This work models spatially uncorrelated (independent) load uncertainty and develops a reduced-order Monte Carlo stochastic isogeometric method to quantify the effect of the load uncertainty on the structural response of thin shells and solid structures. The approach is tested on two demonstrative applications of uncertainty, namely, spatially uncorrelated loading, with (1) Scordelis–Lo Roof shell structure, and (2) a 3D wind turbine blade. This work has three novelties. Firstly, the research models spatially uncorrelated (independent) load uncertainties (including both their magnitude and/or direction) using stochastic analysis. Secondly, the paper advances a reduced-order Monte Carlo stochastic isogeometric method to quantify the spatially uncorrelated load uncertainty. It inherits the merits of isogeometric analysis, which enables the precise representation of geometry and alleviates shell shear locking, thereby reducing the model’s uncertainties. Moreover, the method retains the generality and accuracy of classical Monte Carlo simulation (MCS), with significant efficiency gains. The demonstrative results suggest that there is a cost, which is 3% of the time used by the standard MCS. Furthermore, a significant observation is made from the conducted numerical tests. It is noticed that the standard deviation of the output (i.e., displacement) is strongly influenced when the load uncertainty is spatially uncorrelated. Namely, the standard derivation (SD) of the output is roughly 10 times smaller than the SD for correlated load uncertainties. Nonetheless, the expected values remain consistent between the two cases.

这项工作对空间不相关（独立）的载荷不确定性进行建模，并开发了降阶蒙特卡洛随机等几何方法，以量化载荷不确定性对薄壳和实体结构的结构响应的影响。该方法在不确定性的两个示范应用中进行了测试，即，空间不相关的载荷，具有（1）Scordelis-Lo Roof壳体结构，以及（2）3D风力涡轮机叶片。这项工作有三个新颖之处。首先，研究使用随机分析对空间不相关（独立）的负载不确定性（包括其大小和/或方向）进行建模。其次，本文提出了降阶蒙特卡洛随机等几何方法来量化空间无关的载荷不确定性。它继承了等几何分析的优点，这样就可以精确地表示几何图形并减轻壳的剪切锁定，从而减少了模型的不确定性。此外，该方法保留了经典蒙特卡洛模拟（MCS）的一般性和准确性，并获得了显着的效率提升。演示结果表明存在成本，这是标准MCS使用时间的3％。此外，从进行的数值测试中得出了显着的观察结果。注意，当负载不确定性在空间上不相关时，输出的标准偏差（即位移）会受到很大影响。即，对于相关的负载不确定性，输出的标准导数（SD）大约比SD小10倍。但是，两种情况下的期望值保持一致。