Stiffness Design of Laminated Composites

Abstract

Fibre-reinforced laminated composites are constructed layer-by-layer, allowing their material properties to be easily tailored relative to their isotropic counterparts (metallic alloys). Moreover, a composite structure with variable stiffness (VS) can be made by spatially tailoring stiffness across a laminate. This permits better load distribution within a structure, efficiently using a given material, and allow for lighter construction. Typically, the design of VS structures follows a bi-level procedure: first, the structure’s stiffness distribution is optimised using lamination parameters (LPs), and second, the stacking sequences (SS) of differently oriented fibres are designed to achieve the desired stiffness distribution. However, the designs envisioned using LPs are only sometimes exactly matched by the designed SS. The shortcomings faced during this conversion are called the ’Inverse Problem’. Upon reviewing the existing techniques in literature to handle the inverse problem, it was understood that converting LPs into SS is challenging without incurring substantial computational costs or imposing significant restrictions on allowable fibre orientations in the design. Such restrictions tend to under-utilise the directional properties of the fibres. Thus, there was a need to explore and develop better stiffness design methods for laminated composites by bridging the gap between LPs and SS in a computationally efficient way.

In response to this challenge, a hierarchical design framework was proposed to handle the Inverse Problem. Diverging from conventional methods that directly design the SS and try to match a given set of LPs, this framework divides the problem into two distinct stages. Initially, the focus is to use the In-Plane LPs and determine the number of layers in each orientation within a laminate, also called the Fibre Angle Distribution (FAD). Subsequently, the FAD serves as an interim solution, and the SS can be designed by using the Out-of-Plane LPs along with it. This problem partitioning enhances computational efficiency and offers potential benefits in solving the Inverse Problem more effectively. Given the time constraints inherent to a master thesis, the primary undertaking of this study was to efficiently design the FAD while accommodating a wide range of possible fibre orientations. To address this, a novel method using the Fast-Fourier Transform (FFT) was developed to facilitate FAD design with ply angle multiples of 15° (or [∆15° ] = [0, ±15, ±30, ±45, ±60, ±75, 90]). Moreover, empirical guidelines for SS design, such as the Symmetry and Balancing rule, were incorporated into the design step.

The primary contribution of this report is introducing an FFT-based method to design FADs, a novel addition to the existing body of research. Upon extensive testing, it was shown that this implementation could convert LPs into multiple unique FAD solutions in less than 0.3 seconds on a regular office laptop, outperforming other methods in literature by at least ten times. Furthermore, the implementation was also used to demonstrate the benefits of designing laminated composites using [∆15°] over the conventional [∆45°] orientations (or [0, ±45, 90]). In light of the positive results, it is pointed out that the In-Plane LPs (and consequently the In-Plane stiffness) are known to be sensitive only to the FAD and not their SS. As such, the readers of this thesis are presented with a very computationally efficient approach for designing laminated composites for In-Plane Stiffness...