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Use of sufficient criteria for optimality in designing inhomogeneous plastic structures

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This article contains a survey of papers on optimal design of inhomogeneous structures taking account of plastic deformations.

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Literature Cited

  1. N. V. Banichuk,Optimization of the Shapes of Elastic Bodies [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  2. N. V. Banichuk,Introduction to Optimization of Structures [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  3. G. N. Barsegyan, “On a problem of design of an anisotropic ideally plastic rectangular plate of minimal volume,”Uchen. Zap. Erevan. Gos. Univ., Est. Nauki, No. 3, 23–31 (1981).

    MATH  Google Scholar 

  4. G. N. Barsegyan, “The problem of design of plastic strips according to criteria of equiflexibility and minimal volume,”Uchen. Zap. Erevan. Gos. Univ., Est. Nauki, No. 2, 20–28 (1983).

    MATH  Google Scholar 

  5. S. M. Gabib-Zade, “Optimal design of circular layered plates under the action of two systems of loads,”Issled. Vopr. Teor. Uprug. i Plast., No. 77, 28–34 (1987).

    Google Scholar 

  6. D. D. Gasanova and F. G. Shamiev, “On a problem of optimization of plates having contact with a liquid,”Izv. Akad. Nauk Az. SSR. Ser. Fiz.-Tekh. Mat. Nauk, No. 6, 118–119 (1980).

    Google Scholar 

  7. G. Hopkins and W. Prager, “Limits of economy of material in plates,”Mekhanika: A collection of translations of foreign papers, No. 6, 112–117 (1956).

    Google Scholar 

  8. O. Gross and W. Prager, “Design of structures of minimal weight under moving loads,”Mekhanika: A collection of translations of foreign papers, No. 2, 155–162 (1964).

    Google Scholar 

  9. A. S. Dekhtyar and M. Sh. Varvak, “The optimization problem for a plate of variable thickness,”Izv. Vuzov. Stroitel'stvo i Arkhit., No. 9, 44–48 (1974).

    Google Scholar 

  10. A. Zavelani-Rossi, “Design of two-dimensional structures of minimal weight,”Mekhanika: A collection of translations of foreign papers, No. 1, 138–152 (1971).

    Google Scholar 

  11. T. N. Driyaeva,Optimal Design of Structures: a Bibliographical Index [in Russian], ONTI TsNI-IEPsel'stroi, Moscow (1969).

    Google Scholar 

  12. D. Drucker and R. Shield, “Guidelines for design of structures of minimal weights,”Mekhanika: A collection of translations of foreign papers, No. 3, 77–90 (1958).

    Google Scholar 

  13. M. R. Ibragimov, “Design of a circular plate of minimal weight under two independent load systems,”Izv. Akad. Nauk Az. SSR, Ser. Fiz.-Tekh. Mat. Nauk, No. 3, 33–40 (1965).

    Google Scholar 

  14. M. R. Ibragimov, “Design of a shell of minimal weight under the action of independent loads,” in:Proceedings of the Scientific Conference of Young Scholars and Graduate Students, Academy of Sciences of the Azerbaijan SSR [in Russian], Baku, Azer. Academy of Sciences (1966), pp. 10–19.

    Google Scholar 

  15. M. R. Ibragimov, “On the design of a cylindrical shell of minimal weight,” in:Static and Dynamic Problems of the Theory of Elasticity and Plasticity [in Russian], Az. Academy of Sciences, Baku (1968), 113–118.

    Google Scholar 

  16. M. R. Ibragimov, “Optimal design of a cylindrical reservoir on a rigid base,” in:Static and Dynamic Problems of the Theory of Elasticity and Plasticity [in Russian], Az. Academy of Sciences, Baku (1968), 119–123.

    Google Scholar 

  17. M. R. Ibragimov and F. G. Shamiev, “On the design of a cylindrical reservoir of minimal weight,” in:Proceedings of the Sixth All-Union Conference on the Theory of Shells and Plates [in Russian], Nauka, Moscow (1966), pp. 419–423.

    Google Scholar 

  18. L. M. Kachanov,Foundations of the Theory of Plasticity [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  19. R. M. Kirakosyan, “On a problem of a circular plate of minimal volume,”Izv. Akad. Nauk Arm. SSR,30, No. 1, 18–24 (1977).

    Google Scholar 

  20. R. M. Kirakosyan, “Design of a single-layer plastic cylindrical shell of minimal volume,”Izv. Akad. Nauk Arm. SSR. Mekhanika,31, No. 3, 31–42 (1978).

    MATH  Google Scholar 

  21. R. M. Kirakosyan, V. N. Minasyan, and M. S. Sarkisyan, “On the determination of the optimal thickness of a circular plate under bending,”Prikl. Mekh.,18, No. 10, 68–74 (1982).

    Google Scholar 

  22. J.-L. Lions,Optimal Control of Systems Described by Partial Differential Equations [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  23. G. Maier, “On the optimization of the shape of plastic optimal structures,” in:Progress in the Mechanics of Deformable Media [in Russian], Nauka, Moscow (1975), pp. 359–373.

    Google Scholar 

  24. V. P. Malkov and A. G. Ugodchikov,Optimization of Elastic Systems [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  25. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, eds.Mathematical Theory of Optimal Processes [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  26. V. N. Minasyan, “A circular plate of minimal volume made of an ideally plastic orthotropic material and functioning in a field of solid forces,”Izv. Akad. Nauk Arm. SSR, Mekhanika,35, No. 4, 21–29 (1982).

    Google Scholar 

  27. V. M. Nebogatov, “Optimal design of plastic plates under loads in a plane,” Kand. Diss., Krasnoyarsk (1987).

  28. Yu. V. Nemirovskii, “On estimates of the weight of plastic optimal structures,”Izv. Akad. Nauk SSSR. Mekhanika Tverdogo Tela, No. 4, 159–162 (1968).

    Google Scholar 

  29. Yu. V. Nemirovskii, “Shells of absolutely minimal weight,”Mekh. Def. Sred, No. 3, 3–78 (1978).

    Google Scholar 

  30. Yu. V. Nemirovskii and V. M. Nebogatov, “Optimal design of plastic plates taking account of mass forces,”Zh. Prikl. Mekh. Tekh. Fiz., No. 3, 137–146 (1985).

    Google Scholar 

  31. Yu. V. Nemirovskii and V. M. Nebogatov, “Some solutions of the problem of optimal design of nonaxisymmetric plastic plates,”Prikl. Prob. Proch. Plast., No. 29, 78–87 (1985).

    Google Scholar 

  32. Yu. V. Nemirovskii and V. M. Nebogatov,Optimal Design of Plastic Plates [in Russian], Preprint, Novosibirsk (1985).

  33. Yu. V. Nemirovskii and V. M. Nebogatov, “Numerical solution of the problem of optimal design of plastic plates,” in:Informational-Operational Materials, Pt. 1, Mathematical Modeling [in Russian], Krasnoyarsk (1986), 33–36.

  34. Yu. V. Nemirovskii and V. M. Nebogatov, “A study of the possible couplings of optimal designs of plastic plates,”Izv. Akad. Nauk SSSR, Mekh. Tver. Tela, No. 1, 107–115 (1986).

    Google Scholar 

  35. Yu. V. Nemirovskii and V. M. Nebogatov, “Optimal design of elliptic rigid-plastic plates,”Prikl. Mekh.,22, No. 5, 77–82 (1986).

    Google Scholar 

  36. Yu. V. Nemirovskii and V. M. Nebogatov, “On the ideally plastic state of plates of minimal weight,”Prikl. Mekh.,22, No. 11, 99–104 (1986).

    MathSciNet  Google Scholar 

  37. Yu. V. Nemirovskii and V. M. Nebogatov, “Problems of optimal design and limit equilibrium of inhomogeneous plastic structures,” Preprint, Inst. Teor. Prikl. Mekh. Sib. Otd. Akad. Nauk SSSR, No. 4-88.

  38. F. I. Njordson and P. Pedersen, “A survey of research on optimal design of structures,”Mekhanika: A collection of translations of foreign papers, No. 2, 136–157 (1973).

    Google Scholar 

  39. Yu. V. Nemirovskii and V. N. Mazalov, eds.,Optimal Design of Structures: a Bibliographical Index of Soviet and Foreign Literature from 1948 to 1974 [in Russian], Inst. Gidrodin. Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1975).

    Google Scholar 

  40. Ya. S. Podstrigach, ed.,Optimization of Mechanical Systems: a Bibliographical Index of Soviet and Foreign Literature from 1970 to 1982 [in Russian], L'vov Science Library, Bks. 1, 2 (1986).

  41. V. Prager and R. Shield, “Generalizations of the method of optimal design of structures taking account of plastic deformations,”Trans. Amer. Soc. Mech. Eng., Ser. E,34, No. 4, 36–39 (1967).

    Google Scholar 

  42. M. I. Reitman and G. S. Shapiro, “Optimal design of deformable solid bodies,”Itogi Nauki i Tekhniki. Mekh. Def. Tver. Tela,12, 5–90 (1978).

    MathSciNet  Google Scholar 

  43. D. Rozhvany,Optimal Design of Flexible Systems [in Russian], Stroiizdat, Moscow (1980).

    Google Scholar 

  44. V. V. SokolovskiiTheory of Plasticity [in Russian], Academy of Sciences Press, Moscow (1946).

    Google Scholar 

  45. V. A. Troitskii and L. V. Petukhov,Optimization of the Shapes of Elastic Bodies [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  46. F. G. Hodge,Computation of Structures Taking Account of Plastic Deformations [Russian translation], Mashgiz, Moscow (1963).

    Google Scholar 

  47. F. G. Shamiev, “On the design of shells of minimal weight,”Izv. Akad. Nauk Az. SSR, Ser. Fiz.-Tekh. Mat. Nauk, No. 5, 37–41 (1963).

    Google Scholar 

  48. F. G. Shamiev, “On the design of compound structures of minimal weight,”Izv. Akad. Nauk Az. SSR, Ser. Fiz.-Tekh. Mat. Nauk, No. 5, 36–40 (1965).

    Google Scholar 

  49. F. G. Shamiev, “On the optimal design of plates with a discontinuous inhomogeneity,” in:Mechanics of Deformable Solid Bodies [in Russian], Elm, Baku (1970), pp. 107–112.

    Google Scholar 

  50. F. G. Shamiev, “More on the design of annular plates of minimal weight,”Izv. Akad. Nauk Az. SSR, Ser. Fiz.-Tekh. Mat. Nauk, No. 2, 117–122 (1978).

    MATH  Google Scholar 

  51. F. G. Shamiev and S. M. Gabib-Zade, “On the optimal design of shells under the action of oppositely directed load systems,”Izv. Akad. Nauk Az. SSR, Ser. Fiz.-Tekh. Mat. Nauk, No. 5, 91–95 (1978).

    Google Scholar 

  52. F. G. Shamiev and D. D. Gasanova, “On optimal design of plates in an incompressible fluid,”Izv. Akad. Nauk Za. SSR, Ser. Fiz.-Tekh. Mat. Nauk, No. 3, 25–31 (1977).

    Google Scholar 

  53. R. Shield, “Methods of optimal design of structures,”Mekhanika: A collection of translations of foreign papers, No. 2, 148–159 (1962).

    Google Scholar 

  54. R. Shield, “Methods of optimal design under the action of a number of load systems,”Mekhanika: A collection of translations of foreign papers, No. 2, 147–154 (1964).

    Google Scholar 

  55. M. I. Estrin, “On plates of minimal weight in a plane deformed state,”Tr. TsNII Stroit. Konstr., No. 4, 91–103 (1961).

    Google Scholar 

  56. D. C. Drucker, “On minimum weight design and strength of non-homogeneous plastic bodies,” in:Non-homogeneity in Elasticity and Plasticity, London (1959), pp. 138–146.

  57. D. C. Drucker and R. T. Shield, “Design for minimum weight,”Actes IX Cong. Int. Mech. Appl., Bruxelles,5, 212–222 (1957).

    Google Scholar 

  58. G. Eason, “The minimum weight design of circular sandwich plates,”Z. angew. Math. Phys.,11, No. 5, 368–375 (1960).

    MATH  MathSciNet  Google Scholar 

  59. D. D. Gasanova and F. G. Shamiev, “On the optimization of annular plates in an incompressible liquid,”Rozpr. inz.,27, No. 1, 191–209 (1979).

    MathSciNet  Google Scholar 

  60. T. C. Hu and R. T. Shield, “Minimum-volume design of disks,”Z. angew. Math. Mech.,12, No. 5, 414–443 (1961).

    MathSciNet  Google Scholar 

  61. W. Kozlowski and Z. Mróz, “Optimal design of solid plates,”Int. J. Solids and Struct.,6, No. 8, 781–784 (1969).

    Google Scholar 

  62. W. Kozlowski and Z. Mróz, “Optimal design of disks subjecct to geometric constraints,”Int. J. Mech. Sci.,12, No. 12, 1007–1021 (1970).

    Google Scholar 

  63. G. Maier and A. Zavelani-Rossi, “A finite-element approach to optimal design of plastic discs,”Ist. sci. tecn. costr. politecn. Milano, No. 482, 17–29 (1970).

    Google Scholar 

  64. G. Maier, A. Zavelani-Rossi, and D. A. Benedett, “A finite-element approach to optimal design of plastic structures in plane stress,”Int. J. Numer. Meth. Eng.,4, No. 4, 455–473 (1972).

    Google Scholar 

  65. A. G. M. Michell, “The limits of economy of material in frame structures,”Phil. Mag.,8, 589–597 (1904).

    MATH  Google Scholar 

  66. Z. Mróz, “On a problem of minimum weight design,”Quart. Appl. Math.,19, No. 2, 127–135 (1961).

    MATH  MathSciNet  Google Scholar 

  67. M. I. Reitman, “Analysis of the equations of ideally plastic shells,”Arch. mech. stosow.,19, No. 4, 211–218 (1967).

    Google Scholar 

  68. T. R. Tauchert and W. S. Hemp, “Optimal plastic design of a variable-thickness orthotropic plate under in-plane loading,”Egn. Optim.,4, No. 1, 298–312 (1979).

    Google Scholar 

  69. R. T. Shield, “On the optimum design of shells,”J. Appl. Mech.,27, No. 2, 316–322 (1960).

    MATH  MathSciNet  Google Scholar 

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Authors
  1. V. M. Nebogatov
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  2. Yu. V. Nemirovskii
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Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.

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Nebogatov, V.M., Nemirovskii, Y.V. Use of sufficient criteria for optimality in designing inhomogeneous plastic structures. J Math Sci 81, 3107–3112 (1996). https://doi.org/10.1007/BF02362605

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