含正方形孔热电材料的弹性分析

Analysis on Elasticity of Thermoelectric Materials with Square Hole

基于复变函数理论,对在无穷远处受到电流和能量流共同作用的含正方形孔热电材料的二维断裂问题做了分析。利用保角映射,给出了热电弹性场中应力势函数φ(z)和ψ(z)的复数表达式,并根据电绝缘和热精确边界条件,获得了在曲线坐标系下环向应力σθθ和环向能量流juθ的解析表达式。

The two-dimensional problem of fracture in a thermoelectric material with a square hole under the action of current and energy flow at infinity was analyzed based on the complex function theory in the paper.The analysis gave the expressions of complex function for the sum of the stress potential functions,φ(z)andψ(z),in the thermoelectric elastic field by using conformal mapping and the analytical expressions of toroidal stressσθθand toroidal energy flow juθin curvilinear coordinates according to electrical insulated and thermal exact boundary conditions.