Efficient and High-fidelity Finite Element Models for Fibre Composites

Fibre reinforced composites are widely used as structural components in the aerospace industry. The fabrication of highly tailored fibre composite structures is enabled by advanced composite manufacturing methods, such as Automated Fibre Placement (AFP). AFP enables fibre tows to be placed at arbitrary fibre orientations, either straight or curved, and the local tailoring of composite properties significantly improves the mechanical performance. The conventional finite element approaches assume that the curved fibres are locally straight, and many small elements are needed to model the curved fibres accurately. This increases the computational expense of gradient-based fibre angle optimization as it requires repeated evaluations of the finite element model of the composite. Therefore, the goal of this research is to establish an accurate finite element (FE) model with good computational efficiency for composite structures with complex fibre configurations to be used for gradient-based optimization. In this work, a novel finite element approach that enables the use of larger elements with the desired level of accuracy is formulated for a single-layer thin composite lamina with curved fibres. Fewer elements make the FE analysis more efficient as the dimension of the global stiffness matrices is reduced. The element model represents the real physical system more accurately, as the Gauss quadrature process is modified to capture the stiffness change caused by the fibre curvature in the calculation of element stiffness matrices. As a function of the orientation of fibres in adjacent elements, fibre curvature is calculated by minimizing the fibre discontinuity between adjacent elements given their average fibre orientation. This is a least square minimization problem and solved through its normal equation. Finally, stiffness maximization for the single-layer thin composite lamina is performed using a gradient descent algorithm integrated with the finite element formulation with explicit fibre curvature. The fibre curvature is an intermediate variable to the objective function, and the total derivative of the objective function with respect to fibre orientation is calculated analytically using the adjoint method. The optimal solutions show that this new method gives the same results as optimization using conventional finite elements, but has much faster convergence.Ph.D