Quintela-Estevez, Peregrina A new model for nonlinear elastic plates with rapidly varying thickness. (English) Zbl 0683.73027 Appl. Anal. 32, No. 2, 107-127 (1989). The problem deals with the composition of the two-dimensional models concerning nonlinear elastic plates with rapidly varying thickness. The author’s procedure is based on the assumption that the three-dimensional constitutive equation is linear with respect to the full strain tensor. By using a variational approach with the well-known method of multiple- scale asymptotic expansion he established the existence of the solution to the “limit problem”. The obtained result is the generalization of some earlier models of plates of constant thickness. Reviewer: V.Brčić Cited in 2 ReviewsCited in 4 Documents MSC: 74K20 Plates 74B20 Nonlinear elasticity 35C20 Asymptotic expansions of solutions to PDEs 74S30 Other numerical methods in solid mechanics (MSC2010) Keywords:St. Venant-Kirchhoff material; two-dimensional models; three-dimensional constitutive equation; linear with respect to the full strain tensor; multiple-scale asymptotic expansion; limit problem Citations:Zbl 0405.73050 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Bensoussan A, Studies in Mathematics and its applications 5 (1978) [2] Ciarlet, P.G. 1985. Recent Progresses in the Two Dimensional Approximation of Three-Dimensional Plate Models in Nonlinear 20 nonlinear elastic plates 127 Elastiticty. Proceedings, International Symposium of Numerical Analysis. 1985. [3] Ciarlet P.G, North Holland (1987) [4] DOI: 10.1016/0045-7825(79)90089-6 · Zbl 0405.73050 · doi:10.1016/0045-7825(79)90089-6 [5] Ciarlet P.G, Lecture Notes in Mathematics 826 (1980) [6] Davet J.L, Modelisation Mathematique et Analyse Numerique 20 pp 225– (1985) [7] Destuynder, P. 1980. Sur une Justification Mathematique des Theories de Plaques et de Coques en Elasticite Lindaire. Doctoral Disertation, Universite Pierre et Marie Curie. 1980. [8] DOI: 10.1016/0020-7683(84)90044-1 · Zbl 0532.73055 · doi:10.1016/0020-7683(84)90044-1 [9] Kohn R.V, Quart. Appl. Math 43 pp 1– (1985) · Zbl 0565.73046 · doi:10.1090/qam/782253 [10] Quintela, Estevez P. 1988. Thin plates with rapidly varying thickness II. The effect of the behavior of the various physical data involved when the thickness approaches zero. 1988. · Zbl 0687.73061 [11] Sanchez Palencia E., Lecture Notes in Physics 127 (1980) 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.