Multi-Parameter Layup Optimization and the Effect of Layup Homogenization on the Bending Compliance Matrix of Coupled Composites

Abstract

The behaviour of fibre-reinforced composites greatly depends on their layup structures. Through a full-field layup optimization study based on multiple parameters, this paper investigates how different properties change with the layup. The aim was to maximize the extension-twist coupling performance while ensuring adequate bending stiffness and low thermal warpage to make the laminate suitable for shape-adaptive helicopter rotor blade application. The Classical Laminate Theory-based calculations revealed that satisfying the bending compliance and thermal warpage criteria significantly limited the achievable extension-twist performance. The warpage limit affected the desired coupling behaviour more because both properties are driven by terms in the extensional-bending compliance matrix, unlike bending compliance. Symmetric laminates do not have an intrinsic extension-twist capability, but some asymmetric laminates demonstrated significant coupling performance while being practically warpage-free (based on the ISO2768 standard). The results prove that the advantages of asymmetric laminates can outweigh their sometimes negligible disadvantages. The paper also investigates if there is a universal tendency in how layup homogenization affects the terms of the bending compliance matrix of composites. Through analytical calculations, we showed that depending on the layup of the sub-laminate, homogenization can increase or reduce the value of any term in the bending compliance matrix; therefore, there is no universal tendency. Based on these results, layup homogenization cannot only be exploited for its most general purpose – warpage mitigation – but also for improving other characteristics of the laminate (e.g. reducing the bending compliance for increased bending stiffness or increasing the bend-twist compliance for improved coupling performance).