In this paper, the first large-scale application of multiscale-spectral generalized finite element methods (MS-GFEM) to composite aero-structures is presented. The crucial novelty lies in the introduction of A-harmonicity in the local approximation spaces, which in contrast to [Babuska, Lipton, Multiscale Model. Simul. 9, 2011] is enforced more efficiently via a constraint in the local eigenproblems. This significant modification leads to excellent approximation properties, which turn out to be essential to capture accurately material strains and stresses with a low dimensional approximation space, hence maximising model order reduction. The implementation of the framework in the DUNE software package, as well as a detailed description of all components of the method are presented and exemplified on a composite laminated beam under compressive loading. The excellent parallel scalability of the method, as well as its superior performance compared to the related, previously introduced GenEO method are demonstrated on two realistic application cases, including a C-shaped wing spar with complex geometry. Further, by allowing low-cost approximate solves for closely related models or geometries this efficient, novel technology provides the basis for future applications in optimisation or uncertainty quantification on challenging problems in composite aero-structures.

翻译：本文首次提出了多尺度谱广义有限元方法（MS-GFEM）在复合材料航空结构中的大规模应用。关键创新在于将A-调和性引入局部逼近空间，与[Babuska, Lipton, Multiscale Model. Simul. 9, 2011]不同，该方法通过局部本征问题中的约束更高效地实现此特性。这一重要改进带来了优异的逼近性质，使得低维逼近空间能够精确捕捉材料应变与应力，从而最大化模型降阶效果。本文详细阐述了该框架在DUNE软件包中的实现，以及方法各组成部分的描述，并通过受压复合材料层合梁算例加以演示。在两个实际应用案例（包括复杂几何构型的C形翼梁）中，验证了该方法出色的并行可扩展性，以及相较于此前提出的相关GenEO方法的更优性能。此外，通过支持对相近模型或几何构型进行低成本近似求解，这一高效新技术为未来在复合材料航空结构优化设计或不确定性量化等挑战性问题中的应用奠定了基础。