Using the complex variable method, we study the plane problem of an infinite
thermoelectric material containing an arbitrarily-shaped hole under a uniform remote
electric current and a uniform energy flux. The nonlinear fully coupled thermoelectric
constitutive equations are used to account for the large current or temperature
gradient imposed on thermoelectric materials during their engineering service. The
hole surface is assumed to be electrically and thermally insulated and mechanically
free. The shape of the hole is defined by a polynomial conformal mapping.
Fourier expansion technique is used to solve the corresponding boundary value
problems. A triangular hole is considered for the purpose of illustration.
The bluntness, hole orientation and the load angle as important parameters
are considered. Numerical results show that the effects of these parameters
on stress distribution around the hole are very significant. By the correct
selection of these parameters, the lowest thermal stress concentration can be
achieved.
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