This paper presents a stochastic analysis method for linear elastic fracture mechanics using the Monte Carlo simulations (MCs) and the scaled boundary finite element method (SBFEM) based on proper orthogonal decomposition (POD) and radial basis functions (RBF). The semianalytical solutions obtained by the SBFEM enable us to capture the stress intensity factors (SIFs) easily and accurately. The adoption of POD and RBF significantly reduces the model order and increases computation efficiency, while maintaining the versatility and accuracy of MCs. Numerical examples of cracks in homogeneous and bimaterial plates are provided to demonstrate the effectiveness and reliability of the proposed method, where the crack inclination angles are set as uncertain variables. It is also found that the larger the scale of the problem, the more advantageous the proposed method is.

中文翻译：

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使用由适当正交分解和径向基函数加速的缩放边界有限元方法的随机断裂分析

本文提出了一种基于适当正交分解 (POD) 和径向基函数 (RBF) 的使用蒙特卡罗模拟 (MCs) 和缩放边界有限元方法 (SBFEM) 的线弹性断裂力学随机分析方法。SBFEM 获得的半解析解使我们能够轻松准确地捕获应力强度因子 (SIF)。POD 和 RBF 的采用显着降低了模型阶数并提高了计算效率，同时保持了 MC 的通用性和准确性。提供了均质和双材料板中裂纹的数值示例，以证明所提出方法的有效性和可靠性，其中裂纹倾角设置为不确定变量。还发现问题的规模越大，