Transient dynamic fracture analysis using scaled boundary finite element method: a frequency-domain approach
Transient dynamic fracture analysis using scaled boundary finite element method: a frequency-domain approach
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DOI：
10.1016/j.engfracmech.2006.06.018
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发表时间：
2007-03
影响因子：
5.4
通讯作者：
Zhenjun Yang;A. Deeks;H. Hao
中科院分区：
文献类型：
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作者：
Zhenjun Yang;A. Deeks;H. Hao
在比例边界有限元法（SBFEM）中，径向方向上的解的解析性质允许直接从定义中确定精确的应力强度因子（SIF），因此不需要特殊的裂纹尖端处理，例如细化裂纹尖端网格或使用奇异单元（在传统的有限元和边界元方法中需要）。此外，各向异性材料行为可以容易地处理。这些优点被用于本研究中，其中一个新开发的Frobenius解决方案在频域中的SBFEM的控制微分方程求解程序，适用于模型瞬态动态断裂问题。复频率响应函数首先使用Frobenius解决方案程序计算。然后直接从响应函数中提取动态应力强度因子（DSIF）。随后对瞬态载荷进行快速傅立叶变换（FFT），并进行逆FFT，以获得DSIF的时间历程。各向同性和各向异性材料行为的基准问题建模使用开发的频域方法。本研究的结果与已发表的文献中的结果非常一致。文中还讨论了网格密度、材料内阻尼系数、最大频率和频率间隔对计算精度和计算量的影响。
In the scaled boundary finite element method (SBFEM), the analytical nature of the solution in the radial direction allows accurate stress intensity factors (SIFs) to be determined directly from the definition, and hence no special crack-tip treatment, such as refining the crack-tip mesh or using singular elements (needed in the traditional finite element and boundary element methods), is necessary. In addition, anisotropic material behaviour may be handled with ease. These advantages are used in this study, in which a newly-developed Frobenius solution procedure in the frequency domain for solving the governing differential equations of the SBFEM, is applied to model transient dynamic fracture problems. The complex frequency–response functions are first computed using the Frobenius solution procedure. The dynamic stress intensity factors (DSIFs) are then extracted directly from the response functions. This is followed by a fast Fourier transform (FFT) of the transient load and a subsequent inverse FFT to obtain the time history of DSIFs. Benchmark problems with isotropic and anisotropic material behaviour are modelled using the developed frequency-domain approach. Excellent agreement is observed between the results of this study and those in published literature. The effects of the mesh density, the material internal damping coefficient, the maximum frequency and the frequency interval determining the frequency–response functions on the resultant accuracy and the computational cost are also discussed.