zbMATH — the first resource for mathematics

Asymptotic analysis of bar systems. II. (English) Zbl 0924.73021
In Part I [see the foregoing entry], the author studied a thin bar with elasticity coefficients periodic in the longitudinal direction and obtained a formal asymptotic expansion of infinite order. The present paper is the sequel of this former study. It begins (Section 2.6) with a rather technical justification of the asymptotics previously obtained. In Section 3, the author considers an elastic plate, infinite and periodic in the $$x_2$$ direction, clamped in the $$x_1$$ direction and small in the $$x_3$$ direction. He gives a formal inner asymptotic expansion of infinite order and boundary layer correctors and establishes the structure of the matrices involved. Then he extends these results to nonstationary elasticity in a bar and to a weakly compressed bar.

MSC:
 74E05 Inhomogeneity in solid mechanics 74K10 Rods (beams, columns, shafts, arches, rings, etc.) 74B99 Elastic materials 35Q72 Other PDE from mechanics (MSC2000) 74K20 Plates