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

UQ analysis in calculating SIFs based on SBFEM

应力强度因子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。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(Monte Carlo simulation, MCS),并提出一种新颖的基于MCS的不确定量化分析。与直接的MCS不同,采用奇异值分解构造低阶的子空间,降低系统的自由度,并使用径向基函数对子空间进行近似,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MCS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该算法的准确性和有效性。

Stress intensity factors(SIFs)are important parameters for predicting generation and propagation of cracks in structures under load.The semi-analytical scaled boundary finite element method(SBFEM)combining advantages of finite element and boundary element methods does not require local mesh refinement at crack tip or in areas with singular stress to directly extract SIFs.Here,under the framework of SBFEM for calculating SIFs,random parameters were introduced for Monte Carlo simulation(MCS),and a novel uncertainty quantification(UQ)analysis was proposed based on MCS.Unlike direct MCS,singular value decomposition(SVD)was used to construct lower order subspaces,and reduce DOFs of system.Radial basis functions(RBFs)were used to approximate subspaces.New structural responses were obtained with linear combinations of subspaces to realize fast UQ analysis based on MCS.Considering effects of structural shape parameters and material property parameters on SIFs under different load conditions,an improved MCS was used to calculate statistical characteristics of SIFs and quantify effects of uncertain parameters on structure.Finally,several numerical examples were used to verify the correctness and effectiveness of the proposed UQ analysis.