Implementation of a ply inclination in the Classical Laminate Theory

Abstract

The use of the Classical Laminate Theory (CLT) is limited to laminates where all the fibres in a ply are oriented in the plane of the laminate. In some applications, it is possible that the plies will start at the bottom of a laminate and end at the top of the laminate. This means an inclination is added to the plies, which creates an extra rotation in the fibre direction with respect to the plane of the laminate. Such a laminate with inclined plies is found for example in the skin of InfraCore panels. In the regular CLT, this extra rotation cannot be taken into account, thus the elastic behaviour of a laminate with inclined plies cannot be described properly. The extra rotation that occurs in a laminate with inclined plies has analytically been implemented in the regular CLT to obtain a modified CLT, which has been verified using Finite Element analyses. Using the modified CLT, a reduction in equivalent stiffness can be observed for a single unidirectional ply with an inclination in the fibre direction. The exact value of stiffness reduction strongly depends on the material properties and the lay-up of the laminate. For InfraCore skins, the stiffness reduction is very small (0.15%). Due to the inclination in the plies, the lay-up of the laminate differs along the length of the plate. As a result, the output of the modified CLT is only applicable to one location along the plate. Due to the lay-up differences, the equivalent stiffness will also differ along the inclination direction. The in-plane equivalent stiffnesses will be the highest for symmetric laminates, where the flexural equivalent stiffness will be the highest when the plies with the stiffest fibre direction are located on the outside of a laminate.