【摘要】 正交各向异性板孔边应为集中的求解是比较困难的。Green等人已发表过一些关于各向异性板的著作。而本文的求解是从Airy应力函数出发,对正交各向异性弹性板进行求解。作者分析了各向同性与各向异性弹性体的应力函数,研究了它们之间的相似性,建立了等价空间的概念,发展了空间变换法,将物理空间变换到等价空间,再变换到象空间。作者运用了等价空间和各向同性弹性板的一些结果,简明地解决了各向异性板的问题。本文采用了BEM的虚拟应力法进行求解,为了简化,采用了Fourier变换进行求解,从平面问题的Kelvin奇异解出发,对Kelvin解进行了积分,建立了正交各向导性弹性板的基本解,并用虚拟应力法将此基本解构成该问题的数值解。更多还原

【Abstract】 It is rather difficult to determine the stress concentration along a hole on an orthotropie plate. There have been published a few papers concerning the anisotropic elasic plate, starting with the solution to the problem of a line of concentrated force in an anisotropic elastic body given by Green. In this paper. another method for solving the problem of the orthotropic elastic plate is proposed. The author has made extensive search for papers in this narrow field and has finally been led to the belief that the proposed method is a new way never used by others. Starting from analyzing the Ai- ry’s stress functions of the orthotropie and isotropic plate, the author has found the mathematical similarity between them, established the concept of equivalent space, and developed the space mapping method, which maps the physieal space onto equivalent spaces and then onto image spaces. By utili- zing the equivalent spaces and some results from isotropic elastic plates, the author has solved the problem concisely. In this paper, the problem is solved by the fietitionus stress method, a branch of the indirect boundary element method. For simplicity, the problem is solved by Fourier transformtion. Staring from Kelvin’s singular solution of the plane problem, the author has established the fundamental solution, and reconstructed the fundamental solution into numerical solution by using the fictitious stress mehod (stress discontinuity method).更多还原