ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

16. Applications

1991 MS Classification: 45, 73, 30 Li, Xing and Liu, Shiqiang, Dept. of Math., Ningxia University, P. R. C. Doubly Periodic Punctured Plane Elasticity Problem with Relative Displacement In this paper, three new different formulations of doubly periodic punctured plane elasticity problem with relative displacement are proposed.

κϕ_{0}(t) + t\overline{ϕ′_{0}(t)} + \overline{ψ_{0}(t)} = 2μg_{j}(t) + iνt + C_{j}
[ϕ_{0}(z) + z\overline{ϕ′_{0}(z)} + \overline{ψ_{0}(z)}]_{Γ_{k}} = iF_{k}, k = 1, 2.
Re ∫_{L_{j}} ψ_{0}(t)dt = M_{j}, j = 0, 1, ⋯, m − 1.

First and third equation above and

[κϕ_{0}(z) − z\overline{ϕ′_{0}(z)} − \overline{ψ_{0}(z)}]_{Γ_{1}} = 2μg_{1},
[ϕ_{0}(z) + z\overline{ϕ′_{0}(z)} + \overline{ψ_{0}(z)}]_{Γ_{2}} = iF_{2}.

First and third equation above and

[κϕ_{0}(z) − z\overline{ϕ′_{0}(z)} − \overline{ψ_{0}(z)}]_{Γ_{k}} = 2μg_{k}, (k = 1, 2).

The solutions are given with an illustrated example by using approach of singular integral equations.