双解析函数、双调和函数和平面弹性问题

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基金项目: 国家自然科学基金资助项目(49805005);北方交通大学攀登计划资助项目

Bianalytic Functions, Biharmonic Functions and Elastic Problems in the Plane

1.
Department of Mathematics, Northern Jiaotong University, Beijing 100044, P R China;
2.
Department of Mathematics, Taizhou Teacher's College, Linhai, Zhejiang 317000, P R China

摘要: 通过考虑双解析函数和双调和函数的关系,对单连通区域上平面弹性问题中只有重力体力作用的应力函数建立了唯一性和存在性结果;并对单位圆区域得到了类似于Poisson公式解的积分表示式。
- Airy函数 /
- 双解析函数 /
- 双调和函数 /
- 解的唯一性 /
- 解的积分表示式
Abstract: Let the elastic body only be acted by gravity. By investigating the relations of bianalytic functions and biharmonic functions, the uniqueness and existence of the stress functions (Airy functions) are established in planar simple connected region. Moreover, the integral representation formula of the stress function in the unit disk of the plane is obtained.
- Airy functions /
- bianalytic functions /
- biharmonic functions /
- the uniqueness of the solution /
- integral representation formula

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