  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.
