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A regularized time-domain BIEM for transient elastodynamic crack analysis in piezoelectric solids

机译：正则化时域BIEM用于压电固体瞬态弹性动力学裂纹分析

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摘要

A time domain non-hypersingular traction boundary integral equation method (BIEM) is proposed for dynamic crack analysis of piezoelectric solids. Using the boundary integral equation method, the time domain hypersingular integral equations for a dynamic crack in a 2D infinite piezoelectric solid subjected transient loads are derived. Considering the properties of the fundamental solutions, the hypersingular integral equations are reduced to singular integral equations by using the technique of integration by parts, in which the unknown functions are the tangential derivatives of the displacement and electrical potential discontinuities of the crack surfaces. To solve the time domain singular integral equations numerically, the quadrature formula of Lubich is applied for the temporal discretization, while the Gauss-Chebyshev quadrature method is used for the spatial discretization. Numerical examples are carried out to verify the accuracy of the present method by comparing the numerical results obtained by other scholars. Finally, several numerical results are presented and discussed to show the effects of the mechanical impact loading, crack-face conditions and piezoelectric coupling coefficient on the dynamic stress intensity factors.
机译：提出了一种时域非奇异牵引边界积分方程法（BIEM），用于压电固体的动态裂纹分析。使用边界积分方程法，推导了二维无限压电固体承受瞬态载荷时动态裂纹的时域超奇异积分方程。考虑到基本解的性质，通过使用零件积分技术将超奇异积分方程简化为奇异积分方程，其中未知函数是裂纹表面位移和电势不连续的切向导数。为了数值求解时域奇异积分方程，将Lubich的正交公式用于时间离散化，而将Gauss-Chebyshev正交方法用于空间离散化。通过比较其他学者获得的数值结果，通过数值例子验证了本方法的准确性。最后，给出和讨论了几个数值结果，以显示机械冲击载荷，裂纹面条件和压电耦合系数对动应力强度因子的影响。

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