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 ...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 functions in the unit disk of the plane is obtained.展开更多
By using the Cauchy integral formula of bianalytic functions, the formula of higher derivatives of bianalytic functions and Weierstrass Theorem are obtained.
In this paper, the properties of bianalytic functions w（z） = z^-Ф1（z） ＋Ф2（z） with zero arc at the pole z = 0 are discussed. Some conditions under which there exists an arc γ, an end of which is z = 0, such t...In this paper, the properties of bianalytic functions w（z） = z^-Ф1（z） ＋Ф2（z） with zero arc at the pole z = 0 are discussed. Some conditions under which there exists an arc γ, an end of which is z = 0, such that w（z） =0 for arbitary z ∈γ／{0} are given. Secondly, that the limit set of w（z） is a circle or line as z → 0 is proved in this case. Finally, two numerical examples are given to illustrate our results.展开更多
文摘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 functions in the unit disk of the plane is obtained.
文摘By using the Cauchy integral formula of bianalytic functions, the formula of higher derivatives of bianalytic functions and Weierstrass Theorem are obtained.
基金the National Natural Science Foundation of China(No.10601036)
文摘In this paper, the properties of bianalytic functions w（z） = z^-Ф1（z） ＋Ф2（z） with zero arc at the pole z = 0 are discussed. Some conditions under which there exists an arc γ, an end of which is z = 0, such that w（z） =0 for arbitary z ∈γ／{0} are given. Secondly, that the limit set of w（z） is a circle or line as z → 0 is proved in this case. Finally, two numerical examples are given to illustrate our results.
