Abstract
This paper presents an application of two solution methods to the least-weight optimization of a simple sandwich beam with a frequency constraint. The first method, an adaptation of a numericalshooting technique used in optimal control, is found to give good results if unknown initial conditions can be reasonably approximated. The second method, a perturbation method used widely in theoretical mechanics and aerodynamics, yields approximate analytical expressions. These expressions can be used in turn to estimate starting values for the numerical technique. Converged numerical results are presented for a least-weight cantilever beam with fixed fundamental frequency and for a beam on simple supports with fixed fundamental frequency.
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Sheu, C. Y., andPrager, W.,Recent Developments in Optimal Structural Design, Applied Mechanics Review, Vol. 21, pp. 985–992, 1968.
Prager, W.,Optimization of Structural Design, Journal of Optimization Theory and Applications, Vol. 6, No. 1, 1970.
Pierson, B. L.,A Survey of Optimal Structural Design Under Dynamic Constraints, International Journal for Numerical Methods in Engineering, Vol. 4, pp. 491–499, 1972.
Prager, W., andTaylor, J. E.,Problems of Optimal Structural Design, Journal of Applied Mechanics, Vol. 90, pp. 102–106, 1968.
Ashley, H., andMcIntosh, S. C., Jr.,Application of Aeroelastic Constraints in Structural Optimization, Applied Mechanics, Edited by M. Hetenyi and W. G. Vincente, Springer-Verlag, Berlin, Germany, 1969.
Gwin, L. B., andMcIntosh, S. C., Jr.,A Method of Minimum Weight Synthesis for Flutter Requirements, Part 1, Analytical Investigation, Air Force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, Ohio, Technical Report No. AFFDL-TR-72-22, 1972.
Niordson, F. I.,On the Optimal Design of a Vibrating Beam, Quarterly of Applied Mathematics, Vol. 23, pp. 47–53, 1965.
Turner, M. J.,Design of Minimum-Mass Structures with Specified Natural Frequencies, AIAA Journal, Vol. 5, pp. 406–412, 1967.
Taylor, J. E.,Minimum-Mass Bar for Axial Vibration at Specified Natural Frequencies, AIAA Journal, Vol. 5, pp. 1911–1913, 1967.
Bisplinghoff, R., Ashley, H., andHalfman, R.,Aeroelasticity, Addison-Wesley Publishing Company, Reading, Massachusetts, 1955.
Weisshaar, T. A.,An Application of Control Theory Methods to the Optimization of Structures with Aeroelastic Constraints, Stanford University, Department of Aeronautics and Astronautics, Report No. SUDAAR-412, 1970.
Bryson, A. E., andHo, Y. C.,Applied Optimal Control, Blasidell Publishing Company, Waltham, Massachusetts, 1969.
Ashley, H., McIntosh, S. C., Jr., andWeatherill, W.,Optimization Under Aeroelastic Constraints, Symposium on Structural Optimization, AGARD Conference Proceedings No. 36, AGARD-CP-36-70, 1970.
Armand, J. L., andVitte, W. J.,Foundations of Aeroelastic Optimization and Some Applications to Continuous Systems, Stanford University, Department of Aeronautics and Astronautics, Report No. SUDAAR-390, 1969.
McIntosh, S. C., Jr., Weisshaar, T. A., andAshley, H.,Progress in Aeroelastic Optimization—Analytical vs. Numerical Approaches, Stanford University, Department of Aeronautics and Astronautics, Report No. SUDAAR-383, 1969.
Cole, J. D.,Perturbation Methods in Applied Mathematics, Blaisdell Publishing Company, Waltham, Massachusetts, 1968.
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Communicated by W. Prager
The author is indebted to Professor W. Prager for his helpful comments.
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Weisshaar, T.A. Approximate solutions to idealized structural dynamic optimization problems. J Optim Theory Appl 16, 119–133 (1975). https://doi.org/10.1007/BF00935627
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DOI: https://doi.org/10.1007/BF00935627