter, J. R. Booker, Finite element analysis of coupled thermoelasticity, Coin-put. & Structures 31 (1989) 73–80

    Article  Google Scholar 

  • S. Cescotto, G. Fonder, A finite element approach for large strains of nearly incompressible rubber-lide materials, Int. J. of Solids Si Struct. 15 (1979) 589–605

    Article  MATH  Google Scholar 

  • P. Chadwick, R. W. Ogden, On the definition of elastic moduli, Arch. Rat. Mech. Anal. 44 (1971) 41–53

    MATH  MathSciNet  Google Scholar 

  • P. Chadwick, R. W. Ogden, A theorem of tensor calculus and its applications to isotropic elasticity, Arch. Rat. Mech. Anal. 44 (1971) 54–68

    MATH  MathSciNet  Google Scholar 

  • T. F. Chan, Deflation techniques and block-elimination algorithms for solving bordered singular systems, SIAM J. Sci. Stat. Comput. 5 (1984) 121–134

    Article  MATH  Google Scholar 

  • P. G. Ciarlet, Mathematical elasticity, Volume I, North-Holland, Amsterdam, 1988

    MATH  Google Scholar 

  • M. A. Crisfield, A fast incremental/iterative solution procedure that handles snap through, Comput. & Structures 13 (1981) 55–62

    Article  MATH  Google Scholar 

  • K. Dorninger, F. G. Rammerstorfer, A layered composite shell element for elastic and thermoelastic stress and stability analysis at large deformations, Internat..I. Numer. Meths. Engrg. 30 (1990) 291–306

    Article  Google Scholar 

  • G. Duffett, Some aspects of the numerical solution of equilibrium problems in finite elasticity, Ph.D. Dissertation, University of Cape Town, 1985

    Google Scholar 

  • G. Duffett, B. D. Reddy, The analysis of incompressible hyperelastic bodies by the finite element method, Comp. Meth. Appl. Mech. Engng. 41 (1983) 105–120

    Article  MATH  MathSciNet  Google Scholar 

  • G. Engeln-Müllges, F. Reuter, Formelsammlung zur numerischen Mathematik mit FORTRAN-Programmen, BI Wissenschaftsverlag, 1990

    Google Scholar 

  • B. E. Gatewood, Thermal stresses, McGraw-Hill, New York, 1957

    MATH  Google Scholar 

  • F. Gruttmann, R. L. Taylor, Theory and finite element formulation of rubberlike membrane shells using principal stretches, Internat. J. Numer. Meths. Engrg. 35 (1992), 1111–1126

    Article  MATH  Google Scholar 

  • D. M. Haughton, R. W. Ogden, Bifurcation of inflated circular cylinders of elastic material under axial loading–I. membrane theory for thin-walled tubes, J. Mech. Phys. Solids 27 (1979), 179–212

    Article  MATH  MathSciNet  Google Scholar 

  • D. M. Haughton, R. W. Ogden, Bifurcation of inflated circular cylinders of elastic material under axial loading–II. exact theory for thick-walled tubes, J. Mech. Phys. Solids 27 (1979), 489–512

    Article  MATH  MathSciNet  Google Scholar 

  • R. Hill, On uniqueness and stability in the theory of finite elastic strain, J. of the Mech. and Phys. 5 (1957), 229–241

    Article  MATH  Google Scholar 

  • R. Hill, Uniqueness in general boundary-value problems for elastic or inelastic solids, J. of the Mech. and Phys. 9 (1961), 114–130

    Article  MATH  Google Scholar 

  • R. Hill, Uniqueness criteria and extremum principles in self-adjoint problems of continuum mechanics, J. of the Mech. and Phys. 10 (1962), 185–194

    Article  MATH  Google Scholar 

  • H. B. Keller, Numerical solution of bifurcation and nonlinear eigenvalue problems, in P. Rabinowitz (ed.): Application of bifurcation theory, Academic Press, New York, 1977, 359–384

    Google Scholar 

  • R. S. Martin, J. H. Wilkinson, Similarity reduction of a general matrix to Hessenberg form, Numerische Mathematik 12 (1968) 349–368

    Article  MATH  MathSciNet  Google Scholar 

  • C. Miehe, Zur numerischen Behandlung thermomechanischer Prozesse, Bericht-Nr. F88/6, Institut für Baumechanik und Numerische Mechanik, Universität Hannover, 1988

    Google Scholar 

  • T. H. Miller, A finite element study of instabilities in rubber elasticity, Ph.D. Dissertation, The University of Texas at Austin, Texas, 1982

    Google Scholar 

  • I. Müller, On the stability of a biaxially-loaded rubber sheet, Proceedings 5. Int. Conference on Waves and Stability in Continuum Mediums, 1989, World Scientific, 1992

    Google Scholar 

  • A. Needleman, Inflation of spherical rubber balloons, Int. J. Solids Structures 13 (1977) 409–421

    Article  Google Scholar 

  • J. L. Nowinski, Theory of thermoelasticity with applications, Sijthoff andNoordhoff, Alphen aan den Rijn, The Netherlands, 1978

    Book  Google Scholar 

  • R. W. Ogden, Large deformation isotropic elasticity–on the correlation of theory and experiment for incompressible rubberlike solids, Proc. R. Soc. Lond. A. 326 (1972) 565–584

    Article  MATH  Google Scholar 

  • R. W. Ogden, Large deformation isotropic elasticity: on the correlation of theory and experiment for incompressible rubberlike solids, Proc. R. Soc. Lond. A. 328 (1972) 567–583

    Article  MATH  Google Scholar 

  • R. W. Ogden, Non-linear elastic deformations, Ellis Horwood, Chichester, 1984

    Google Scholar 

  • R. W. Ogden, Local and global bifurcation phenomena in plane-strain finite elasticity, Int. J. Solids Structures 21 (1985), 121–132

    Article  MATH  Google Scholar 

  • O. Rand, D. Givoli, A finite element spectral method with application to the thermoelastic analysis of space structures, Internat. J. Numer. Meths. Engrg. 30 (1990) 291–306

    Article  MATH  Google Scholar 

  • S. Reese, P. Wriggers, A finite element method for stability problems in finite elasticity, to appear

    Google Scholar 

  • E. Riks, The application of Newton’s method to the problem of elastic stability., J. Appl. Mech. 39 (1972) 1060–1066

    Article  MATH  Google Scholar 

  • K. H. Schweizerhof, P. Wriggers, Consistent linearization for path following methods in nonlinear FE analysis, Comput. Meths. Appl. Mech. Engrg. 59 (1986) 261–279

    Article  MATH  Google Scholar 

  • J. C. Simo, T. J. R. Hughes, Plasticity, viscoplasticity and viscoelasticity: formulation, algorithms and numerical analysis, Springer-Verlag, Berlin, to appear

    Google Scholar 

  • J. C. Simo, F. Armero, Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes, Internat. J. Numer. Meths. Engrg. 33 (1992), 1413–1449

    Article  MATH  MathSciNet  Google Scholar 

  • J. C. Simo, F. Armero, R. L. Taylor, Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems, to appear

    Google Scholar 

  • J. C. Simo, R. L. Taylor, Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms, Comp. Methods Appl. Mech. Eng. 85 (1991), 273–310

    Article  MATH  MathSciNet  Google Scholar 

  • A. Spence, A. D. Jepson, The numerical calculation of cusps, bifurcation points and isola formation points in two parameter problems, in: Köpper, Mittelmann, Weber, eds., Numerial methods for bifurcation problems, ISNM 70 ( Birkhäuser, Basel, 1984 ), 502–514

    Chapter  Google Scholar 

  • T. Sussman, K.-J. Bathe, A finite element formulation for nonlinear incompressible elastic and inelastic analysis, Computer & Structures 26 (1987) 357–409

    Article  MATH  Google Scholar 

  • W. Wagner, Zur Behandlung von Stabilitätsproblemen der Elastostatik mit der Methode der Finiten Elemente, Forschungs- und Seminarberichte aus dem Bereich der Mechanik der Universität Hannover, F91 /1, 1991

    Google Scholar 

  • W. Wagner, P. Wriggers, A simple method for the calculation of post-critical branches, Engineering Computations 5 (1988) 103–109

    Article  Google Scholar 

  • E. W. Wilkes, On the stability of a circular tube under end thrust, Q. J. Mech. appl. Math. 8 (1955), 88–100

    Article  MATH  MathSciNet  Google Scholar 

  • P. Wriggers, S. Reese, Thermoelastic stability of trusses with temperature- dependent constitutive relations, Internat. J. Numer. Meths. Engrg. 35 (1992), 1891–1906

    Article  MATH  Google Scholar 

  • P. Wriggers, J. C. Simo, A general procedure for the direct computation of turning and bifurcation points, Internat. J. Numer. Meths. Engrg. 30 (1990) 155–176

    Article  MATH  Google Scholar 

  • P. Wriggers, R. L. Taylor, A fully non-linear axisymmetrical membrane element for rubber-like materials, Eng. Comput. 7 (1990) 303–310

    Article  Google Scholar 

  • P. Wriggers, W. Wagner, C. Miehe, A quadratically convergent procedure for the cal-culation of stability points in finite element analysis., Comput. Meths. Appl. Mech. Engrg. 70 (1988) 329–347

    Article  MATH  Google Scholar 

  • F. Ziegler, Snap-through buckling of a viscoelastic von Mises truss in a random temperature field, J. Appl. Mech. 36 (1969) 338–340

    Article  Google Scholar 

  • F. Ziegler, F. G. Rammerstorfer, Thermoelastic stability in R. P. IIetnarski, Thermal stresses III, North-Holland, Amsterdam, 1989

    Google Scholar 

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Authors and Affiliations

  1. T.H. Darmstadt, Darmstadt, Germany

    P. Wriggers & S. Reese

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  1. P. Wriggers
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  2. S. Reese
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Editor information

Editors and Affiliations

  1. Technical University of Athens, Greece

    A. N. Kounadis

  2. Ruhr-University Bochum, Germany

    W. B. Krätzig

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© 1995 Springer-Verlag Wien

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Wriggers, P., Reese, S. (1995). Applications. In: Kounadis, A.N., Krätzig, W.B. (eds) Nonlinear Stability of Structures. International Centre for Mechanical Sciences, vol 342. Springer, Vienna. https://doi.org/10.1007/978-3-7091-4346-9_10

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  • DOI: https://doi.org/10.1007/978-3-7091-4346-9_10

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82651-5

  • Online ISBN: 978-3-7091-4346-9

  • eBook Packages: Springer Book Archive

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