Shape optimization of elastic axisymmetric plate on an elastic foundation

Petr Salač

Applications of Mathematics (1995)

  • Volume: 40, Issue: 4, page 319-338
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Salač, Petr. "Shape optimization of elastic axisymmetric plate on an elastic foundation." Applications of Mathematics 40.4 (1995): 319-338. <http://eudml.org/doc/32922>.

@article{Salač1995,
abstract = {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.},
author = {Salač, Petr},
journal = {Applications of Mathematics},
keywords = {shape optimization; axisymmetric elliptic problems; elasticity; existence; optimal design; circular plate; Lipschitz functions; concentrated force; weighted Sobolev space; convergence; approximate solutions},
language = {eng},
number = {4},
pages = {319-338},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Shape optimization of elastic axisymmetric plate on an elastic foundation},
url = {http://eudml.org/doc/32922},
volume = {40},
year = {1995},
}

TY - JOUR
AU - Salač, Petr
TI - Shape optimization of elastic axisymmetric plate on an elastic foundation
JO - Applications of Mathematics
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 40
IS - 4
SP - 319
EP - 338
AB - 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.
LA - eng
KW - shape optimization; axisymmetric elliptic problems; elasticity; existence; optimal design; circular plate; Lipschitz functions; concentrated force; weighted Sobolev space; convergence; approximate solutions
UR - http://eudml.org/doc/32922
ER -

References

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  1. 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. (1975) MR0443372
  2. The finite element method for elliptic problems, North-Holland, Amsterdam, 1978. (1978) Zbl0383.65058MR0520174
  3. Optimization of the shape of axisymmetric shells, Apl. Mat. 28 (1983), 269–294. (1983) MR0710176
  4. Mathematical Theory of Elastic and Elasto-Plastic Bodies, An Introduction, Elsevier, Amsterdam, 1981. (1981) MR0600655
  5. Optimal design of an elastic beam on an elastic basis, Apl. Mat. 31 (1986), 118–140. (1986) Zbl0606.73108MR0837473
  6. Variational methods in mathematics, science and engineering, D. Reidel Publishing Company, Dordrecht-Holland/Boston U.S.A., 1977. (1977) MR0487653
  7. Weighted Sobolev spaces, John Wiley & Sons, New York, 1985. (1985) Zbl0579.35021MR0802206
  8. Interpolation theory, function spaces, differential operators, VEB Deutscher Verlag der Wissenschaften, Berlin, 1975. (1975) MR0500580
  9. Differential calculus II, Academia, Praha, 1976. (Czech) (1976) 
  10. Mathematical analysis II, Differential calculus of functions of several variables, UK, Praha, 1975. (Czech) (1975) 

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