Optimal design of cylindrical shell with a rigid obstacle. (English) Zbl 0678.73059

The paper deals with the study of optimal design problems in mechanics, whose variational form are inequalities expressing the principle of virtual power in its inequality form. The optimal design of an elastic cylindrical shell subject to unilateral constraints is considered. It is assumed that the bending of the shell is limited by a rigid obstacle. The thickness of the shell is taken as the design variable.
The paper has a cognizable character, but is is not far from technical applications.
Reviewer: St.Jendo


74P99 Optimization problems in solid mechanics
49J27 Existence theories for problems in abstract spaces
74K15 Membranes
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
49J40 Variational inequalities
49J99 Existence theories in calculus of variations and optimal control
Full Text: DOI EuDML


[1] R. A. Adams: Sobolev Spaces. Academic Press, New York, San Francisco, London 1975, · Zbl 0314.46030
[2] H. Attouch: Convergence des solution d’inéquations variationnelles avec obstacle. Proceedings of the International Meeting on Recent Methods in Nonlinear analysis. (Rome, May 1978) by E. De Giorgi - E. Magenes - U. Mosco. · Zbl 0404.49007
[3] V. Barbu: Optimal control of variational inequalities. Pitman Advanced Publishing Program, Boston. London, Melbourne 1984. · Zbl 0574.49005
[4] I. Boccardo C. Dolcetta: Stabilita delle soluzioni di disequazioni variazionali ellittiche e paraboliche quasi-lineari. Ann. Universeta Ferrara, 24 (1978), 99-111. · Zbl 0408.49011
[5] J. Céa: Optimisation, Théorie et Algorithmes. Dunod Paris, 1971. · Zbl 0211.17402
[6] G. Duvaut J. L. Lions: Inequalities in mechanics and physics. Berlin, Springer Verlag 1975. · Zbl 0331.35002
[7] R. Glowinski: Numerical Methods for Nonlinear Variational Problems. Springer Verlag 1984. · Zbl 0536.65054
[8] I. Hlaváček I. Bock J. Lovíšek: Optimal Control of a Variational Inequality with Applications to Structural Analysis. II. Local Optimization of the Stress in a Beam. III. Optimal Design of an Elastic Plate. Appl. Math. Optimization 13: 117-136/1985. · Zbl 0582.73081 · doi:10.1007/BF01442202
[9] D. Kinderlehrer G. Stampacchia: An introduction to variational inequalities and their applications. Academic Press, 1980. · Zbl 0457.35001
[10] V. G. Litvinov: Optimal control of elliptic boundary value problems with applications to mechanics. Moskva ”Nauka” 1987) · Zbl 0628.49001
[11] M. Bernadou J. M. Boisserie: The finite element method in thin shell. Theory: Application to arch Dam simulations. Birkhäuser Boston 1982. · Zbl 0497.73069
[12] J. Nečas I. Hlaváček: Mathematical theory of elastic and elasto-plastic bodies: An introduction. Elsevier Scientific Publishing Company, Amsterdam 1981.
[13] U. Mosco: Convergence of convex sets of solutions of variational inequalities. Advances of Math. 3 (1969), 510-585. · Zbl 0192.49101 · doi:10.1016/0001-8708(69)90009-7
[14] K. Ohtake J. T. Oden N. Kikuchi: Analysis of certain unilateral problems in von Karman plate theory by a penalty method - PART 1. A variational principle with penalty. Computer Methods in Applied Mechanics and Engineering 24 (1980), 117-213, North Holland Publishing Company. · Zbl 0457.73095 · doi:10.1016/0045-7825(80)90045-6
[15] P. D. Panagiotopoulos: Inequality Problems in Mechanics and Applications. Convex and Nonconvex Energy functions. Birkhäuser-Verlag, Boston-Basel-Stutgart, 1985. · Zbl 0579.73014
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.