Abstract
Steepest-descent optimal control techniques have been used extensively for dynamic systems in one independent variable and with a full set of initial conditions. This paper presents an extension of the steepest-descent technique to mechanical design problems that are described by boundary-value problems with one or more independent variables. The method is illustrated by solving finite-dimensional problems, problems with distribution of design over one space dimension, and problems with distribution of design over two space dimensions.
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References
Bryson, A. E., andDenham, W. F.,A Steepest-Ascent Method for Solving Optimum Programing Problems, Journal of Applied Mechanics, Vol. 29, pp. 247–257, 1962.
Bryson, A. E., andHo, Y. C.,Applied Optimal Control, Blaisdell Publishing Company, Waltham, Massachusetts, 1969.
Miele, A., Pritchard, R. E., andDamoulakis, J. N.,Sequential Gradient Restoration Algorithm for Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 5, pp. 235–282, 1970.
Hennig, G. R., andMiele, A.,Sequential Gradient Restoration Algorithm for Optimal Control Problems with Bounded State, Journal of Optimization Theory and Applications, Vol. 12, pp. 61–98, 1973.
Arora, J. S., Haug, E. J., andRim, K.,Optimal Design of Trusses Under Multiple Constraint Conditions of Mechanics, Development in Mechanics, Vol. 6, Edited by L. H. N. Lee and A. A. Szewazyk, University of Notre Dame Press, South Bend, Indiana, 1971.
Haug, E. J., Pan, K. C., andStreeter, T. D.,A Computational Method for Optimal Structural Design, I: Piecewise Uniform Structures, International Journal for Numerical Methods in Engineering, Vol. 5, pp. 171–184, 1972.
Haug, E. J., Pan, K. C., andStreeter, T. D.,A Computational Method for Optimal Structural Design, II: Continuous Problems, International Journal for Numerical Methods in Engineering (to appear).
Haug, E. J.,Computer Aided Design of Mechanical Systems, Headquarters, US Army Material Command, Washington, DC, Engineering Design Handbook No. 706–192, 1973.
Schmit, L. A.,Structural Design by Systematic Synthesis, Proceedings of the Second National Conference on Electronic Computation, Structural Division, American Society for Civil Engineering, Pittsburgh, Pennsylvania, 1960.
Gallagher, R. H., andZienkiewicz, O. C.,Optimum Structural Design: Theory and Applications, John Wiley and Sons, New York, New York, 1973.
Lanczos, C.,Linear Differential Operators, Van Nostrand, London, England, 1961.
Forshad, M.,Variation of Eigenvalues and Eigenfunctions in Continuum Mechanics, AIAA Journal, Vol. 12, pp. 560–561, 1974.
Luenberger, D. G.,Optimization by Vector Space Methods, John Wiley and Sons, New York, New York, 1969.
Przemieniecki, J. S.,Theory of Matrix Structural Analysis, McGraw-Hill Book Company, New York, New York, 1968.
Arora, J. S.,On Improving Efficiency of an Algorithm for Structural Optimization and a User's Manual for Program TRUSSOPT 2, University of Iowa, Iowa City, Iowa, Department of Mechanics and Hydraulics, Technical Report No. 12, 1974.
Bathe, K. J., andWilson, E. L.,Solution Methods for Eigenvalue Problems in Structural Mechanics, International Journal for Numerical Methods in Engineering, Vol. 6, pp. 213–216, 1973.
Venkayya, V. B.,Design of Optimum Structures, Journal of Computers and Structures, Vol. 1, pp. 265–309, 1971.
Venkayya, V. B., Khot, N. S., andReddy, V. S.,Energy Distribution in an Optimum Structural Design, Wright-Patterson Air Force Base, Ohio, Air Force Flight Dynamics Laboratory, Technical Report No. AFFDL-TR-68-156, 1969.
Pickett, R. M., Jr., Rubinstein, M. F., andNelson, R. B.,Automated Structural Synthesis Using a Reduced Number of Design Coordinates, AIAA Journal, Vol. 11, pp. 489–494, 1973.
Schmit, L. A., andFarshi, B.,Some Approximation Concepts for Structural Synthesis, AIAA Journal, Vol. 12, pp. 692–699, 1974.
Haug, E. J., andKirmser, P. G.,Minimum Weight Design of Beams with Inequality Constraints on Stress and Deflection, Journal of Applied Mechanics, Vol. 34, pp. 999–1004, 1967.
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Communicated by C. T. Leondes
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Haug, E.J., Arora, J.S. & Matsui, K. A steepest-descent method for optimization of mechanical systems. J Optim Theory Appl 19, 401–424 (1976). https://doi.org/10.1007/BF00941484
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DOI: https://doi.org/10.1007/BF00941484