  This work presents a novel methodology for speeding up the assembly of
stiffness matrices for laminate composite 3D structures in the context of
isogeometric and finite element discretizations. By splitting the involved
terms into their in-plane and out-of-plane contributions, this method computes
the problems's 3D stiffness matrix as a combination of 2D (in-plane) and 1D
(out-of-plane) integrals. Therefore, the assembly's computational complexity is
reduced to the one of a 2D problem. Additionally, the number of 2D integrals to
be computed becomes independent of the number of material layers that
constitute the laminated composite, it only depends on the number of different
materials used (or different orientations of the same anisotropic material).
Hence, when a high number of layers is present, the proposed technique reduces
by orders of magnitude the computational time required to create the stiffness
matrix with standard methods, being the resulting matrices identical up to
machine precision. The predicted performance is illustrated through numerical
experiments.
