Geodesic
Weight minimization of an elastic plate with a unilateral inner obstacle by a mixed finite element method
Applications of Mathematics, Tome 39 (1994) no. 5, pp. 375-394
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Unilateral deflection problem of a clamped plate above a rigid inner obstacle is considered. The variable thickness of the plate is to be optimized to reach minimal weight under some constraints for maximal stresses. Since the constraints are expressed in terms of the bending moments only, Herrmann-Hellan finite element scheme is employed. The existence of an optimal thickness is proved and some convergence analysis for approximate penalized optimal design problem is presented.
Unilateral deflection problem of a clamped plate above a rigid inner obstacle is considered. The variable thickness of the plate is to be optimized to reach minimal weight under some constraints for maximal stresses. Since the constraints are expressed in terms of the bending moments only, Herrmann-Hellan finite element scheme is employed. The existence of an optimal thickness is proved and some convergence analysis for approximate penalized optimal design problem is presented.
DOI : 10.21136/AM.1994.134266
Classification : 49A29, 49J40, 65K10, 65N30, 73K10, 74K20, 74P99, 74S05
Keywords: weight minimization; penalty method; unilateral plate bending; mixed finite elements 
@article{10_21136_AM_1994_134266,
     author = {Hlav\'a\v{c}ek, Ivan},
     title = {Weight minimization of an elastic plate with a unilateral inner obstacle by a mixed finite element method},
     journal = {Applications of Mathematics},
     pages = {375--394},
     year = {1994},
     volume = {39},
     number = {5},
     doi = {10.21136/AM.1994.134266},
     mrnumber = {1288150},
     zbl = {0812.73039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134266/}
}
TY  - JOUR
AU  - Hlaváček, Ivan
TI  - Weight minimization of an elastic plate with a unilateral inner obstacle by a mixed finite element method
JO  - Applications of Mathematics
PY  - 1994
SP  - 375
EP  - 394
VL  - 39
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134266/
DO  - 10.21136/AM.1994.134266
LA  - en
ID  - 10_21136_AM_1994_134266
ER  - 
%0 Journal Article
%A Hlaváček, Ivan
%T Weight minimization of an elastic plate with a unilateral inner obstacle by a mixed finite element method
%J Applications of Mathematics
%D 1994
%P 375-394
%V 39
%N 5
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134266/
%R 10.21136/AM.1994.134266
%G en
%F 10_21136_AM_1994_134266
Hlaváček, Ivan. Weight minimization of an elastic plate with a unilateral inner obstacle by a mixed finite element method. Applications of Mathematics, Tome 39 (1994) no. 5, pp. 375-394. doi: 10.21136/AM.1994.134266

[1] Brezzi, F. – Raviart, P.A.: Mixed finite element methods for 4th order elliptic equations. J.J.H. Miller (ed.), Topics in Numer. Anal., vol. III, Academic Press, London, 1977, pp. 33–56. | MR

[2] Comodi, M.I.: Approximation of a bending plate problem with a boundary unilateral constraint. Numer. Math. 47 (1985), 435–458. | DOI | MR | Zbl

[3] Glowinski, R. – Lions, J.L. – Trémolières, R.: Numerical analysis of variational inequalities. North-Holland, Amsterdam, 1981. | MR

[4] Hlaváček, I.: A mixed finite element method for plate bending with a unilateral inner obstacle. Appl. Math. 39 (1994), 25–44. | MR

[5] Collatz, L.: Functional analysis and numerical mathematics. Academic Press, New York, 1966. | MR

[6] Litvinov, V.G.: Optimizacija v eliptičeskich graničnych zadačach s priloženijami v  mechanike. Nauka, Moscow, 1987. (Russian) | MR

Cité par Sources :