By V. Komkov

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**Extra info for Sensitivity of Functionals with Applications to Engineering Sciences: Proceedings of a Special Session of the American Mathematical Society Spring Mee**

**Sample text**

Leonhardi Euleri Opera Omnia, Vol. X, ser. secundae, Society for Natural Sciences of Switzerland, 1960, in particular the section of C. Truesdell's historical notes, p. 1638-1788, on the rational mechanics of flexible or elastic bodies. 2. L. Lagrange Sur la figure des colonnes, Miscellanea Taurinensia, Vol. V, 1970, (see p. 123-125). 3. B. Keller, The shape of the strongest column, Archives of Rational Mechanics and Analysis, Vol. 5 (1960), p. 275-285. 4. I. B. Keller, Strongest columns and isoperimetric inequalities for eigenvalues, J.

Therefore, the F i n i t e Element technique can be employed to solve the problem numerically. In section 2, such a v a r i a t i o n a l formulation and admissible function space are defined and the equivalence between the v a r i a t i o n a l formulation and the Equations 1-4. We also prove the existence and uniqueness o f the s o l u t i o n . In section 3, the material d e r i v a t i v e concept is employed to obtain the d i r e c t i o n a l d e r i v a t i v e of t o r s i o n a l r i g i d i t y with respect to the shape of the domain by allowing both Fi and Fo to vary.

60, (1980), p. 503-507. 24. V. Komkov and C. S. meeting in New York, special session on sensitivity of functionals, April 1983. 25. G. Litvinov, Optimal Control Problem for the Fundamental Frequency of a Plate having a Variable Thickness, Vichesl. Mat. i Mat. Fiz. 19, #4 (1979), p. 866-877. 26. A. Krys'ko, The Optimal Control Problems for the Fundamental Frequency of Inhomogeneous Shells, Prikl. Mekh. Vol. i_8, #4, (1982), p. 41-47. , New York, as Soviet Applied Mechanics) 27. P. Seyranian, Quasioptimal Solutions to Optimal Design Problems with Various Constraints, Soviet Applied Mechanics, Vol.