摘要
利用广义Betti--Rayleigh互易公式给出了二维压电材料非渗透裂纹问题的一般解和奇异积分方程,其中未知函数为裂纹上的位移间断和电势间断的导数.在理论分析的基础上,使用高斯--切比雪夫求积公式及Lubich卷积积分方法建立了问题的数值求解方法,并给出典型算例的广义动应力强度因子随时间变化的规律.
Using the Betti-Rayleigh reciprocity theorem, the general solutions and the singular integral equa- tions for a two dimensional impermeable crack problem in an infinite transversely isotropic piezoelectric solid under mechanical and electrical impact loads are obtained. The unknown functions are the derivatives of the discontinuities of elastic displacements and electric potentials of the crack. Then, Gauss-Chebyshev quadrature formula and Lubich convolution quadrature formula are applied to solve the integral equations numerically. Finally, numerical solutions are obtained for a typical example. It is shown that the numerical solutions are satisfactory.
出处
《力学与实践》
北大核心
2014年第4期433-436,共4页
Mechanics in Engineering
基金
国家自然科学基金资助项目(11172320)
关键词
压电材料
裂纹
奇异积分方程
广义动应力强度因子
piezoelectric material, crack, singular integral equations, extended stress intensity factor
