On a problem of minimum weight design
Author:
Zenon Mróz
Journal:
Quart. Appl. Math. 19 (1961), 127-135
MSC:
Primary 73.49
DOI:
https://doi.org/10.1090/qam/135327
MathSciNet review:
135327
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Abstract: A problem of optimal design for perfectly plastic, isotropic structures is analyzed. It is shown that for such structures as plates or shells, an extremum of the volume, if it exists, is either a local maximum or a minimum.
H. G. Hopkins and W. Prager, Limits of economy of material in plates, J. Appl. Mech. 22, 372–374 (1955)
W. Prager, Minimum weight design of plates, De Ing. 67, 141–142 (1955)
- Walter Freiberger and Bekir Tekinalp, Minimum weight design of circular plates, J. Mech. Phys. Solids 4 (1956), 294–299. MR 80466, DOI https://doi.org/10.1016/0022-5096%2856%2990038-2
D. C. Drucker and R. T. Shield, Design for minimum weight, Proc. 9th Intern. Congr. Appl. Mech., Brussels, 1956
- D. C. Drucker and R. T. Shield, Bounds on minimum weight design, Quart. Appl. Math. 15 (1957), 269–281. MR 90269, DOI https://doi.org/10.1090/S0033-569X-1957-90269-X
E. T. Onat, W. Shumann and R. T. Shield, Design of plates for minimum weight, ZAMP 8, 485–489 (1957)
Z. Mróz, The load carrying capacity and minimum weight design of annular plates (in Polish) Rozpr. Inzyn. 4, 605–625 (1958)
- R. T. Shield, Plate design for minimum weight, Quart. Appl. Math. 18 (1960/61), 131–144. MR 112409, DOI https://doi.org/10.1090/S0033-569X-1960-0112409-2
- William Prager and Richard T. Shield, Minimum weight design of circular plates under arbitrary loading, Z. Angew. Math. Phys. 10 (1959), 421–426 (English, with German summary). MR 108938, DOI https://doi.org/10.1007/BF01601046
- Walter Freiberger, Minimum weight design of cylindrical shells, J. Appl. Mech. 23 (1956), 576–580. MR 0088919
- Walter F. Freiberger, On the minimum weight design problem for cylindrical sandwich shells, J. Aero. Sci. 24 (1957), 847–848. MR 89615
- R. T. Shield, On the optimum design of shells, J. Appl. Mech. 27 (1960), 316–322. MR 0112410
- M. Mikeladze, Weight and strength analysis of orthotropic rigid-plastic shells, Arch. Mech. Stos. 11 (1959), 17–31 (Russian, with English and Polish summaries). MR 102255
- William Prager, An introduction to plasticity, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1959. MR 0105910
- D. C. Drucker, W. Prager, and H. J. Greenberg, Extended limit design theorems for continuous media, Quart. Appl. Math. 9 (1952), 381–389. MR 45573, DOI https://doi.org/10.1090/S0033-569X-1952-45573-2
H. G. Hopkins and W. Prager, Limits of economy of material in plates, J. Appl. Mech. 22, 372–374 (1955)
W. Prager, Minimum weight design of plates, De Ing. 67, 141–142 (1955)
W. Freiberger and B. Tekinalp, Minimum weight design of circular plates, J. Mech. Phys. Solids 4, 294–299(1956)
D. C. Drucker and R. T. Shield, Design for minimum weight, Proc. 9th Intern. Congr. Appl. Mech., Brussels, 1956
D. C. Drucker and R. T. Shield, Bounds on minimum weight design, Quart. Appl. Math. 15, 269–281 (1957)
E. T. Onat, W. Shumann and R. T. Shield, Design of plates for minimum weight, ZAMP 8, 485–489 (1957)
Z. Mróz, The load carrying capacity and minimum weight design of annular plates (in Polish) Rozpr. Inzyn. 4, 605–625 (1958)
R. T. Shield, Plate design for minimum weight, Quart. Appl. Math. 28, 131–144 (1960)
W. Prager and R. T. Shield, Minimum weight design of circular plates under arbitrary loading, ZAMP 10, 421–426 (1959)
W. Freiberger, Minimum weight design of cylindrical shells, J. Appl. Mech. 23, 576–580 (1956)
W. Freiberger, On the minimum weight design problem for cylindrical sandwich shells, J. Aeron. Sciences 24, 847–848 (1957)
R. T. Shield, On the optimum design of shells, J. Appl. Mech. 27, 316–322 (1960)
M. Mikeladze, Weight and strength analysis of orthotropic rigid-plastic shells, (in Russian), Arch. Mech. Appliquee 11, 1 (1959)
W. Prager, An introduction to plasticity, Addison-Wesley Co., 1959
D. C. Drucker, W. Prager, H. T. Greenberg, Extended limit design theorems for continuous media, Quart. Appl. Math. 9, 381–389 (1952)
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Article copyright:
© Copyright 1961
American Mathematical Society