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  antiplane elasticity
A large class of problems of mathematical physics, and especially several plane and antiplane elasticity problems, not possessing closed-form solutions, can be reduced to the solution of certain systems of such a type of singular integral equations.
      
Four applications to simple plane and antiplane elasticity problems are made for the illustration of the theoretical results.
      
A new singular integral equation for the classical crack problem in plane and antiplane elasticity
      
Solutions of multiple crack problems of a circular region with free or fixed boundary condition in antiplane elasticity
      
Four cases of multiple crack problems in antiplane elasticity, circular region or an infinite region exterior to a circle with free or fixed boundary condition, are considered in this paper.
      
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In this paper the functionally-invariant solution of the wave equation of an anti-plane problem in the orthotropic material is obtained. On the basis of this solution, a complete solution for the anti-plane elastic dynamical problem with an arbitrary index of self-similarity in the orthotropic body is given. An arbitrary continuous function of variablet can be uniformly approximated in any closed region by a polynomial, of the form 3Στotn.By the theory of complex function, the problem of crack propagation subjected...

In this paper the functionally-invariant solution of the wave equation of an anti-plane problem in the orthotropic material is obtained. On the basis of this solution, a complete solution for the anti-plane elastic dynamical problem with an arbitrary index of self-similarity in the orthotropic body is given. An arbitrary continuous function of variablet can be uniformly approximated in any closed region by a polynomial, of the form 3Στotn.By the theory of complex function, the problem of crack propagation subjected to τotn and Iδ(t)loads on interface between two different orthotropic media can be changed into the Keldysh-Sedov mixing problem of analytic functions. In this paper, the closed solution of this problem is given.

本文给出了正交异性体反平面问题波动方程的函数不变解。基于这个解,文中导出了具有任意自相似指数的正交异性体反平面弹性动力学问题的一般解。变量t的任意连续函数在任意闭域中都可以用t_0l~n的多项式来一致地逼近。利用复变函数理论,我们将不同正交异性材料界面上受t_0l_n型及1δ(l)型载荷作用的扩展裂纹问题化为解析函数论中的Keldysh-Sedov混合问题。并给出了这类问题的闭合解。

In this paper the functionally invariant solution of the wave equation of anti-plane problems in the orthotropic material is obtained. On the basic of this solution, a complete solution for anti-plane elasticity dynamic problems with an arbitrary index of self-similarity in the orthotropic body is given. Using conditions of interface and the complete solution, the shock problem of propagating crack in interface between different orthotropic media can be changed into the Keldysh-Sedov mixed problem of theory...

In this paper the functionally invariant solution of the wave equation of anti-plane problems in the orthotropic material is obtained. On the basic of this solution, a complete solution for anti-plane elasticity dynamic problems with an arbitrary index of self-similarity in the orthotropic body is given. Using conditions of interface and the complete solution, the shock problem of propagating crack in interface between different orthotropic media can be changed into the Keldysh-Sedov mixed problem of theory of analytic functions. In the paper, the closed solution of this problem is given. Using this solution, we have analysed effect to the dynamic stress intensity factor by the constant of media and the velocity of crack propagation.

本文给出了正交异性材料反平面间题波动方程的函数不变解。根据这个解,对正交异性体具有任意自相似指数的反平面弹性动力学问题给出了完全解。对受冲击载荷作用,在不同正交异性材料结合面上扩展的裂纹动力学问题,利用结合面的条件及本文给出的完全解,可以化为解析函数论中的Keldysh-Sedov混合问题。文中求解了这一问题,并得到了解的解析表达式。利用这个解,我们分析了不同材料常数及裂纹扩展速度对应力场分布及动应力强度因子的影响,得到具有实际意义的结论。

In this paper, the fixed rigid line problem in antiplane elasticity is discussed. By means of using conformal mapping, several solutions concerning the fixed rigid line problems of half-plane are obtained. Stress singularity coefficients are derived for the investigated examples.

文中分析了反平面弹性中的刚性线问题。通过保角映像,又得出了一系列带刚性半平面边界问题的解。此外,还求出了刚性线端的应力奇异系数。

 
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