Some boundary value problems and models for coupled elastic bodies
Authors:
J. A. Arango, L. P. Lebedev and I. I. Vorovich
Journal:
Quart. Appl. Math. 56 (1998), 157-172
MSC:
Primary 73C35; Secondary 73K99, 73V05
DOI:
https://doi.org/10.1090/qam/1604825
MathSciNet review:
MR1604825
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Abstract: A new class of boundary value problems is presented. These problems are described by related equations of different nature and possess such properties as the appearance of highest derivatives in boundary conditions. Such problems appear to model common engineering constructions composed of elements of different mechanical natures like plates, shells, membranes, or three-dimensional elastic bodies. Two problems are considered in detail, namely a three-dimensional elastic body with flat elements taken as a plate or a membrane, and a plate-membrane system. The existence-uniqueness theorems for the corresponding boundary value problems are established and an application of a conforming FEM is justified.
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M. Bernardou and S. Fayolle, Numerical junctions between plates, Computer Methods in Applied Mechanics and Engineering, vol. 74, 1989, pp. 307–326
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R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975
M. Bernardou and S. Fayolle, Numerical junctions between plates, Computer Methods in Applied Mechanics and Engineering, vol. 74, 1989, pp. 307–326
P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1968
L. P. Lebedev and I. I. Vorovich, On the Bubnov-Galerkin Method in the Nonlinear Theory of Vibrations of Viscoelastic Shells, Prikl. Mat. Meh., Vol. 37, 1973, pp. 1117–1124
J. Necǎs and I. Hlaváček, Mathematical Theory of Elastic and Elasto-Plastic Bodies, Elsevier Scientific Publishing, Amsterdam-Oxford-New York, 1981
C. Truesdell and W. Noll, The Non-linear Field Theories of Mechanics, Handbuch der Physik III/3, Springer-Verlag, Berlin-Göttingen-Heildelberg, 1958
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Article copyright:
© Copyright 1998
American Mathematical Society
