Optimal design of an elastic beam with a unilateral elastic foundation: semicoercive state problem

Roman Šimeček

Applications of Mathematics (2013)

  • Volume: 58, Issue: 3, page 329-346
  • ISSN: 0862-7940

Abstract

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A design optimization problem for an elastic beam with a unilateral elastic foundation is analyzed. Euler-Bernoulli's model for the beam and Winkler's model for the foundation are considered. The state problem is represented by a nonlinear semicoercive problem of 4th order with mixed boundary conditions. The thickness of the beam and the stiffness of the foundation are optimized with respect to a cost functional. We establish solvability conditions for the state problem and study the existence of a solution to the optimization problem.

How to cite

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Šimeček, Roman. "Optimal design of an elastic beam with a unilateral elastic foundation: semicoercive state problem." Applications of Mathematics 58.3 (2013): 329-346. <http://eudml.org/doc/252483>.

@article{Šimeček2013,
abstract = {A design optimization problem for an elastic beam with a unilateral elastic foundation is analyzed. Euler-Bernoulli's model for the beam and Winkler's model for the foundation are considered. The state problem is represented by a nonlinear semicoercive problem of 4th order with mixed boundary conditions. The thickness of the beam and the stiffness of the foundation are optimized with respect to a cost functional. We establish solvability conditions for the state problem and study the existence of a solution to the optimization problem.},
author = {Šimeček, Roman},
journal = {Applications of Mathematics},
keywords = {shape optimization; semicoercive beam problem; unilateral foundation; shape optimization; semicoercive beam problem; unilateral foundation},
language = {eng},
number = {3},
pages = {329-346},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Optimal design of an elastic beam with a unilateral elastic foundation: semicoercive state problem},
url = {http://eudml.org/doc/252483},
volume = {58},
year = {2013},
}

TY - JOUR
AU - Šimeček, Roman
TI - Optimal design of an elastic beam with a unilateral elastic foundation: semicoercive state problem
JO - Applications of Mathematics
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 3
SP - 329
EP - 346
AB - A design optimization problem for an elastic beam with a unilateral elastic foundation is analyzed. Euler-Bernoulli's model for the beam and Winkler's model for the foundation are considered. The state problem is represented by a nonlinear semicoercive problem of 4th order with mixed boundary conditions. The thickness of the beam and the stiffness of the foundation are optimized with respect to a cost functional. We establish solvability conditions for the state problem and study the existence of a solution to the optimization problem.
LA - eng
KW - shape optimization; semicoercive beam problem; unilateral foundation; shape optimization; semicoercive beam problem; unilateral foundation
UR - http://eudml.org/doc/252483
ER -

References

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  9. Kufner, A., John, O., Fučík, S., Function Spaces, Noordhoof International Publishing/Academia Praha Nordhoof/Prague (1977). (1977) MR0482102
  10. Nečas, J., Hlaváček, I., Mathematical Theory of Elastic and Elasto-Plastic Bodies. An Introduction, Elsevier Amsterdam (1980). (1980) MR0600655
  11. Netuka, H., Horák, J. V., System beam-spring-foundation after two years, Proceedings, Conference ``Olomouc Days of Applied Mathematics ODAM 2007'' (2007), 18-42 Czech. (2007) 
  12. Salač, P., Shape optimization of elastic axisymmetric plate on an elastic foundation, Appl. Math. 40 (1995), 319-338. (1995) Zbl0839.73036MR1331921
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