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Homogenization and a Galerkin approximation in three-dimensional beam theory. (English) Zbl 0699.73005

Summary: In this work we study the limit relations between a Galerkin approximation method, of the spectral type, for the three-dimensional linearized elasticity model of a multicellular beam, and the respective homogenization process. We show that the choice of the basis functions, of the Galerkin approximation, commutes with the homogenization process but the same does not hold for the final approximations of the three- dimensional solution.

MSC:

74E05 Inhomogeneity in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
49M15 Newton-type methods
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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References:

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