Dependence of the buckling load of a nonshallow arch with respect to the shape of its midcurve

D. Chenais; B. Rousselet

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1990)

  • Volume: 24, Issue: 3, page 307-341
  • ISSN: 0764-583X

How to cite

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Chenais, D., and Rousselet, B.. "Dependence of the buckling load of a nonshallow arch with respect to the shape of its midcurve." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 24.3 (1990): 307-341. <http://eudml.org/doc/193598>.

@article{Chenais1990,
author = {Chenais, D., Rousselet, B.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {simple eigenvalue; Fréchet differentiable; multiple eigenvalue; directional derivative; static buckling load; smallest eigenvalue of a linear operator; Hilbert space; existence of a smallest eigenvalue; differentiability},
language = {eng},
number = {3},
pages = {307-341},
publisher = {Dunod},
title = {Dependence of the buckling load of a nonshallow arch with respect to the shape of its midcurve},
url = {http://eudml.org/doc/193598},
volume = {24},
year = {1990},
}

TY - JOUR
AU - Chenais, D.
AU - Rousselet, B.
TI - Dependence of the buckling load of a nonshallow arch with respect to the shape of its midcurve
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1990
PB - Dunod
VL - 24
IS - 3
SP - 307
EP - 341
LA - eng
KW - simple eigenvalue; Fréchet differentiable; multiple eigenvalue; directional derivative; static buckling load; smallest eigenvalue of a linear operator; Hilbert space; existence of a smallest eigenvalue; differentiability
UR - http://eudml.org/doc/193598
ER -

References

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  1. [1] D. CHENAIS, B. ROUSSELET, R. BENEDICT, Design Sensitivity for Arch Structures with Respect to Midsurface Shape under Static Loading, Journal of of Optimization Theory & Applications, 58-2, 1988. Zbl0631.49015MR953655
  2. [2] N. OLHOFF, S. H. RASMUSSEN, On Single and Bimodal Buckling Modes of Clamped Columns, In, t. J. of Solids & Structures, 13, 605-614, 1977. Zbl0357.73041
  3. [3] T. KATO, Perturbation Theory for Linear Operators, Springer Verlag, 1966. Zbl0148.12601MR203473
  4. [4] B. ROUSSELET, Étude de la régularité des valeurs propres par rapport à des déformations bilipschitziennes du domaine, CRAS, 1, 283, 1976, Paris, p. 507. Zbl0355.65081MR427865
  5. [5] MYSUNSKI-SOKOLOWSKI, Non-Differentiable Optimization Problems for Elliptic Systems, SIAM J. Optim. Contr. 23 (1985), pp. 632-648. Zbl0571.49010
  6. [6] J. P. ZOLÉSIO, Semi-Derivatives of Repeated Eigenvalues, Optim. of Distr. Param. Struct. E. J. Haug and J. Céa, Edit., Sithoff-Noordhoff, 1981, Rocheville, Maryland. Zbl0518.73086
  7. [7] B. ROUSSELET, D. CHENAIS, Continuité et différentiabilité des éléments propres ; application à l'optimisation des structures, to be published. Zbl0741.73029
  8. [8] P. G. CIARLET, The finite element method for elliptic problems, North Holland, 1978. Zbl0383.65058MR520174
  9. [9] H. BREZIS, Analyse fonctionnelle, Théorie et applications, Masson 1983. Zbl0511.46001MR697382
  10. [10] P. GRISVARD, Elliptic Problems in Nonsmooth Domains, Pitman 1985. Zbl0695.35060MR775683
  11. [11] IOFFE, TIHOMIROV, Theory of External Problems, North Holland, 1979. Zbl0407.90051

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