×

zbMATH — the first resource for mathematics

Optimal design of midsurface of shells: Differentiability proof and sensitivity computation. (English) Zbl 0626.73097
The paper deals with optimal design of the midsurface of shells with special emphasis on calculation of the gradient of the objective function. It has been assumed that criteria of optimization depend on the midsurface shape directly and also through the displacement field. This second assumption is not conventional and in the reviewer’s opinion it is incorrect. The displacements of certain points or regions might be the optimization criteria themself. The physical meaning of the optimization criteria applied in the paper are not discussed. The paper has a cognizable character, but it is far from technical applications.
The author ignores all previous results obtained in the area of optimal shell design. The state-of-the-art paper in this area was written by J. Kruzelecki and M. Zyczkowski [Solid Mech. Arch. 10, 101-170 (1985; Zbl 0567.73092)].
Reviewer: St.Jendo

MSC:
74P99 Optimization problems in solid mechanics
49K40 Sensitivity, stability, well-posedness
74K15 Membranes
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abraham, Holmes, Marsden (1983) Manifolds, Tensor Analysis and Applications. Addison-Wesley, Reading, MA. · Zbl 0508.58001
[2] Ahmad, Irons, Zienkiewicz (1970) Analysis of thick and thin shell structures by curved finite elements. Internat J Numer Methods Engng 2:419-451 · doi:10.1002/nme.1620020310
[3] Argyris, Lochner (1972) On the application of the SHEBA shell element. Comput. Methods Appl Mech Engng 1:317-347 · doi:10.1016/0045-7825(72)90012-6
[4] Bathe, Batoz, Leewing (1980) A study of three node triangular plate bending elements. Internat J Numer Methods Engng 15:1771-1812 · Zbl 0463.73071 · doi:10.1002/nme.1620151205
[5] Batoz (1982) An explicit formulation for an efficient triangular plate bending element. Internat J Numer Methods Engng 18:1077 · Zbl 0487.73087 · doi:10.1002/nme.1620180711
[6] Bernadou, Boisserie (1982) The Finite Element Method in Thin Shell Theory: Application to Arch Dam Simulations. Birkhäuser, Basle · Zbl 0497.73069
[7] Bernadou, Ciarlet (1976) Sur l’ellipticité du modèle linéaire de coques de W. T. Koiter. In Glowinsky, Lions (eds) Comp Meth Appl Sci & Eng. Lecture Notes in Economics and Mathematical Systems, vol 134. Springer-Verlag, Berlin, pp 89-136 · Zbl 0356.73066
[8] Chen, Olhoff (1981) Optimal design of solid elastic plates, optimization of distributed parameter structures. In Haug, Céa (eds) vol 1. Sijthoff and Noordhoff, Amsterdam, pp 278-303
[9] Ciarlet (1980) The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam · Zbl 0511.65078
[10] Ciarlet, Destuynder (1979) Approximations of 3-dimensional models by 2-dimensional models in plate theory. In Glowinsky, Rodin, Zienkiewicz (eds) Energy Methods in Finite Element Analysis. Wiley, Chichester, pp 33-45
[11] Clough, Johnson (1970) Finite element analysis of arbitrary thin shells. Proceedings of the ACI Symposium on Concrete Thin Shells, New York, pp 333-363
[12] Destuynder (1985) Acta Applicandae Mathematicae, vol 4. Reidel, Dordrecht, p 1563
[13] Dieudonne (1960) Foundations of Modern Analysis. Academic Press, New York
[14] Koiter (1970) On the foundations of the linear theory of thin elastic shells. Proc Kon Ned Akad Wetensch B73:169-195 · Zbl 0213.27002
[15] Lelong, Ferrand (1963) Géométrie différentielle. Masson, Paris
[16] Lions (1968) Contrôle Optimal des Systèmes Gouvernés par des Équations aux Dérivées Partielles. Dunod-Gauthier Villars, Paris
[17] Love (1934) The Mathematical Theory of Elasticity. Cambridge University Press, Cambridge
[18] Naghdi (1972) The theory of shell and plates. In Handbuch der Physik, vol VI a-2. Springer-Verlag, Berlin, pp 425-640
[19] Novozhilov (1970) Thin Shell Theory. Noordhoff, Amsterdam
[20] Rousselet (1982) Note on design differentiability of the static response of elastic structures. J Structural Mech 10:353-358
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.