Dynamic reliability analysis of crack problems is of great concern to engineering practice. To tackle this problem, dynamic stress intensity factors (SIFs) of cracks need to be computed at high accuracy and efficiency with wide adaptability. In this study, a cracked superelement is first proposed to model the near-crack region. The stiffness matrix and mass matrix of the cracked superelement are formulated by the dynamic spline fictitious boundary element method (SFBEM) based on the Erdogan fundamental solutions. The proposed superelement is then incorporated into a finite element mesh, and the global equation of motion of the crack problem is established and solved within the frame of finite element method (FEM). The explicit time-domain expressions of dynamic SIFs of the crack problem are finally constructed by a backward analysis of the cracked superelement with SFBEM. On this basis, the explicit time-domain method (ETDM) is utilized to conduct random vibration analysis of the crack problem subjected to nonstationary random loads. The statistical moments of dynamic SIFs and the failure probability of initial crack propagation can be evaluated at high efficiency by ETDM in conjunction with the SFBEM-FEM coupling method. Numerical examples are investigated to show the effectiveness of the proposed hybrid approach.

中文翻译：

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SFBEM-FEM耦合法裂纹板非平稳随机振动分析


裂纹问题的动态可靠性分析备受工程实践关注。为了解决这个问题，需要高精度、高效且具有广泛适应性的裂纹动态应力强度因子（SIF）计算。在本研究中，首先提出了裂纹超单元来模拟近裂纹区域。基于埃尔多安基本解，通过动态样条虚拟边界元法（SFBEM）制定了裂纹超单元的刚度矩阵和质量矩阵。然后将所提出的超单元纳入有限元网格，并在有限元法 (FEM) 框架内建立并求解裂纹问题的全局运动方程。通过SFBEM对裂纹超单元的逆向分析，最终构建了裂纹问题动态SIF的显式时域表达式。在此基础上，利用显式时域方法（ETDM）对非平稳随机载荷作用下的裂纹问题进行随机振动分析。 ETDM 结合 SFBEM-FEM 耦合方法可以高效评估动态 SIF 的统计矩和初始裂纹扩展的失效概率。研究数值示例以显示所提出的混合方法的有效性。