Bianalytic Functions, Biharmonic Functions and Elastic Problems in the Plane

ZHENG Shen-zhou; ZHENG Xue-liang

Volume 21 Issue 8

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Article Navigation > Applied Mathematics and Mechanics > 2000 > 21(8): 797-802

ZHENG Shen-zhou, ZHENG Xue-liang. Bianalytic Functions, Biharmonic Functions and Elastic Problems in the Plane[J]. Applied Mathematics and Mechanics, 2000, 21(8): 797-802.

Citation:

ZHENG Shen-zhou, ZHENG Xue-liang. Bianalytic Functions, Biharmonic Functions and Elastic Problems in the Plane[J]. Applied Mathematics and Mechanics, 2000, 21(8): 797-802.

Citation:

ZHENG Shen-zhou, ZHENG Xue-liang. Bianalytic Functions, Biharmonic Functions and Elastic Problems in the Plane[J]. Applied Mathematics and Mechanics, 2000, 21(8): 797-802.

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Bianalytic Functions, Biharmonic Functions and Elastic Problems in the Plane

ZHENG Shen-zhou¹,
ZHENG Xue-liang²

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

Received Date: 1998-09-02
Rev Recd Date: 2000-02-02
Publish Date: 2000-08-15

Abstract

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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References

[1]	路见可.平面弹性复方法[M].武汉;武汉大学出版社,1986,35-79.
[2]	铁摩辛柯,古地尔.弹性理论[M].徐芝纶译.北京;高等教育出版社,1990,65-132.
[3]	维库阿IN.广义解析函数[M].北京大学数力组译.北京;人民教育出版社,1960,45-86.
[4]	赵桢.双解析函数、复调和函数和其边值问题[J].北京师范大学学报,1995,31(2);175-179.
[5]	ZHAO Zhen.Bianalytic functions and its applications[A].In:Proceedings of the Second Asian Mathematical Conference[C].Thailand,1995.
[6]	ZHAO Zhen.Schwarz's problem for some complex partial differential equations of second order[J].Beijing Mathematics,1996,2(1);131-137.
[7]	Ahlfors Lars V.Complex Analysis[M].2nd Edition.New York:McGraw-Hill Book Company,1973,236-285.

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