On a certain case of thermoelastic interaction of an opening and a heat spot of elliptic shape. (English. Russian original) Zbl 0882.73082

Obratzov, I. F.; Nerubailo, B. V.; Smirnov, L. G.

Phys.-Dokl. 40, No. 3, 142-145 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 341, No. 2, 194-197 (1995).

Using complex potentials, the authors solve an elastic plane problem as the following boundary value problem. Given a Hölder continuous function \(f(t)\) on an ellipse \(L\). Find the functions \(\varphi\) and \(\psi\) analytic in \(D^+\) and \(D_-\), respectively, where \(D^+\) is the interior domain to \(L\), \(D^-\) is the exterior domain to \(L\), with the boundary condition \(\varphi(t)+t \overline{\varphi'(t)}+ \overline{\psi(t)}= f(t)\), \(t\in \ell\subset L\), and with given jumps of \(\varphi\) and \(\psi\) on \(L\setminus \ell\).

Reviewer: V.Mityushev (Słupsk)

MSC:

74S30	Other numerical methods in solid mechanics (MSC2010)
74B99	Elastic materials
30E25	Boundary value problems in the complex plane
80A20	Heat and mass transfer, heat flow (MSC2010)

Keywords:

Muskhelishvili method; complex potentials; elastic plane problem; boundary value problem; Hölder continuous function; ellipse