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A justification of the one-dimensional linear model of elastic beam. (English) Zbl 0603.73056
The authors discuss the title problem by showing that the one-dimensional model of an elastic beam is an approximation to the three-dimensional linear theory of elasticity. The beam is assumed to be homogeneous and isotropic. The proof is based upon an analysis given earlier by the authors [Ber. Math.-Stat. Sekt. Forschungszent. Graz 154, 5 S. (1981; Zbl 0516.73022)].
The paper is very specialized but it could be of interest to theoreticians in elasticity.
Reviewer: R.L.Huston

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74B99 Elastic materials
74H99 Dynamical problems in solid mechanics
Full Text: DOI
[1] Aganović , I. Tutek , Z. Eindimensionale Approximation der Lameschen Gleichung. Berichte 1981
[2] Ciarlet, A justification of the two-dimensional linear plate model, J. mécanique 18 (2) pp 315– (1979) · Zbl 0415.73072
[3] Ciarlet, Two-dimensional approximation of three-dimensional eigenvalue problem in plate theory, Comput. Math. Appl. Mech. Engrg. 26 pp 145– (1981) · Zbl 0489.73057
[4] Destuynder, Comparaison entre les modeles tridimensionales et bidimensionales des plaques en elasticité, RAIRO Analyse Numérique 15 pp 331– (1981)
[5] Duvaut, Les inéquations en mécanique et en physique (1972)
[6] Germain, Mécanique des milieux continus (1962)
[7] Lions, Perturbations singuliéres dans les problémes aux limites et en contràle optimal (1973)
[8] Lions, Problémes aux limites non homogènes et applications (1968)
[9] Neas, Mathematical theory of elastic and elastico-plastic bodies (1981)
[10] Rigolot, Sur une théorie asymptotic des poutres, J. mécanique 11 (4) pp 673– (1972)
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