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Derivation of generalized models for linear elastic beams by asymptotic expansion methods. (English) Zbl 0646.73024
Applications of multiple scaling in mechanics, Proc. Int. Conf., Paris 1986, Rech. Math. Appl. 4, 302-315 (1987).
[For the entire collection see Zbl 0625.00020.]
The authors develop in this paper a generalization of some of the classical linear elastic bending theories such as the Saint-Venant’s classical torsion theory, the Bernoulli-Euler and the Timoshenko’s beam- bending theories. The analysis is based on an asymptotic expansion method applied to the Hellinger-Reissner variational model. Three-dimensional models are also discussed.
Reviewer: M.N.L.Narasimhan

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74S30 Other numerical methods in solid mechanics (MSC2010)
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)