Optimal spectral approximation in linearized plate theory.(English)Zbl 0645.35002

Spectral methods are frequently used to replace a partial differential equation posed over an open set in $$R^ 3$$ by a series of partial differential equations posed over an open set of lower dimension and which are thus easier to approximate. In the framework of three- dimensional linearized elasticity those methods have already been used to derive two-dimensional approximate models for plates and one-dimensional approximate models for beams. The object of this paper is to show how to construct the “best” Galerkin spectral approximation for thin clamped plates, possibly multi-layered, made of homogeneous or of non-homogeneous materials. To this end, we use a technique introduced by M. Vogelius and I. Babuška.
Reviewer: B.Miara

MSC:

 35A35 Theoretical approximation in context of PDEs 35C20 Asymptotic expansions of solutions to PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 74B05 Classical linear elasticity
Full Text:

References:

 [1] DOI: 10.1090/S0025-5718-1986-0842127-7 [2] Ciarlet P.G., Journal de Mecanique 18 pp 315– (1979) [3] DOI: 10.1016/0045-7825(81)90091-8 · Zbl 0489.73057 [4] Ciarlet P.G., Three-dimensional elasticity (1988) · Zbl 0648.73014 [5] Destuynder P. Sur une Justification des Modeles de Plaques et de Coques par les Methodes Asymptotiques 1980 [6] Gottlieb, D. and Orszag, S.A. 1977. Numerical Analysis of Spectral Methods : Theory and Applications. Philadelphia. 1977. · Zbl 0412.65058 [7] Lions J.L., Perturbations Singulieres dans les Problemes aux Limites et en Controle Optimal (1973) [8] Miaral B., Optimal Spectral Approximation In Linearized Beams Theory [9] Naghdi, P.M. 1972.Handbuch Der Physik, 425–640. Berlin: Springer -Verlag. [10] Necas J., Les Methodes Directes en Theorie des Equations Elliptiques (1967) [11] Vogelius M., Mathematics of Computation 37 pp 31– (1981)
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.