Approximate solutions to some static and dynamic optimal structural design problems
Author:
Raymond H. Plaut
Journal:
Quart. Appl. Math. 30 (1973), 535-539
DOI:
https://doi.org/10.1090/qam/99713
MathSciNet review:
QAM99713
Full-text PDF Free Access
References |
Additional Information
- C. Y. Sheu and W. Prager, Minimum-weight design with piecewise constant specific stiffness, J. Optim. Theory Appl. 2 (1968), no. 3, 179–186. MR 1551285, DOI https://doi.org/10.1007/BF00926999
R. T. Shield and W. Prager, Optimal structural design for given deflection, Zeit. angewandte Math. Phys. 21, 513–523 (1970)
L. J. Icerman, Optimal structural design for given dynamic deflection, Int. J. Solids Struct. 5, 473–490 (1969)
Z. Mróz, Optimal design of elastic structures subjected to dynamic, harmonically-varying loads, Zeit. angewandte Math. Mech. 50, 303–309 (1970)
R. H. Plaut, Optimal structural design for given deflection under periodic loading, Quart. Appl. Math. 29, 315–318 (1971)
R. M. Brach, Minimum dynamic response for a class of simply supported beam shapes, Int. J. Mech. Sci. 10, 429–439 (1968)
R. H. Plaut, On minimizing the response of structures to dynamic loading, Zeit. angewandte Math. Phys. 21, 1004–1010 (1970)
- Frithiof I. Niordson, On the optimal design of a vibrating beam, Quart. Appl. Math. 23 (1965), 47–53. MR 175392, DOI https://doi.org/10.1090/S0033-569X-1965-0175392-8
M. J. Turner, Design of minimum mass structures with specified natural frequencies, AIAA J. 5, 406–412 (1967)
W. Prager and J. E. Taylor, Problems of optimal structural design, J. Appl. Mech. 35, 102–106, (1968)
R. M. Brach, On the extremal fundamental frequencies of vibrating beams, Int. J. Solids Struct. 4, 667–674 (1968)
C. Y. Sheu, Elastic minimum-weight design for specified fundamental frequency, Int. J. Solids Struct. 4, 953–958 (1968)
T. A. Weisshaar, An application of control theory methods to the optimization of structures having dynamic or aeroelastic constraints, SUDAAR No. 412, Oct. 1970, Department of Aeronautics and Astronautics, Stanford University
- Joseph B. Keller, The shape of the strongest column, Arch. Rational Mech. Anal. 5 (1960), 275–285 (1960). MR 128160, DOI https://doi.org/10.1007/BF00252909
- I. Tadjbakhsh and J. B. Keller, Strongest columns and isoperimetric inequalities for eigenvalues, Trans. ASME Ser. E. J. Appl. Mech. 29 (1962), 159–164. MR 137381
J. E. Taylor, The strongest column: an energy approach, J. Appl. Mech. 34, 486 (1967)
M. Zyczkowski and A. Gajewski, Optimal structural design in non-conservative problems of elastic stability, in Proceedings of the IUTAM Symposium on Instability of Continuous Systems (H. Leipholz, ed.), Springer-Verlag, Berlin, 1971, pp. 295–301
- Mark Levinson, Application of the Galerkin and Ritz methods to nonconservative problems of elastic stability, Z. Angew. Math. Phys. 17 (1966), 431–442 (English, with German summary). MR 204000, DOI https://doi.org/10.1007/BF01594536
C. Y. Sheu and W. Prager, Minimum-weight design with piecewise constant specific stiffness, J. Optimization Theory and Applications 2, 179–186 (1968)
R. T. Shield and W. Prager, Optimal structural design for given deflection, Zeit. angewandte Math. Phys. 21, 513–523 (1970)
L. J. Icerman, Optimal structural design for given dynamic deflection, Int. J. Solids Struct. 5, 473–490 (1969)
Z. Mróz, Optimal design of elastic structures subjected to dynamic, harmonically-varying loads, Zeit. angewandte Math. Mech. 50, 303–309 (1970)
R. H. Plaut, Optimal structural design for given deflection under periodic loading, Quart. Appl. Math. 29, 315–318 (1971)
R. M. Brach, Minimum dynamic response for a class of simply supported beam shapes, Int. J. Mech. Sci. 10, 429–439 (1968)
R. H. Plaut, On minimizing the response of structures to dynamic loading, Zeit. angewandte Math. Phys. 21, 1004–1010 (1970)
F. I. Niordson, On the optimum design of a vibrating beam, Quart. Appl. Math. 23, 47–53 (1965)
M. J. Turner, Design of minimum mass structures with specified natural frequencies, AIAA J. 5, 406–412 (1967)
W. Prager and J. E. Taylor, Problems of optimal structural design, J. Appl. Mech. 35, 102–106, (1968)
R. M. Brach, On the extremal fundamental frequencies of vibrating beams, Int. J. Solids Struct. 4, 667–674 (1968)
C. Y. Sheu, Elastic minimum-weight design for specified fundamental frequency, Int. J. Solids Struct. 4, 953–958 (1968)
T. A. Weisshaar, An application of control theory methods to the optimization of structures having dynamic or aeroelastic constraints, SUDAAR No. 412, Oct. 1970, Department of Aeronautics and Astronautics, Stanford University
J. B. Keller, The shape of the strongest column, Arch. Rat. Mech. Anal. 5, 275–285 (1960)
I. Tadjbakhsh and J. B. Keller, Strongest columns and isoperimetric inequalities, J. Appl. Mech. 29, 159–164 (1962)
J. E. Taylor, The strongest column: an energy approach, J. Appl. Mech. 34, 486 (1967)
M. Zyczkowski and A. Gajewski, Optimal structural design in non-conservative problems of elastic stability, in Proceedings of the IUTAM Symposium on Instability of Continuous Systems (H. Leipholz, ed.), Springer-Verlag, Berlin, 1971, pp. 295–301
M. Levinson, Application of the Galerkin and Ritz methods to nonconservative problems of elastic stability, Zeit. angewandte Math. Phys. 17, 431–442 (1966)
Additional Information
Article copyright:
© Copyright 1973
American Mathematical Society
