Review Questions 689
References and Bibliography
12.1 R. S. Schechter,The Variational Method in Engineering, McGraw-Hill, New York, 1967.
12.2 M. M. Denn,Optimization by Variational Methods, McGraw-Hill, New York, 1969.
12.3 M. J. Forray,Variational Calculus in Science and Engineering, McGraw-Hill, New York,
1968.
12.4 A. E. Bryson and Y. C. Ho,Applied Optimal Control, Wiley, New York, 1975.
12.5 A. Shamaly, G. S. Christensen, and M. E. El-Hawary, Optimal control of a large tur-
boalternator,Journal of Optimization Theory and Applications, Vol. 34, pp. 83–97,
1981.
12.6 W. Prager, Optimality criteria in structural design,Proceedings of the National Academy
of Science, Vol. 61, No. 3, pp. 794–796, 1968.
12.7 V. B. Venkayya, N. S. Khot, and V. S. Reddy,Energy Distribution in Optimum Structural
Design, AFFDL-TR-68-156, 1968.
12.8 L. Berke,Convergence Behavior of Optimality Criteria Based Iterative Procedures,
AFFDL-TM-72-1-FBR, Jan. 1972.
12.9 V. B. Venkayya, Structural optimization using optimality criteria: a review and some
recommendations,International Journal for Numerical Methods in Engineering, Vol. 13,
pp. 203–228, 1978.
12.10 N. S. Khot, Algorithms based on optimality criteria to design minimum weight structures,
Engineering Optimization, Vol. 5, pp. 73–90, 1981.
12.11 S. K. Hati and S. S. Rao, Determination of optimum profile of one-dimensional cooling
fins,ASME Journal of Vibration, Acoustics, Stress and Reliability in Design, Vol. 105,
pp. 317–320, 1983.
Review Questions
12.1 Answer true or false:
(a)Design variables of an optimal control problem include both state and control
variables.
(b)Reciprocal approximations consider reciprocals of member areas as design vari-
ables.
(c)Optimality criteria methods can be used for the optimization of nonlinear struc-
tures with displacement constraints.
(d)A variational operator is similar to a differential operator.
(e)Calculus of variations can be used only for finding the extrema of functionals
with no constraints.
(f)Optimality criteria methods can be used to solve any optimization problem.
12.2 Define the following terms:
(a)Brachistochrone
(b)State vector
(c)Performance index
(d)Adjoint equations
(e)Transversality condition
(f)Optimality criteria methods
