适用于二维和三维问题中动态裂纹扩展的混合s型等几何策略
A hybrid s-version isogeometric strategy for dynamic crack propagation in 2D and 3D problems
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中文总结 AI 辅助
本文提出混合s型等几何分析（hS-IGA）策略，用于二维和三维动态裂纹扩展分析，可精确高效评估近裂纹断裂量，耦合积分点数量较传统s方法大幅减少。
中文摘要 AI 辅助
本文提出了一种混合s型等几何分析（hS-IGA）策略，用于动态裂纹扩展分析中近裂纹断裂量的精确且高效评估。该策略保留了传统s方法的全局-局部叠加框架，仅在全局离散化中引入B样条基函数，并在裂纹域保留基于拉格朗日的局部网格。这种混合公式的提出，是为了解决传统基于拉格朗日的s方法在全局-局部耦合积分中与连续性相关的瓶颈问题，同时满足保留基于拉格朗日的局部网格以用于裂纹表示和动态应力强度因子（DSIF）及局部应力后处理的需求。所得公式消除了由全局近似引起的耦合积分被积函数中的不连续性，并且无需递归细分即可通过标准高斯求积实现精确的耦合积分。通过二维静态和动态直裂纹问题，将所提策略与标准有限元法和传统s方法进行对比验证；还通过三维静态和动态扩展圆裂纹问题，与传统s方法进行进一步评估。结果表明，所提hS-IGA策略可精确评估DSIF和局部应力，同时保留s方法的全局-局部建模优势；与传统s方法相比，其耦合积分所需的积分点数量大幅减少，在二维动态基准测试中减少约81%，在三维动态基准测试中减少95.6%。这些结果证明，所提hS-IGA框架为需要可靠评估近裂纹断裂量的动态裂纹扩展分析提供了一种精确且高效的全局-局部策略。
英文摘要
A hybrid s-version of isogeometric analysis (hS-IGA) strategy is proposed for accurate and efficient evaluation of near-crack fracture quantities in dynamic crack propagation analysis. The strategy retains the global-local superposition framework of the conventional s-method, while introducing B-spline basis functions only into the global discretisation and preserving a Lagrange-based local mesh in the crack domain. This hybrid formulation is motivated by the continuity-related bottleneck in the global-local coupling integration of the conventional Lagrange-based s-method, and by the need to retain a Lagrange-based local mesh for crack representation and post-processing of the dynamic stress intensity factor (DSIF) and local stress. The resulting formulation removes discontinuities in the coupling integrands caused by the global approximation and enables accurate coupling integration by standard Gauss quadrature without recursive subdivision. The proposed strategy is verified using two-dimensional stationary and dynamic straight-crack problems against the standard finite element method and the conventional s-method, and is further assessed using three-dimensional stationary and dynamically propagating circular-crack problems against the conventional s-method. Results show that the proposed hS-IGA strategy accurately evaluates the DSIF and local stress while retaining the global-local modelling advantages of the s-method. It also substantially reduces the number of integration points required for coupling integration, by approximately 81% in the two-dimensional dynamic benchmark and 95.6% in the three-dimensional dynamic benchmark relative to the conventional s-method. These results demonstrate that the proposed hS-IGA framework provides an accurate and efficient global-local strategy for dynamic crack propagation analyses requiring reliable evaluation of near-crack fracture quantities.
