Article
MSC:
49A29,
49J40,
65K10,
65N30,
73K10,
74K20,
74P99,
74S05 | MR 1288150 | Zbl 0812.73039 | DOI: 10.21136/AM.1994.134266
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Keywords:
weight minimization; penalty method; unilateral plate bending; mixed finite elements
weight minimization; penalty method; unilateral plate bending; mixed finite elements
Summary:
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.
References:
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[2] Comodi, M.I.: Approximation of a bending plate problem with a boundary unilateral constraint. Numer. Math. 47 (1985), 435–458. DOI 10.1007/BF01389591 | MR 0808562 | Zbl 0581.73022
[3] Glowinski, R. – Lions, J.L. – Trémolières, R.: Numerical analysis of variational inequalities. North-Holland, Amsterdam, 1981. MR 0635927
[4] Hlaváček, I.: A mixed finite element method for plate bending with a unilateral inner obstacle. Appl. Math. 39 (1994), 25–44. MR 1254745
[5] Collatz, L.: Functional analysis and numerical mathematics. Academic Press, New York, 1966. MR 0205126
[6] Litvinov, V.G.: Optimizacija v eliptičeskich graničnych zadačach s priloženijami v mechanike. Nauka, Moscow, 1987. (Russian) MR 0898435
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