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Keywords:
convergence of finite element approach; bending of plates with ribs; density theorem
convergence of finite element approach; bending of plates with ribs; density theorem
Summary:
In the present paper the convergence of the finite element method to the solution of the problem of a plate with ribs which are stiff against torsion in the sense of Vlasov is studied. According to the conclusions of a paper by the author and J. Haslinger it suffices to prove a density theorem (Theorem 2.1).
References:
[1] P. G. Ciarlet P. A. Raviart: General Lagrange and Hermite Interpolation in $R_n$ with Aplications to Finite Element Methods. Arch. Rat. Mech. Anal., sv. 46, 1972. MR 0336957
[2] J. Haslinger: Sur la solution d'un problème de la plaque. Apl. mat. с. 5, sv. 19, 1974. MR 0369902 | Zbl 0324.73049
[3] J. Haslinger P. Procházka: Conforming finite element method in the problem of a plate with ribs. Apl. mat. c. 4, sv. 22 1977. MR 0449141
[4] V. Janovský P. Procházka: The nonconforming finite element method in the problem of clamped plate with ribs. Apl. mat. č. 4, sv. 21, 1976. MR 0413548
[5] V. Janovský P. Procházka: Convergence analysis of a nonconforming finite element method solving a plate with ribs. Apl. mat. c. 1, sv. 23, 1978. MR 0462100
[6] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Praha, 1967. MR 0227584
[7] P. Procházka: Plate with ribs. (in Czech). CSc-dissertation, ČVUT, Praha, 1975.
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