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

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References | Additional Information

**[1]**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**, https://doi.org/10.1007/BF00926999**[2]**R. T. Shield and W. Prager,*Optimal structural design for given deflection*, Zeit. angewandte Math. Phys.**21**, 513-523 (1970)**[3]**L. J. Icerman,*Optimal structural design for given dynamic deflection*, Int. J. Solids Struct.**5**, 473-490 (1969)**[4]**Z. Mróz,*Optimal design of elastic structures subjected to dynamic, harmonically-varying loads*, Zeit. angewandte Math. Mech.**50**, 303-309 (1970)**[5]**R. H. Plaut,*Optimal structural design for given deflection under periodic loading*, Quart. Appl. Math.**29**, 315-318 (1971)**[6]**R. M. Brach,*Minimum dynamic response for a class of simply supported beam shapes*, Int. J. Mech. Sci.**10**, 429-439 (1968)**[7]**R. H. Plaut,*On minimizing the response of structures to dynamic loading*, Zeit. angewandte Math. Phys.**21**, 1004-1010 (1970)**[8]**Frithiof I. Niordson,*On the optimal design of a vibrating beam*, Quart. Appl. Math.**23**(1965), 47–53. MR**0175392**, https://doi.org/10.1090/S0033-569X-1965-0175392-8**[9]**M. J. Turner,*Design of minimum mass structures with specified natural frequencies*, AIAA J.**5**, 406-412 (1967)**[10]**W. Prager and J. E. Taylor,*Problems of optimal structural design*, J. Appl. Mech.**35**, 102-106, (1968)**[11]**R. M. Brach,*On the extremal fundamental frequencies of vibrating beams*, Int. J. Solids Struct.**4**, 667-674 (1968)**[12]**C. Y. Sheu,*Elastic minimum-weight design for specified fundamental frequency*, Int. J. Solids Struct.**4**, 953-958 (1968)**[13]**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**[14]**Joseph B. Keller,*The shape of the strongest column*, Arch. Rational Mech. Anal.**5**(1960), 275–285 (1960). MR**0128160**, https://doi.org/10.1007/BF00252909**[15]**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**0137381****[16]**J. E. Taylor,*The strongest column: an energy approach*, J. Appl. Mech.**34**, 486 (1967)**[17]**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**[18]**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**0204000**, https://doi.org/10.1007/BF01594536

Additional Information

DOI:
https://doi.org/10.1090/qam/99713

Article copyright:
© Copyright 1973
American Mathematical Society