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