Abstract A new stochastic isogeometric analysis method based on reduced basis vectors (SRBIGA) is proposed for engineering structures with random field material properties and external loads. Based on the Galerkin isogeometric functions, the proposed SRBIGA applies the Karhunen–Loeve expansion to discretize the random field uncertainties. Inspired by the stochastic Krylov subspace theory, the structural responses of linear elasticity structures with random field uncertainties are represented based on the reduced basis vectors. The tremendous advantage of SRBIGA over the spectral stochastic isogeometric analysis (SSIGA) in terms of the computational efficiency is disclosed through the comparison analysis in theoretical aspects. Three illustrative examples demonstrate that the proposed SRBIGA has not only significantly higher efficiency but also higher accuracy and better robustness than the SSIGA and that it can provide a novel and expedient stochastic structural analysis method for practical large-scale complex engineering structures when both material properties and external loads are spatially random.

中文翻译：

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基于约简基向量的随机场不确定工程结构随机等几何分析新方法

摘要 针对具有随机场材料特性和外载荷的工程结构，提出了一种新的基于约简基向量的随机等几何分析方法（SRBIGA）。基于伽辽金等几何函数，提出的 SRBIGA 应用 Karhunen-Loeve 展开来离散随机场的不确定性。受随机 Krylov 子空间理论的启发，具有随机场不确定性的线弹性结构的结构响应基于约简基向量表示。通过理论方面的比较分析，揭示了SRBIGA在计算效率方面相对于谱随机等几何分析（SSIGA）的巨大优势。