基于比例边界有限元法计算应力强度因子的不确定量化分析

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摘要应力强度因子（SIFs）是预测荷载作用下结构中裂纹产生和扩展的重要参数。半解析的比例边界有限元法（SBFEM）结合了有限元和边界元法的优势，在裂纹尖端或存在奇异应力的区域不需要局部网格细化，可以直接提取应力强度因子。本文在比例边界有限元法计算应力强度因子的框架下，引入随机参数进行蒙特卡罗模拟(MCs)，并提出一种新颖的基于蒙特卡罗模拟的不确定量化（UQ）分析。与直接的蒙特卡罗模拟不同，采用奇异值分解（SVD）构造低阶的子空间，降低系统的自由度，并使用径向基函数（RBF）对子空间进行近似，通过子空间的线性组合获得新的结构响应，实现基于MCs的快速不确定量化分析。考虑不同荷载状况下，结构形状参数和材料属性参数对应力强度因子的影响，使用改进的蒙特卡罗模拟计算应力强度因子的统计特征，量化不确定参数对结构的影响。最后通过若干算例验证了本文算法的准确性和有效性。

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	胡昊文1
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关键词 ：应力强度因子, 比例边界有限元法, 蒙特卡罗模拟, 不确定性量化分析, 奇异值分解

Abstract：Stress intensity factors (SIFs) are important parameters in predicting the initiation and propagation of cracks in structures subjected to loads. The semi-analytical scaled boundary finite element method (SBFEM) combines the advantages of finite element and boundary element method, and without local mesh refinement around crack tips or regions existing stress singularities. The stress intensity factors can be directly extracted. Within the framework of the scaled boundary finite element method in evaluating stress intensity factors, random parameters are introduced for Monte Carlo simulation (MCs), a novel uncertainty quantification (UQ) analysis based on Monte Carlo simulation is proposed in this manuscript. Unlike direct Monte Carlo simulation, singular value decomposition (SVD) is used to construct lower order subspaces to reduce the degree of freedom of the system. Radial basis function (RBF) is used to approximate the subspaces and obtain new structural responses through linear combinations of subspaces, achieving fast uncertainty quantification analysis based on MCs. Considering the effects of structural shape parameters and material property parameters on stress intensity factors under different load conditions, an improved Monte Carlo simulation is used to calculate the statistical characteristics of stress intensity factors and quantify the impact of uncertain parameters on the structure. Finally, the accuracy and effectiveness of the algorithm proposed in this paper are verified by several examples.

Key words： stress intensity factors scaled boundary finite element method Monte Carlo simulation uncertainty quantification singular value decomposition

收稿日期: 2023-04-24 出版日期: 2024-03-15

引用本文:

胡昊文1，2，陈灯红1，2，王乾峰1，2，胡记磊1，2，骆欢1，2. 基于比例边界有限元法计算应力强度因子的不确定量化分析[J]. 振动与冲击, 2024, 43(5): 250-259.
HU Haowen1,2,CHEN Denghong1,2,WANG Qianfeng1,2,HU Jilei1,2,LUO Huan1,2. UQ analysis in calculating SIFs based on SBFEM. JOURNAL OF VIBRATION AND SHOCK, 2024, 43(5): 250-259.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2024/V43/I5/250

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