Transient analysis of the dynamic stress intensity factors using SGBEM for frequency-domain elastodynamics
Transient analysis of the dynamic stress intensity factors using SGBEM for frequency-domain elastodynamics
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DOI：
10.1016/j.cma.2010.06.019
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发表时间：
2010-11
影响因子：
7.2
通讯作者：
A. Phan;L. Gray;A. Salvadori;A. Salvadori
中科院分区：
文献类型：
--
作者：
A. Phan;L. Gray;A. Salvadori;A. Salvadori
本文提出了一种在频域中进行弹性动力断裂分析的二维边界积分公式。数值实现采用二次单元进行，允许使用改进的四分之一点单元来准确确定动态应力强度因子（DSIF）的频率响应。为了处理奇异和超奇异积分，该公式被分解为两部分：第一部分是相同的，而第二部分包含最多对数奇异性的弹性静力学。第二部分对弹性静力奇异积分和超奇异积分的处理采用了外边界的方法，而对弱奇异积分的处理则采用了Gauss求积法。DSIF的时间历程（瞬态响应）可以在后处理步骤中通过将标准快速傅立叶变换（FFT）和算法应用于这些DSIF的频率响应来获得。文中给出了几个算例，计算了两种冲击荷载作用下的结构应力强度因子：Heaviside阶跃荷载和爆炸荷载。结果表明，在确定瞬态响应的DSIF的DSA-Galerkin边界元法和标准的FFT算法的组合是一个强大的和有效的技术。
In this paper, a two-dimensional symmetric-Galerkin boundary integral formulation for elastodynamic fracture analysis in the frequency domain is described. The numerical implementation is carried out with quadratic elements, allowing the use of an improved quarter-point element for accurately determining frequency responses of the dynamic stress intensity factors (DSIFs). To deal with singular and hypersingular integrals, the formulation is decomposed into two parts: the first part is identical to that for elastostatics while the second part contains at most logarithmic singularities. The treatment of the elastostatic singular and hypersingular singular integrals employs an exterior limit to the boundary, while the weakly singular integrals in the second part are handled by Gauss quadrature. Time histories (transient responses) of the DSIFs can be obtained in a post-processing step by applying the standard fast Fourier transform (FFT) and algorithm to the frequency responses of these DSIFs. Several test examples are presented for the calculation of the DSIFs due to two types of impact loading: Heaviside step loading and blast loading. The results suggest that the combination of the symmetric-Galerkin boundary element method and standard FFT algorithms in determining transient responses of the DSIFs is a robust and effective technique.