Article
MSC:
31A30,
35J20,
49A29,
65K05,
65N30,
73K10,
74K20,
74S05,
74S30,
90C20 | MR 0502470 | Zbl 0399.65084 | DOI: 10.21136/AM.1978.103760
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Keywords:
quadratic programming; elastic clamped plate; algorithm; energy functional; convergence; minimization problem; numerical solution; finite element method
quadratic programming; elastic clamped plate; algorithm; energy functional; convergence; minimization problem; numerical solution; finite element method
Summary:
The problem of a thin elastic plate, deflection of which is limited below by a rigid obstacle is solved. Using Ahlin's and Ari-Adini's elements on rectangles, the convergence is established and SOR method with constraints is proposed for numerical solution.
References:
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[3] Ciarlet P. G., Raviart P. A.: General Lagrange and Hermite interpolation in $R_n$ with applications to finite element methods. Arch. Rat. Anal. Vol. 46 (1972), 177- 199. DOI 10.1007/BF00252458 | MR 0336957 | Zbl 0243.41004
[4] Glowinski R.: Analyse numerique d'inequations variationnelles d'ordre 4. (preprint of University Paris VI).
[5] Jakovlev G. N.: The boundary properties of the functions belonging to the class $W^{1,p} on domains with conical or angular points. Trans. Moscow Math. Soc. (1967), 227--313.
[6] Janovský V., Procházka P.: The nonconforming finite element method in the problem of clamped plate with ribs. Apl. Mat. 21 (1976), No 4, 273 - 289. MR 0413548
[7] Glowinski R., Lions J. L., Trémolieres R.: Analyse numérique des inéquations variationnelles. Dunod, Paris 1976.
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