【作者】 汪文帅；

【导师】 李星；

【作者基本信息】 宁夏大学 ， 应用数学， 2005， 硕士

【摘要】 本文是在压电材料线性宏观理论下,主要运用复变函数理论研究了无限大压电材料中静态反平面裂纹问题。首先研究了周期分布的共线反平面裂纹问题,借助于Riemann-Schwarz延拓技术和保形映照方法,分别就电学渗透性和非渗透性边界条件的两种情况做了探讨,获得了封闭形式的解,得到了裂纹尖端的应力和电位移强度因子,并数值化了周期裂纹间的干涉效应和尺度效应。 其次借助于圆域的延拓技术,研究了远场载荷下无限大平面中的圆弧裂纹问题,采用了非渗透性边界条件,得到了封闭形式的解及裂纹尖端力学和电学强度因子的表达式。 最后利用复变函数级数展开法对无限大平面中含有孔洞的反平面问题的一般解进行了探讨,然后借助于保形映照,对远场载荷作用下的抛物线型裂纹进行了研究,采用渗透性边界条件,得出了裂纹尖端的力学和电学强度因子。更多还原

【Abstract】 In this thesis, the static ant-plane crack problems of an infinite piezoelectric materials are investigated by using complex variables method on the basis of linear macroscopic theory of piezoelectric materials.Firstly, by continuation technology and conformal mapping, the periodic collinear crack problems are studied in the two cases of permeable and impermeable boundary conditions, and solutions in closed form are obtained, then the formulae for the stress intensity factors and electric displacement intensity factors are derived, and the interaction effects and scale effects of periodicity are shown by figures.secondly, using continuation technology on circular domain, the circular arc crack problem is investigated subjected to anti-plane shear and inplane electric loading at infinity, the explicit form solutions are obtained and the formulae for intensity factors of both mechanics and electric are presented with impermeable boundary condition.Finally, by using series expansion of complex variables, the general solution of multiple circular holes is discussed subjected to uniform loading at infinity. By conformal mapping, the parabolic curve crack are investigated with permeable boundary condition, and the formulae for intensity factors of both mechanics and electric are obtained.更多还原