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An asymptotic analysis of junctions of non-homogeneous elastic rods: Boundary layers and asymptotic expansions. (English) Zbl 0816.73025
Comput. Math. Math. Phys. 33, No. 11, 1483-1508 (1993) and Zh. Vychisl. Mat. Mat. Fiz. 33, No. 11, 1693-1721 (1993).
Summary: The problem of the junction of two non-homogeneous rods, the rigidity of one being an order of magnitude greater than that of the other, is considered. The problem depends on two parameters, \(e\) and \(w\), where \(e\) is the ratio of the rod diameter to its length, and \(w\) is the ratio of the elastic moduli of the rods. A complete asymptotic series is constructed for solving the problem as \(e \to 0,w \to \infty\).

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
35Q72 Other PDE from mechanics (MSC2000)
35C20 Asymptotic expansions of solutions to PDEs
two parameters