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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 $$e \to 0,w \to \infty$$.

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