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Recent progress in the two-dimensional approximation of three-dimensional plate models in nonlinear elasticity. (English) Zbl 0612.73060
Numerical approximation of partial differential equations, Sel. Pap. Int. Symp. Numer. Anal., Madrid/Spain 1985, North-Holland Math. Stud. 133, 3-19 (1987).
[For the entire collection see Zbl 0599.00010.]
The asymptotic expansion method is applied to the basic equations of nonlinear three-dimensional elasticity. The leading term can be identified with the well-known two-dimensional von Kármán plate model. Recent process in the application of this method are presented. Open problems regarding especially the existence of three-dimensional solutions are discussed. Neither special problems nor numerical examples are handled.
Reviewer: W.Schnell

MSC:
74K20 Plates
74B20 Nonlinear elasticity