Shape optimization in two-dimensional elasticity by the dual finite element method

I. Hlaváček

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1987)

  • Volume: 21, Issue: 1, page 63-92
  • ISSN: 0764-583X

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Hlaváček, I.. "Shape optimization in two-dimensional elasticity by the dual finite element method." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 21.1 (1987): 63-92. <http://eudml.org/doc/193497>.

@article{Hlaváček1987,
author = {Hlaváček, I.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {minimization of cost functional; respect to part of boundary; elastic body fixed; existence of optimal boundary; Castigliano principle; approximate cost functional of stresses; piecewise linear stress field; convergence; Finite element approximations; dual state problem; continuous dependence; approximate stress functions; approximate control},
language = {eng},
number = {1},
pages = {63-92},
publisher = {Dunod},
title = {Shape optimization in two-dimensional elasticity by the dual finite element method},
url = {http://eudml.org/doc/193497},
volume = {21},
year = {1987},
}

TY - JOUR
AU - Hlaváček, I.
TI - Shape optimization in two-dimensional elasticity by the dual finite element method
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1987
PB - Dunod
VL - 21
IS - 1
SP - 63
EP - 92
LA - eng
KW - minimization of cost functional; respect to part of boundary; elastic body fixed; existence of optimal boundary; Castigliano principle; approximate cost functional of stresses; piecewise linear stress field; convergence; Finite element approximations; dual state problem; continuous dependence; approximate stress functions; approximate control
UR - http://eudml.org/doc/193497
ER -

References

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  2. [2] N. V. BANICHUK, Problems and methods of optimal structural design. PlenumN. V. BANICHUK, Problems and me Press, New York and London, 1983. Zbl0649.73041MR715778
  3. [3] D. BEGIS, R. GLOWINSKI, Application de la méthode des éléments finis à l'approximation d'un problème de domaine optimal. Appl. Math. & Optim. 2 (1975), 130-169. Zbl0323.90063MR443372
  4. [4] I. HLAVACEK, Convergence of an equilibrium finite element model for plane elastostatics. Apl. Mat.24 (1979), 427-456. Zbl0441.73101MR547046
  5. [5] I. HLAVACEK, Dual finite element analysis for some elliptic variational equations and inequalities. Acta Applicandae Math. 1 (1983), 121-150. Zbl0523.65049MR713475
  6. [6] J. HLAVACEK : Optimization of the domain in elliptic problems by the dual finite element method. Api.Mat.30 (1985), 50-72. Zbl0575.65103MR779332
  7. [7] J. HASLINGER, I. HLAVACEK, Approximation of the Signorini problem with friction by a mixed finite element method. J. Math. Anal. Appl. 86 (1982), 99-122. Zbl0486.73099MR649858
  8. [8] J. HASLINGER, J. LOVISEK, The approximation of the optimal shape control problem governed by a variational inequality with flux cost functional. To appear in Proc. Zbl0625.73025MR831811
  9. [9] J. HASLINGER, P. NEITTAANMÄKI, On the existence of optimal shapes in contact problems, Numer. Funct. Anal, and Optimiz. 7 (1984), 107-124. Zbl0559.73099MR767377
  10. [10] J. HASLINGER, P. NEITTAANMÄKI, T TIIHONEN, On optimal shape design of an elastic body on a rigid foundation. To appear in Proc. of the MAFELAP Confe-rence 1984. Zbl0588.73159MR811062
  11. [11] J. NECAS, I. HLAVACEK, Mathematical theory of elastic and elasto-plastic bodies.Elsevier, Amsterdam 1981. Zbl0448.73009
  12. [12] V. B WATWOOD, B. J. HARTZ, An equilibrium stress field model for finite element solution of two-dimensional elastostatic problems. Internat. J. Solids Structures 4 (1968), 857-873. Zbl0164.26201

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