Fully 3-D models can be prohibitively expensive when dealing with industrial-scale problems while plate and shell models are not able to capture localized 3-D effects around cracks, welds, and other structural features. This paper presents an iterative multiscale Generalized Finite Element Method (GFEM) able to automatically couple 3-D solid and shell models and capture interactions among structural scales. Three scales and corresponding models and discretizations are considered: A global shell model that captures only the overall behavior of a structure; a 3-D mesoscale model that bridges the solutions between the global and finer scales; and a 3-D fine-scale model, denoted local model, used to simulate localized defects, such as cracks, or structural features, such as welds. The coupling between global and mesoscale models is done using the iterative global-local algorithm and a Generalized Finite Element Method with analytically or numerically defined enrichments is used for the meso and local scales coupling. The proposed multiscale framework combines software with complementary capabilities. The shell problem is solved with the commercial software Abaqus while the meso and local scale problems are solved with an in-house GFEM solver. Another contribution of this work is a staggered algorithm for the solution of the coupled problems defined at the global, meso, and local scales. The performance of the methodology is compared against fully 3-D models and the sub-modeling approach which is widely adopted in engineering practice for the analysis of problems with multiple spatial scales of interest.

在处理工业规模的问题时，全 3-D 模型可能会非常昂贵，而板壳模型无法捕捉裂缝、焊缝和其他结构特征周围的局部 3-D 效果。本文提出了一种迭代多尺度广义有限元方法(GFEM)，能够自动耦合 3-D 实体和壳模型并捕获结构尺度之间的相互作用。考虑了三个尺度和相应的模型和离散化： 仅捕获结构整体行为的全局壳模型；3-D中尺度模型，在全球尺度和更精细尺度之间架起桥梁；以及一个 3-D 精细模型，表示为局部模型，用于模拟局部缺陷，例如裂缝，或结构特征，例如焊缝。全局和中尺度模型之间的耦合是使用迭代全局-局部算法完成的，并且具有解析或数值定义的富集的广义有限元方法用于中尺度和局部尺度耦合。提议的多尺度框架将软件与互补功能相结合。使用商业软件Abaqus解决了 shell 问题而使用内部 GFEM 求解器解决中观和局部尺度问题。这项工作的另一个贡献是交错算法，用于解决在全局、中观和局部尺度上定义的耦合问题。将该方法的性能与全 3-D 模型和工程实践中广泛采用的子建模方法进行比较，以分析具有多个感兴趣的空间尺度的问题。