zbMATH — the first resource for mathematics

A new finite element scheme for bending plates. (English) Zbl 0626.73070
Using a mixed formulation a new finite element for bending plates is suggested. It appears as an extension of numerical scheme used in fluid mechanics. One of its advantages is that both triangular and quadrangular element can be used. Furthermore, it implies an accuracy \(O(h^ 2)\) on the bending moments or the transverse shear for a low cost. Finally, the element works for arbitrary boundary conditions.

74S05 Finite element methods applied to problems in solid mechanics
74K20 Plates
Full Text: DOI
[1] Brezzi, F., On the existence uniqueness and approximation saddle point problems arising from Lagrange multipliers, Rairo r2, 129-151, (1974) · Zbl 0338.90047
[2] Ciarlet, P.G., The finite element method for elliptic problems, (1978), North-Holland Amsterdam · Zbl 0445.73043
[3] Destuynder, Ph.; Nevers, Th., Une modificaiton du modèle de Mindlin, 22, 2, 31-56, (1988)
[4] Duvaut, G.; Lions, J.L., LES inéquations en Mécanique et en physique, (1972), Dunod Paris · Zbl 0298.73001
[5] Girault, V.; Raviart, P.A., Finite element methods for the Navier Stokes equations, (1986), Springer Berlin · Zbl 0396.65070
[6] Glowinski, R.; Pironneau, O., On a mixed finite element approximation of the Stokes problem, Numer. math., 33, 397-424, (1979) · Zbl 0423.65059
[7] Raviart, P.A.; Thomas, J.M., Introduction à l’analyse numérique des equations aux Dérivées partielles, (1983), Masson Paris · Zbl 0561.65069
[8] Temam, R., Navier-Stokes equations, () · Zbl 0572.35083
[9] Brezzi, F.; Fortin, M., Numerical approximation of Mindlin-Reissner plates, Math. comp., 47, 175, 151-158, (1986) · Zbl 0596.73058
[10] Davet, J.L.; Destuynder, Ph., Singularités logarithmiques dans LES effets de bord d’une plaque en matériaux composites, J. mta., 4, 357-380, (1985) · Zbl 0564.73066
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.