Skip to Main Content
Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

A problem in the optimal design of networks under transverse loading


Authors: Elio Cabib, Cesare Davini and Chong Qing Ru
Journal: Quart. Appl. Math. 48 (1990), 251-263
MSC: Primary 73K40; Secondary 49J45, 49N99, 73V25
DOI: https://doi.org/10.1090/qam/1052135
MathSciNet review: MR1052135
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

    R. Kohn and G. Strang, Optimal design and relaxation of variational problems, Comm. Pure Appl. Math. 34, Part I 113–137, Part II 139–182, Part III 353–377 (1986)
  • N. V. Banichuk, Problems and methods of optimal structural design, Mathematical Concepts and Methods in Science and Engineering, vol. 26, Plenum Press, New York, 1983. Translated from the Russian by Vadim Komkov; Translation edited by Edward J. Haug; With a preface by Haug and Komkov. MR 715778
  • N. Olhoff and J. E. Taylor, On structural optimization, Trans. ASME Ser. E. J. Appl. Mech. 50 (1983), no. 4, 1139–1151. MR 726559, DOI https://doi.org/10.1115/1.3167196
  • N. C. Huang, Optimal design of elastic structures for maximum stiffness, Internat. J. Solids and Structures 17, 305–311 (1981)
  • Keng Tung Cheng and Niels Olhoff, An investigation concerning optimal design of solid elastic plates, Internat. J. Solids Structures 17 (1981), no. 3, 305–323. MR 610907, DOI https://doi.org/10.1016/0020-7683%2881%2990065-2
  • N. C. Huang, Optimal design of elastic beams for minimum-maximum deflection, J. Appl. Mech. 38, 1078–1081 (1971) W. Prager and J. E. Taylor, Problems of optimal structural design, J. Appl. Mech. 35, 102–106 (1968)
  • Robert Reiss, Optimal compliance criterion for axisymmetric solid plates, Internat. J. Solids Structures 12 (1976), no. 5, 319–329. MR 411331, DOI https://doi.org/10.1016/0020-7683%2876%2990022-6
  • K. A. Lurie and A. V. Cherkaev, $G$-closure of a set of anisotropically conducting media in the two-dimensional case, J. Optim. Theory Appl. 42 (1984), no. 2, 283–304. MR 737972, DOI https://doi.org/10.1007/BF00934300
  • K. A. Lurie, A. V. Cherkaev, and A. V. Fedorov, Regularization of optimal design problems for bars and plates, J. Optim. Theory Appl. 37, Part 1 499–522, Part 2 523–543 1982)
  • K. A. Lurie, A. V. Cherkaev, and A. V. Fedorov, On the existence of solutions to some problems of optimal design for bars and plates, J. Optim. Theory Appl. 42 (1984), no. 2, 247–281. MR 737971, DOI https://doi.org/10.1007/BF00934299
  • K. A. Lurie and A. V. Cherkaev, Optimal structural design and relaxed controls, Optimal Control Appl. Methods 4, 387–392 (1983) F. Murat and L. Tartar, Calcul des variations et homogénéization, Cours de l’Ecole d’Eté d’Analyse Numérique CEA-EDF-INRIA sur l’homogénéisation, Bréau sans Nappe, Juillet 1983, Eyrolles, Paris, 1984
  • E. Cabib and G. Dal Maso, On a class of optimum problems in structural design, J. Optim. Theory Appl. 56 (1988), no. 1, 39–65. MR 922377, DOI https://doi.org/10.1007/BF00938526
  • R. S. Rivlin, Plane strain of a net formed by inextensible cords, J. Rational Mech. Anal. 4 (1955), 951–974. MR 74998, DOI https://doi.org/10.1512/iumj.1955.4.54037
  • Sergio Spagnolo, Convergence in energy for elliptic operators, Numerical solution of partial differential equations, III (Proc. Third Sympos. (SYNSPADE), Univ. Maryland, College Park, Md., 1975) Academic Press, New York, 1976, pp. 469–498. MR 0477444
  • E. De Giorgi and S. Spagnolo, Sulla convergenza degli integrali dell’energia per operatori ellittici del secondo ordine, Boll. U.M.I. (4) 8, 391–411 (1973)
  • W. Velte and P. Villaggio, Are the optimum problems in structural design well posed?, Arch. Rational Mech. Anal. 78 (1982), no. 3, 199–211. MR 650843, DOI https://doi.org/10.1007/BF00280036
  • François Murat, Un contre-exemple pour le problème du contrôle dans les coefficients, C. R. Acad. Sci. Paris Sér. A-B 273 (1971), A708–A711 (French). MR 288651
  • François Murat, Contre-exemples pour divers problèmes où le contrôle intervient dans les coefficients, Ann. Mat. Pura Appl. (4) 112 (1977), 49–68. MR 438205, DOI https://doi.org/10.1007/BF02413475
  • George I. N. Rozvany, Niels Olhoff, Keng Tung Cheng, and John E. Taylor, On the solid plate paradox in structural optimization, J. Structural Mech. 10 (1982), no. 1, 1–32. MR 668257, DOI https://doi.org/10.1080/03601218208907399
  • Walter Rudin, Real and complex analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210528
  • H. W. Kuhn and A. W. Tucker, Nonlinear programming, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley and Los Angeles, 1951, pp. 481–492. MR 0047303
  • J. E. Taylor, Maximum strength elastic structural design, Journal of the Engineering Mechanics Division, ASCE, 95, No. EM3, 653–663 (1969)
  • Olga A. Ladyzhenskaya and Nina N. Ural’tseva, Linear and quasilinear elliptic equations, Academic Press, New York-London, 1968. Translated from the Russian by Scripta Technica, Inc; Translation editor: Leon Ehrenpreis. MR 0244627

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73K40, 49J45, 49N99, 73V25

Retrieve articles in all journals with MSC: 73K40, 49J45, 49N99, 73V25


Additional Information

Article copyright: © Copyright 1990 American Mathematical Society