Bounds on minimum weight design
Authors:
D. C. Drucker and R. T. Shield
Journal:
Quart. Appl. Math. 15 (1957), 269-281
MSC:
Primary 73.2X
DOI:
https://doi.org/10.1090/qam/90269
MathSciNet review:
90269
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: A somewhat limited design procedure for elastic-perfectly plastic structures was developed previously [1]$^{**}$. It is extended here to provide upper and lower bounds on the minimum weight of three dimensional structures and is specialized to safe one and two dimensional structures in which either direct stresses or bending stresses are negligible. The generalization also includes the influence of body forces. In principle, therefore, such troublesome factors as the weight of the structure itself or centrifugal “forces” may be designed for in a direct manner. Radially symmetric plane stress and plate bending examples are solved to demonstrate direct design procedures.
- A. C. Pipkin (ed.), $\{$Collection of articles dedicated to William Prager on the occasion of his seventieth birthday$\}$, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973. With a preface by D. C. Drucker; SIAM J. Appl. Math. 25 (1973), no. 3. MR 0323208
J. Heyman, Plastic design of plane frames for minimum weight, Struct. Eng. 31, 125-129 (1953)
- J. Foulkes, The minimum-weight design of structural frames, Proc. Roy. Soc. London Ser. A 223 (1954), 482–494. MR 65379, DOI https://doi.org/10.1098/rspa.1954.0132
W. Prager, Minimum weight design of a portal frame, to appear in J. Eng. Mech. Div., A.S.C.E.
R. K. Livesley, The automatic design of structural frames, Quart. J. Mech. Appl. Math. 9, 257-278 (1956)
A. G. M. Michell, The limits of economy of material in frame-structures, Phil. Mag. (6) 8, 589-597 (1904)
H. G. Hopkins and W. Prager, Limits of economy of material in plates, J. Appl. Mech. Trans. A.S.M.E. 22, 372-374 (1955)
W. Prager, Minimum weight design of plates, De Ing. (sect. 0) 67, 0.141-0.142 (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, 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
- D. C. Drucker, A more fundamental approach to plastic stress-strain relations, Proceedings of the First U. S. National Congress of Applied Mechanics, Chicago, 1951, The American Society of Mechanical Engineers, New York, N. Y., 1952, pp. 487–491. MR 0054502
- D. C. Drucker and W. Prager, Soil mechanics and plastic analysis or limit design, Quart. Appl. Math. 10 (1952), 157–165. MR 48291, DOI https://doi.org/10.1090/S0033-569X-1952-48291-2
D. C. Drucker and R. T. Shield, Design for minimum weight, to appear in Proc. 9th Intern. Congr. Appl. Mech., Brussels, 1956
J. Heyman, Plastic design of plane frames for minimum weight, Struct. Eng. 31, 125-129 (1953)
J. Foulkes, Minimum weight design and the theory of plastic collapse, Quart. Appl. Math. 10, 347-358 (1953); Minimum weight design of structural frames, Proc. Roy. Soc. A223, 482-494(1954)
W. Prager, Minimum weight design of a portal frame, to appear in J. Eng. Mech. Div., A.S.C.E.
R. K. Livesley, The automatic design of structural frames, Quart. J. Mech. Appl. Math. 9, 257-278 (1956)
A. G. M. Michell, The limits of economy of material in frame-structures, Phil. Mag. (6) 8, 589-597 (1904)
H. G. Hopkins and W. Prager, Limits of economy of material in plates, J. Appl. Mech. Trans. A.S.M.E. 22, 372-374 (1955)
W. Prager, Minimum weight design of plates, De Ing. (sect. 0) 67, 0.141-0.142 (1955)
W. Freiberger and B. Tekinalp, Minimum weight design of circular plates, J. Mech. Phys. Solids 4, 294-299 (1956)
D. C. Drucker, W. Prager and H. J. Greenberg, Extended limit design theorems for continuous media, Quart. Appl. Math. 9, 381-389 (1952)
D. C. Drucker, A more fundamental approach to plastic stress-strain relations, Proc. 1st Natl. Congr. Appl. Mech., 487-491 (1951)
D. C. Drucker and W. Prager, Soil mechanics and plastic analysis or limit design, Qu art. Appl. Math. 10, 157-165 (1952); D. C. Drucker, Limit analysis of two and three dimensional soilmechanics problems, J. Mech. Phys. Solids 1, 217-226 (1953)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
73.2X
Retrieve articles in all journals
with MSC:
73.2X
Additional Information
Article copyright:
© Copyright 1957
American Mathematical Society