This paper presents an n-th high order perturbation-based stochastic isogeometric Kirchhoff–Love shell method, formulation and implementation for modeling and quantifying geometric (thickness) uncertainty in thin shell structures. Firstly, the Non-Uniform Rational B-Splines (NURBS) is used to describe the geometry and interpolate the variables in a deterministic aspect. Then, the shell structures with geometric (thickness) uncertainty are investigated by developing an nth order perturbation-based stochastic isogeometric method. Here, we develop the shell stochastic formulations in detail (particularly, expand the random input (thickness) and IGA Kirchhoff-Love shell element based state functions analytically around their expectations via n-th order Taylor series using a small perturbation parameterε), whilst freshly providing the Matlab core codes helpful for implementation. This work includes three key novelties: 1) by increasing/utilizing the high order of NURBS basis functions, we can exactly represent shell geometries and alleviate shear locking, as well as providing more accurate deterministic solution hence enhancing stochastic response accuracy. 2) Via increasing the nth order perturbation, we overcome the inherent drawbacks of first and second-order perturbation approaches, and hence can handle uncertainty problems with some large coefficients of variation. 3) The numerical examples, including two benchmarks and one engineering application (B-pillar in automobile), simulated by the proposed formulations and direct Monte Carlo simulations (MCS) verify that thickness randomness does strongly affect the response of shell structures, such as the displacement caused by uncertainty can increase up to 35%; Moreover, the proposed formulation is effective and significantly efficient. For example, compared to MCS, only 0.014% computational time is needed to obtain the stochastic response.

本文提出了一种基于n次高阶扰动的随机等几何Kirchhoff-Love壳方法，公式化和实现，用于建模和量化薄壳结构中的几何（厚度）不确定性。首先，非均匀有理B样条（NURBS）用于描述几何形状并在确定性方面内插变量。然后，通过开发基于n阶扰动的随机等几何方法，研究具有几何（厚度）不确定性的壳结构。在这里，我们详细开发了壳的随机公式（特别是扩展了随机输入（厚度）和基于IGA Kirchhoff-Love壳元素的状态函数，通过n-使用小扰动参数ε）的泰勒级数，同时新鲜提供有助于实现的Matlab核心代码。这项工作包括三个关键的新颖性：1）通过增加/利用NURBS基函数的高阶，我们可以精确地表示壳的几何形状并减轻剪切锁定，并提供更准确的确定性解决方案，从而提高随机响应的准确性。2）通过增加n阶扰动克服了一阶和二阶扰动方法的固有缺点，因此可以处理具有较大变异系数的不确定性问题。3）数值示例，包括两个基准和一个工程应用（汽车中的B柱），由拟议的公式和直接蒙特卡洛模拟（MCS）进行了仿真，验证了厚度随机性确实会严重影响壳结构的响应，例如由不确定性引起的位移最多可增加35％；而且，提出的制剂是有效的并且显着有效的。例如，与MCS相比，仅需要0.014％的计算时间即可获得随机响应。