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computer aided design; existence of optimal control; axisymmetric thin elastic shells; constant thickness; meridian curves of middle surfaces taken for designe variable; given volume; own weight loading; hydrostatic pressure of liquid; external or internal pressure; cost functional is second invariant of stress deviator; Banach space; existence of solution; convergence

References:

[1] O. C. Zienkiewicz: **The finite element method in Engineering Science**. Mc Graw Hill, London 1971. MR 0315970 | Zbl 0237.73071

[2] J. Nečas I. Hlaváček: **Mathematical theory of elastic and elasto-plastic bodies**. Elsevier, Amsterdam 1981.

[3] J. M. Boisserie R. Glowinski: **Optimization of the thickness law for thin axisymmetric shells**. Computers & Structures, 8 (1978), 331 - 343. DOI 10.1016/0045-7949(78)90176-1

[4] J. H. Ahlberg E. N. Nilson J. L. Walsh: **The theory of splines and their applications**. Academic Press, New York 1967. (Russian translation - Mir, Moskva 1972.) MR 0239327

[5] Š. B. Stečkin, Ju. N. Subbotin: **Splines in numerical mathematics**. (Russian). Nauka, Moskva 1976. MR 0455278

[6] J. Céa: **Optimisation, théorie et algorithmes**. Dunod, Paris 1971. MR 0298892