具有孔洞的双周期热弹性平面问题的复势  

ON THE COMPLEX POTENTIALS FOR A BODY WITH HOLES IN DOUBLY PERIODIC PLANE THERMOELASTICITY

作　　者：彭南陵[1] 王敏中[1] 

机构地区：[1]北京大学力学与工程科学系湍流与复杂系统国家重点实验室

出　　处：《力学学报》2005年第2期175-182,共8页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金资助项目(10172003;10372003)

摘　　要：首先论述了针对调和变温场的热弹性平面问题的复变函数方法,给出了受调和变温时有限多连通域中复势的一般表达式.然后基于已知实部的双周期解析函数及其原函数的表示和多值性分析,导出了双周期调和变温下具有双周期分布孔洞物体平面弹性问题的两个复势函数的一般公式,由此论证了两种特殊情形下物体的温度应力为零.First, the complex variable method in plane thermoelasticity for harmonic temperature change field is discussed, and the general expression of the complex potentials in a finite multi-connected region under harmonic temperature change is derived. Then, based on the analysis for the expression and multivalue property of the doubly-periodic analytic function (the real part of which is given) and its object function, the general expression of the two complex potentials in plane elasticity for a body with a doubly periodic set of holes under doubly-periodic harmonic temperature change is obtained. Finally, the conclusion that the heat stresses vanish in two special cases is deduced.

关 键 词：双周期 热弹性 平面弹性问题 复变函数方法 椭圆函数 

分 类 号：O343.6[理学—固体力学]