椭圆夹杂点热源问题的研究

The Study on the Thermoelastic Problem of an Elliptical Inclusion with a Point Heat Source in the Matrix

研究了点热源作用下弹性椭圆夹杂的热弹性问题.将复变函数的分区全纯函数理论,保角变换,奇性主部分析,解析延拓技术,Cauchy型积分与Riemann边值问题相结合,求得各分区函数之间的解析关系,将问题归结为一个初等复势方程的求解.获得了椭圆内外热应力函数的精确解答.为求解复杂多连通多相域的亚纯函数边值问题发展了一种有效的分析方法,解答结果不仅可作为格林函数,求得任意分布热源下的相应解答,而且作为其特例包含以往文献的研究成果.

The thermoelastic problem was investigated for a point heat source in the matrix outside an elliptical inclusion. By combining the complex variable theories of sectional holomorphic function, conformal transformation, the analysis of the singularity, analytical continuation, Cauchy-type integral and Riemann boundary problem, the relation between the sectional functions was obtained and the problem was transformed into solving an elementary complex potential function equation. The thermal stress functions were provided both in the matrix and in the inclusion. An efficient method was developed to solve sectional subholomorphic boundary problems on complex multiple connection and multiple phase region. The results can not only be used as a Green function to solve problems under arbitrary thermal loads, but also contain several previously known solutions as special cases.