On the optimal design of elastic shafts

Raul B. Gonzalez de Paz

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1989)

  • Volume: 23, Issue: 4, page 615-625
  • ISSN: 0764-583X

How to cite

top

Gonzalez de Paz, Raul B.. "On the optimal design of elastic shafts." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 23.4 (1989): 615-625. <http://eudml.org/doc/193582>.

@article{GonzalezdePaz1989,
author = {Gonzalez de Paz, Raul B.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {minimization of a functional associated with shape of shaft; Maximal torsional rigidity; relaxation; duality; convex analysis techniques; existence},
language = {eng},
number = {4},
pages = {615-625},
publisher = {Dunod},
title = {On the optimal design of elastic shafts},
url = {http://eudml.org/doc/193582},
volume = {23},
year = {1989},
}

TY - JOUR
AU - Gonzalez de Paz, Raul B.
TI - On the optimal design of elastic shafts
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1989
PB - Dunod
VL - 23
IS - 4
SP - 615
EP - 625
LA - eng
KW - minimization of a functional associated with shape of shaft; Maximal torsional rigidity; relaxation; duality; convex analysis techniques; existence
UR - http://eudml.org/doc/193582
ER -

References

top
  1. [1] A. ACKER, A free boundary optimization problem. SIAM J. Math. Anal. 9(1978) pp.1179-1191. Zbl0335.31002MR512520
  2. [2] H. W. ALT and L. A. CAFARELLI, Existence and regularity for a minimum problem with free boundary. J. Reine u. Angew. Mathematik 325 (1981)pp. 104-144. Zbl0449.35105MR618549
  3. [3] N. V. BANICHUK, Problems and methods of optimal structural design. Plenum Press, London (1983). Zbl0649.73041MR715778
  4. [4] N. BOURBAKI, Espaces Vectoriels Topologiques, Hermann, Paris (1973). 
  5. [5] Ch. CASTAING and M. VALADIER, Convex Analysis and Measurable Multifonctions. Lect. Notes in Math. no. 580, Springer-Verlag, New York (1977). Zbl0346.46038MR467310
  6. [6] J. CEA, Optimisation, théorie et algorithmes. Dunod, Paris (1971). Zbl0211.17402MR298892
  7. [7] J. CEA, Problems of shape optimal design in « Optimization of distributed parameter structures, NATO Proceedings » (Eds. Haug, E. J. and Cea, J. ). Sijthoff and Noordhoff (1981). Zbl0517.73096
  8. [8] J. CEA and K. MALANOWSKI, An example of a max-min problem in partial differential equations. SIAM J. Control and Optimization (1970) pp. 305-316. Zbl0204.46603MR274915
  9. [9] D. CHENAIS, On the exixtence of a solution in a domain identification problem, J. Math. Anal. and Appl. 52 (1975) pp. 189-219. Zbl0317.49005MR385666
  10. [10] I. EKELAND and R. TEMAM, Analyse convexe et problèmes variationels. Dunod, Paris (1974). Zbl0281.49001MR463993
  11. [11] Cl. GEBHARDT, Regularity of solutions of non-linear variational inequalities. Arch. Rat. Mech. and Anal. 52 (1973) pp. 383-393. Zbl0277.49003
  12. [12] D. GILBARG and N. TRUDINGER, Elliptic Partial Differential Aquations of second order. Springer, New York (1977). Zbl0361.35003MR473443
  13. [13] R. B. GONZALEZ DE PAZ, Sur un problème d'optimisation de domaine. Numer. Funct. Anal. and Optimiz. 5 (1982) pp. 173-197. Zbl0503.49017MR704111
  14. [14] B. KAWOHL, Geometrical properties of level sets of solutions to elliptic problems. Proc. Symp. in Pure Math. A.M.S. (1986), part 2, pp. 25-36. Zbl0597.35016MR843592
  15. [15] D. KINDERLEHRER and G. STAMPACCHIA, An introduction to variational inequalities and their applications. Academic Press, New York (1980). Zbl0457.35001MR567696
  16. [16] H. LANCHON, Torsion élastoplastique d'un arbre. J. de Mech. 13 (1974) pp. 367-318. Zbl0285.73020MR363107
  17. [17] J. J. MOREAU, Fonctionnelles convexes. Séminaire sur les équations aux dérivées partielles. Collèges de France (1966-67). 
  18. [18] J. NEÇAS, Les méthodes directes en théorie des équations elliptiques. Masson, Paris (1967). MR227584
  19. [19] J. PIRONNEAU, Optimal shape design for elliptic systems. Springer-Verlag, New York (1984). Zbl0534.49001MR725856
  20. [20] G. POLYA and A. WEINSTEIN, On the torsional rigidity of multiply-connected cross sections. Ann. Math. 52 (1950) pp. 154-163. Zbl0038.37502MR40159
  21. [21] M. VALADIER, Sous-différentiels d'une borne supérieure et d'une somme continue de fonctions convexes. C. R. Acad. Sc. Paris, Serie A, 268, pp. 39-42 (janvier 1969). Zbl0164.43302MR241975
  22. [22] J. P. ZOLESIO, Domain variational formulation for free boundary problem, in « Optimization of distributed parameter structures. NATO-Proceedings » (Eds. Haug, E. J. and Cea. J.). Sijthoff and Noordhoff (1981). Zbl0537.35074MR690992
  23. [23] J. P. ZOLESIO, Indentification de domaines par déformation. Doctoral Thesis, Université de Nice (1979). 
  24. [24] R. JENSEN, Boundary regularity for variational inequalities. Indiana Univ. Math. J. 29 (1980) pp. 495-511. Zbl0469.49008MR578201

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.