Skip to main content

Application of Strength and Weight Criteria

  • Chapter
Introduction to Optimization of Structures
  • 170 Accesses

Abstract

Strength criteria constitute the fundamental constraints that must be taken into account in any optimal design. Such constraints are local in nature and are stated in terms of the components of the stress tensor. At the present time various theories of strength have been investigated and some of them have been extensively applied in optimal design research. The choice of any specific strength criteria, or the use of such approximate criteria, depends on the structural materials, the type of loads, the use of a specific computational scheme, and on other factors.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References for Chapter 6

  1. Aleksandrov, M.A., Korshinin, M.S., and Smoliarov, N.N., Computation of elastic plates and shells that are close to uniform strength, Prikl. Mekh., 1978, 14, No. 10, pp. 41–46.

    Google Scholar 

  2. Banichuk, N.V., On a game theoretic approach to optimization problems for elastic bodies, Prikl. Mat. Mekh., 1973, 37, No. 6, pp. 1098–1108.

    MathSciNet  Google Scholar 

  3. Banichuk, N.V., Optimal design for a one-dimensional bending problem for fixed and moving loads, Izv. Akad. Nauk SSSR. MTT, 1974, No. 5, pp. 113–123.

    Google Scholar 

  4. Banichuk, N.V., The problem of optimizing the shape of a hole in a plate subjected to bending, Izv. Akad. Nauk SSSR. MTT, 1977, No. 3, pp. 81–88.

    Google Scholar 

  5. Banichuk, N.V., Conditions for optimality in problem of finding the shapes of holes in elastic bodies, Prikl. Mat. Mekh., 1977, 41, No. 5, pp. 920–925.

    MathSciNet  Google Scholar 

  6. Banichuk, N.V., Designing of plates for minimum stress and deflection, In: Optimization of Distributed Parameter Structures, Iowa, 1980, E.J. Haug and J.J. Cea (eds.), Alphen aan den Rijn, Sijthoff-Noordhoff, 1981, pp. 333–361.

    Google Scholar 

  7. Banichuk, N.V., and Kobelev, V.V., Some problems of optimal design of shells of revolution, lzv. Arm. SSR, Mekhanika, 1983, No. 2, pp. 10–17.

    Google Scholar 

  8. Banichuk, N.V., and Kobelev, V.V., On optimal but not uniformly strong shapes of cross-sections of beams, Izv. Akad. Nauk SSSR. MTT, 1983, No. 5, pp. 162–167.

    Google Scholar 

  9. Barnett, R.L., Survey of optimum structural design, Exp. Mech., 1966, 6, No. 12, pp. 19–26.

    Article  Google Scholar 

  10. Beliaev, N.V., Strength of Materials, Gostekhizdat., Moscow-Leningrad 1951, 856 pp.

    Google Scholar 

  11. Cherepanov, G.P., Inverse problems in the two-dimensional theory of elasticity, Prikl. Mat. Mekhanika, 1974, 38, No. 6, pp. 963–979.

    MathSciNet  Google Scholar 

  12. Chiras, A.A., Barkauskas, A.E., and Karkauskas, R.P., Theory and Technique in Optimizing Elastoplastic Systems, Leningrad, Stroiizdat., 1974.

    Google Scholar 

  13. Cinquini, C., and Sacchi, G., Problems of optimal design for elastic and plastic structures, J. Mech. Appl., 1980, 4, No. 1, pp. 1–29.

    MathSciNet  Google Scholar 

  14. Cinquini, C, Limit analysis and optimal plastic design of circular cylindrical shells. In: Optimization Methods in Structural Design, H. Eschenauer and N. Olhoff (eds.), Mannheim Bibliogr. Institute, 1983, pp. 309–318.

    Google Scholar 

  15. Cinquini, C., Structural optimization of plates of general shape by finite elements, J. Structural Mechanics, 1981, 9, No. 4, pp. 465–481.

    Article  Google Scholar 

  16. Dorn, W.S., Gomory, R.E., and Greenberg, H.G., Automatic design of optimal structures, J. Mech., 3, No. 1, 1964.

    Google Scholar 

  17. Drucker, D.C., and Shields, R.T., Design for minimum weight. In: Proc. 9th International Congr. Applied Mechanics, Brussels, 1957, Vol. 5, pp. 212–222.

    Google Scholar 

  18. Drucker, D.C., and Shields, R.T., Bounds on minimum weight design. Quart. Appl. Math., 1957, 15, No. 3, pp. 269–281.

    MathSciNet  MATH  Google Scholar 

  19. Erkhov, M.I., On the theory of optimal design for dynamically loaded rigid-plastic bodies. In: Mechanics of deformable solid bodies, Novosibirsk, Institute of Hydrodynamics, 1979, pp. 44–47.

    Google Scholar 

  20. Flügge, W., Statics and Dynamics of Shells, Moscow, Gostekhizdat., 1961, 306 pp.

    Google Scholar 

  21. Francavilla, A., Ramakrishnan, C.V., and Zienkiewicz, O.C., Optimization of shape to minimize stress concentration, J. Strain Analysis, 1975, 10, pp. 6370.

    Article  Google Scholar 

  22. Galilei, Galileo, Discorsus et demonstrationes mathematicae, circa duas novas scientias, Leyden, 1699, a Latin translation from the 1638 edition by Mathias Bernegger, including Galileo’s direction to Elzeviers. New translation into English with introduction and notes by Stillman Drake, University of Wisconsin Press, Madison, 1974.

    Google Scholar 

  23. Ganeeva, M.S., Kornishin, M.S., and Malakhov, V.G., Uniformly stressed elastic shells of revolution. In: Seminar on Theory of Shells, Kazan’, Phys: Tekh. In., 1975, Vol. 3, pp. 92–106.

    Google Scholar 

  24. Gol’denblat, I.I., and Kozhnov, V.A., Strength and Plasticity Criteria for Structural Materials, Moscow, Mashinostroenie, 1968, 192 pp.

    Google Scholar 

  25. Haug, E.J., and Kwak, B.M., Contact stress minimization by contour design, Intern. J. Numer. Meth. Eng., 1978, 12, pp. 917–930.

    Article  MATH  Google Scholar 

  26. Hegemeier, G.A., and Prager W., On Michell trusses, Intern. J. Mech. Science, 1969, 11, p. 209.

    Article  Google Scholar 

  27. Hemp, W., On Michell framework for uniform load between fixed supports, Eng. Optim., 1974, 1, No. 1, pp. 61–69.

    Article  Google Scholar 

  28. Hodge, F.G., Computation of Structures with Plastic Deformations, Moscow GNTI, 1963, 380 pp.

    Google Scholar 

  29. Hopkins, H.G., and Prager, W., Limits on economy of material in plates, J. Appl. Mech. 1955, 22, pp. 372–374.

    MATH  Google Scholar 

  30. Ivanov, G.B., Computation of an optimal variable thickness of a shell. In: Problems of Mekhanics of a Solid Deformable Body, Leningrad, Sudpromgiz, 1970, pp. 171–177.

    Google Scholar 

  31. Ivanov, G.B., and Kosmodem’ianskii, A.S., Inverse problem of bending for thin isotropic plates, Izv. Akad. Nauk SSSR. MTT, 1974, No. 5, pp. 53–56.

    Google Scholar 

  32. Il’iushin, A.A., A theory of elastoplastic strains, Prikl. Mat. Mekh., 1946, 10, No 3, pp. 347–356.

    Google Scholar 

  33. Il’iushin, A.A., Plasticity, Moscow and Leningrad, Gostekhizdat., 1948, 308 pp.

    Google Scholar 

  34. Ishlinskii, A.Iu., Mechanics, Ideas, Problems and Applications, Moscow, Nauka, 1985, 624 pp.

    Google Scholar 

  35. Ishlinskii, A.Iu., On a uniformly stressed cross-section of a beam, Nauchn. Zap, Mekh. Moscow State University, 1940, 39, pp. 87–90.

    Google Scholar 

  36. Ishlinskii, A.Iu., Strength hypothesis for a change of shape, Nauchn. Zap. Mekh. Moscow State University Scientific Notes (Mechanics) Moscow State University 1940, 16, pp. 111–124.

    Google Scholar 

  37. Khuberian, K.M., Rational Shapes of Pipes, Reservoirs, and Pressure Vessels, Moscow, Gosstroiizdat, 1956.

    Google Scholar 

  38. Khutorianskii, N.M., Certain inverse and optimization problems in a two-dimensional theory of elasticity. In: Applied Problems of Strength and Plasticity, Gorkii, Gorkii University, 1978, 6, pp. 81–87.

    Google Scholar 

  39. Khutorianskii, N.M., On solution of certain two-dimensional and three-dimensional shape optimization problems in elastic bodies. In: Applied Problems of Strength and Plasticity, Gorkii, Gorkii University, 1978, 8, pp. 66–74.

    Google Scholar 

  40. Koiter, V.T., A General Theory of Elastoplastic Media, Moscow, Innostr. Liter. ( Russian translation ) 1961, 80 pp.

    Google Scholar 

  41. Komarov, V.A., On a rational distribution of material in structures, Izv. Akad. Nauk SSSR (Mekhanika), 1965, No. 5, pp. 85–87.

    Google Scholar 

  42. Konig, J.A., On optimum shakedown design. In: Proc. I UTAM Symposium on Optimal Design, Warsaw, 1973, Springer-Verlag, Berlin, 1975, pp. 405–414.

    Google Scholar 

  43. Kornishin, M.S., Aleksandrov, M.A., and Smoliarov, N.N., Computation of close to uniformly stressed deformable plates and shallow shells using numerical techniques. In: Proc. All-Union Conf. on Numerical Solutions of Problems in Elasticity and Plasticity; Part II, Novosibirsk, V.Ts. SO Akad. Nauk SSSR, 1976, pp. 69–76.

    Google Scholar 

  44. Kristenson, E.S., and Madson, N.F., On optimum shape of a fillet in plates subjected to multiple in-plane loading cases, Intern. J. Numer. Meth. Eng., 1976, 10, pp. 1007–1019.

    Article  Google Scholar 

  45. Kurshin, L.M., and Rastorguyev, G.I., On the problem of reinforcing the boundary of a hole in a plate, Izv. Akad. Nauk SSSR. MTT, 1979, No. 6, pp. 94–102.

    Google Scholar 

  46. Kurshin, L.M., and Rastorguyev, G.I., On the problem of reinforcing the boundary of a hole in a plate, using a moment-free, elastic rod, Prikl. Mat. Mekh., 1980, 44, No. 5, pp. 905–915.

    Google Scholar 

  47. Lepik, Iu.R., Application of Pontryagin’s maximality principle for an optimal design of cylindrical shells made from rigid-plastic materials. In: Advances in Mechanics of Deformable Media, Moscow, Nauka, 1975, pp. 340–349.

    Google Scholar 

  48. Lepik, U. [Iu.], Application of Pontryagin’s maximum principle for minimum weight design of rigid-plastic circular plates. Intern. J. Solids Structures, 1973, 9, pp. 615–624.

    Article  MATH  Google Scholar 

  49. Litvinov, V.G., and Panteleev, A.D., The problem of optimization of plates with variable thickness, Izv. Akad. Nauk SSSR. MTT, 1980, No. 2, pp. 174–181.

    MathSciNet  Google Scholar 

  50. Maier, G., Zavelani-Rossi, A., and Benedetti, D., A finite element approach to optimal design of plastic structures in plane stress, Intern. J. Numer. Meth. Eng., 1972, 4, pp. 455–473.

    Article  MATH  Google Scholar 

  51. Malkov, V.P., and Strongin, R.G., Optimization of structures with respect to weight and strength criteria. In: Solution techniques for problems in elasticity and plasticity. Gorkii, Gorkii University, 1971, 4, pp. 138–149.

    Google Scholar 

  52. Malkov, V.P., and Salganskaya, E.A., Optimal distribution of material in rotat- ing discs from a strength criterion, Izv. Vuzov, Aviats. Tekhnika,1976, No. 3.

    Google Scholar 

  53. Malkov, V.P., Equivalent reinforcement for a boundary of a cutout in a thin-walled member. In: Applied Problems of Strength and Plasticity. Gorkii, Gorkii University, 1979, 10, pp. 96–113.

    Google Scholar 

  54. Mansfield, E.H., An optimum surface of revolution for pressured shells, Intern. J. Mech. Science, 1981, 23, pp. 57–62.

    Article  MATH  Google Scholar 

  55. Mansfield, E.H., Neutral holes in plane sheet-reinforced plates which are elastically equivalent to the uncut sheet, Quart. J. Mech. Appl. Math., 1953, 6, Part 3, pp. 370–378.

    Article  MathSciNet  Google Scholar 

  56. Maxwell, C., Scientific Papers, Cambridge University Press, 1880, Vol. 2, pp. 175–177.

    Google Scholar 

  57. Mazzarella, C., and Polizzotto C., Optimum design of rigid-workhardening structures with constraints on deformation, Eng. Struct. 1980, 2, No. 3, pp. 138–146.

    Article  Google Scholar 

  58. Medvedev, N.G., and Totskii, N.P., Optimization of cylindrical shells with variable thickness and axially symmetric loads, Prikl. Mat. Mekh. 1984, 20,No. pp. 53–57.

    Google Scholar 

  59. Michell, A.G., and Melbourne, M.C.S., The limits of economy of material, Phil. Mag., Series 6, 1904, 8, pp. 589–597.

    Google Scholar 

  60. Mikhailovskii, E.I., Optimal reinforcement for the edges of a shell, Izv. Akad. Nauk SSSR-MTT, 1975, No. 1, pp. 42–51.

    Google Scholar 

  61. Mushtari, Kh.A., On the bending theory for a rectangular plate with variable thickness, Inzh. Zh., 1964, 4, No. 1, pp. 45–49.

    MATH  Google Scholar 

  62. Mushtari, Kh.A., On the bending theory for a plate with minimal weight and made of a composite material, Prikl. Mekh., 1967, 3, No. 4, pp. 1–7.

    Google Scholar 

  63. Nemirovskii, Iu.V., Estimates of the weight of optimal plastic structures, Inzh. Zhurnal, Mekh. Tve. Tela, 1968, No. 4, pp. 159–162.

    Google Scholar 

  64. Nemirovskii, Iu.V., and Reznikov, B.S., Uniform strength in conditions of creep for beams and plates, Mashinovedenie, 1969, No. 2, pp. 58–64.

    Google Scholar 

  65. Neuber, H., Der Zugbeanspruchte Flachstab mit optimalen Querschnittsubergang, Forsch. Ingenieurwiss. 1969, 35, pp. 29–30.

    Article  Google Scholar 

  66. Neuber, H., Zur Optimierung der Spannungskonzentration. In: Mechanics of Continuous Media and Related Problems of Analysis, Moscow, Nauka, 1972, pp. 375–380.

    Google Scholar 

  67. Oda, J., On a technique to obtain an optimum strength shape by the finite element method, Bull. JSME, 1977, 20, pp. 160–167.

    Article  Google Scholar 

  68. Onat, E.T., and Prager, W, Limit of economy of material in shells, Ingenieur, 1955, 67, pp. 46–49.

    Google Scholar 

  69. Onat, E.T., Shumann, W., and Shield, R.T., Design of circular plates for minimum weight, ZAMP, 1957, 8, No. 6, pp. 485–499.

    Article  MATH  Google Scholar 

  70. Pisarenko, G.S., and Lebedev, A.A., Deformation and Strength of Materials in a Complex Stressed State. Kiev, Naukova Dumka, 1976, 415 pp.

    Google Scholar 

  71. Pochtman, Iu.M., and Piatigorskii, Z.I., Computation and Optimal Design of a Structure with Consideration of Adaptability. Moscow, Nauka, 1978, 208 pp.

    Google Scholar 

  72. Polizzotto, C., Optimal design for multiple sets of loads, Meccanica, 1974, 9, pp. 206–219.

    Article  MathSciNet  MATH  Google Scholar 

  73. Polizzotto, C., Mazzarella, C., and Panzeca, T., Optimal design for work-hardening adaptation, Comp. Meth. Appl. Mech. Eng., 1977, 12, No. 2, pp. 129–144.

    Article  MATH  Google Scholar 

  74. Polizzotto, C., and Panzeca, T., Optimal design of beams for workhardening adaptation. In: Optimization of Distributed Parameter Structures, Iowa, 1980, E.J. Haug and J. Cea (eds.), Alphen aan den Rijn, Sijthoff-Noordhoff, 1981, pp. 910–927.

    Google Scholar 

  75. Prandtl, L., Anwendungsbeispiele zu einem Henkyschen Satz über das plastische Gleichgewicht, Ztschrft angew. Math. Mech., 1923, 3, No. 6.

    Google Scholar 

  76. Rabinovich, I.M., Beam systems of minimal weight. In: Proc. II-nd All-Union Conf. Theoretical and Applied Mechanics, Moscow, Nauka, 1966, Vol. 3, pp. 265–275.

    Google Scholar 

  77. Runge, C., and Konig, H., Vorlesungen uber numerischen Rechnen, Berlin, 1924.

    Google Scholar 

  78. Save, M.A., Some aspects of minimum weight design. In: Engineering Plasticity, J. Heymann and F.A. Leckie (eds.), Cambridge Univ. Press, 1968, pp. 611–6626.

    Google Scholar 

  79. Save, M.A., A unified formulation of the theory of optimal plastic design with convex cost functions, J. Struct. Mech., 1972, 1, No. 2, pp. 257–276.

    Article  Google Scholar 

  80. Savin, G.N., Stress Distribution around Openings, Kiev, Naukova Dumka, 1968, 887 pp.

    Google Scholar 

  81. Savin, G.N., Stress Concentration around Openings, Moscow and Leningrad, Gostekhizdat, 1951, 496 pp.

    Google Scholar 

  82. Schnack, E., An optimization procedure for stress concentrations by the finite element technique, Intern. J. Numer. Meth. Eng., 1979, 14, pp. 115–124.

    Article  MATH  Google Scholar 

  83. Shamiev, F.G., On designing ring-shaped plates of minimal weight, Izv. Akad. Nauk. Az. SSR, Fiz-Mat. Tekh. Nauk, 1963, No. 3, pp. 13–20.

    Google Scholar 

  84. Shamiev, F.G., On designing elliptically shaped plates of minimal weight, lzv. Akad. Nauk, Az. SSR, Fiz-Mat Tekh. Nauk, 1966, No. 4, pp. 23–27.

    Google Scholar 

  85. Shefer, G., and Demkowicz, L., Optimal design of elastic nonlinear plates by means of the mini-max theory. In: Optimization Methods in Structural Design, H. Eschenauer and N. Olhoff (eds.), Mannheim Bibliogr. Institute, 1983, pp. 409–414.

    Google Scholar 

  86. Shirko, I.V., Axially symmetric bending of a cylindrical shell with uniform strength. Prikl. Mekh., 1969, 5, No. 4, pp. 45–53.

    Google Scholar 

  87. Shirko, I.V., The shape of a plate with uniform strength, Inzhin. Zh., 1965, 5, No. 2, pp. 293–298.

    Google Scholar 

  88. Sirazutdinov, Iu.K., Beam cross-sections of uniform strength, Proc. Kazan Aviation Institute, 1974, No. 168, pp. 11–18.

    Google Scholar 

  89. Strang, G., and Kohn, R.V., Hencky-Prandtl nets and constrained Michell trusses. In: Proc. Intern. Symp. Optimum Structural Design, University of Arizona, Tucson, Arizona, 1981, pp. 4. 17–4. 22.

    Google Scholar 

  90. Sirazutdinov, Iu.K., Designs of optimal systems of beams, Archivum Inzynierji Lgdowej, 1979, 25, No. 2, pp. 245–264.

    Google Scholar 

  91. Sofronov, Iu.D., Designs of uniformly stressed and of uniform strength trusses, beams and frames subjected to cyclic loads, with consideration of hysteresis losses in materials. In: Loss of Energy in Vibrations of Mechanical Systems. Kiev, Naukova Dumka, 1968, pp. 76–82.

    Google Scholar 

  92. Timoshenko, S.P., Strength of Materials, Moscow, Fizmatgiz, 1960, Vol. 1, 380 pp.

    Google Scholar 

  93. Timoshenko, S.P., and Voinovski-Krieger, S., Plates and Shells, Moscow, Nauka, 1966, 636 pp.

    MATH  Google Scholar 

  94. Tveergand, V., On the optimum shape of a fillet bar with restrictions. In: IUTAM Symposium on Optimal Design, Warsaw, 1973. Springer Verlag, Berlin, 1975, pp. 181–195.

    Google Scholar 

  95. Vigderhauz, S.B., An integral equation for a problem in two-dimensional theory of elasticity, Prikl. Mat. Mekh., 1976, 40, No. 3, pp. 566–569.

    Google Scholar 

  96. Vigderhauz, S.B., On a case of the inverse problem of two-dimensional theory of elasticity, Prikl. Mat. Mekh., 1977, 41, No. 5, pp. 902–908.

    Google Scholar 

  97. Vigderhauz, S.B., Optimality conditions in axially symmetric problems of the theory of elasticity, Prikl. Mat. Mekh., 1982, 46, No. 2, pp. 278–282.

    Google Scholar 

  98. Vigderhauz, S.B., An inverse problem in a three-dimensional theory of elasticity, Izv. Akad. Nauk SSSR. MTT, 1983, No. 2, pp. 90–93.

    Google Scholar 

  99. Wheeler, L., On the role of constant stress surfaces in the problem of minimizing elastic stress concentrations, Intern. J. Solids Structures, 1976, 12, No. 11, pp. 779–789.

    Article  MATH  Google Scholar 

  100. Zavelani, A., Maier, G., and Binda, L., Shape optimization of plastic structures. In: IUTAM Symposium on Optimal Design, Warsaw, 1973. Springer Verlag, Berlin, 1975, pp. 181–195.

    Google Scholar 

  101. Zienkiewicz, O.C., and Campbell, J.S., Shape optimization and sequential linear programming. In: Optimum Structural Design, R.H. Gallagher and O.C. Zienkiewicz (eds.), Wiley, New York, 1973, pp. 109–126.

    Google Scholar 

  102. Ziegler, N., Dome with uniform strength, Mechanika, 1952, pp. 127–132.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Banichuk, N.V. (1990). Application of Strength and Weight Criteria. In: Introduction to Optimization of Structures. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3376-3_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-3376-3_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7988-4

  • Online ISBN: 978-1-4612-3376-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics