About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

First Page Preview
Salač, Petr
Shape optimization of elastic axisymmetric plate on an elastic foundation. (English). Applications of Mathematics, vol. 40 (1995), issue 4, pp. 319-338
MSC: 73C99, 73K10, 73k40, 74B99, 74K20, 74P99 | MR 1331921 | Zbl 0839.73036 | DOI: 10.21136/AM.1995.134297
Keywords:
shape optimization; axisymmetric elliptic problems; elasticity
Summary:
An elastic simply supported axisymmetric plate of given volume, fixed on an elastic foundation, is considered. The design variable is taken to be the thickness of the plate. The thickness and its partial derivatives of the first order are bounded. The load consists of a concentrated force acting in the centre of the plate, forces concentrated on the circle, an axisymmetric load and the weight of the plate. The cost functional is the norm in the weighted Sobolev space of the deflection curve of radius. Existence of a solution of the optimization problem of the state problem is proved. Approximate problem is introduced and convergence of its solutions to that of the continuous problem is established.
References:
[1] D. Begis, R. Glowinski: Application de la méthode des éléments finis à l’approximation d’un problème de domaine optimal. Méthodes de résolution des problèmes approchés. Applied Mathematics. Optimization 2 (1975), 130–169. MR 0443372
[2] P.G. Ciarlet: The finite element method for elliptic problems. North-Holland, Amsterdam, 1978. MR 0520174 | Zbl 0383.65058
[3] I. Hlaváček: Optimization of the shape of axisymmetric shells. Apl. Mat. 28 (1983), 269–294. MR 0710176
[4] J. Nečas, I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies, An Introduction. Elsevier, Amsterdam, 1981. MR 0600655
[5] J. Chleboun: Optimal design of an elastic beam on an elastic basis. Apl. Mat. 31 (1986), 118–140. MR 0837473 | Zbl 0606.73108
[6] K. Rektorys: Variational methods in mathematics, science and engineering. D. Reidel Publishing Company, Dordrecht-Holland/Boston U.S.A., 1977. MR 0487653
[7] A. Kufner: Weighted Sobolev spaces. John Wiley & Sons, New York, 1985. MR 0802206 | Zbl 0579.35021
[8] H. Triebel: Interpolation theory, function spaces, differential operators. VEB Deutscher Verlag der Wissenschaften, Berlin, 1975. MR 0500580
[9] V. Jarník: Differential calculus II. Academia, Praha, 1976. (Czech)
[10] S. Fučík, J. Milota: Mathematical analysis II, Differential calculus of functions of several variables. UK, Praha, 1975. (Czech)
Partner of
EuDML logo