Structural Topology Optimisation for Fibre Reinforced Composites

Fibre-reinforced composites are widely used in aeronautics and astronautics due to their high specific strength and lightweight properties. Though advanced manufacturing techniques like automated fibre placement and additive manufacturing have dramatically reduced fabrication costs by placing fibre tows along curvilinear paths and creating laminates with tailored stiffness, their great potential still has not been fully explored because of limitations in fibre path design. Therefore, it is necessary to develop a specific optimisation method for the properties and manufacturing of fibre-reinforced composites to take full advantage of their capabilities. The primary aim of this thesis is to introduce a systematic optimisation method using the well-known non-uniform rational B-splines (NURBS) to express fibres in the composites and design their paths to enhance structural stiffness. Besides mean compliance, the repulsive energy is integrated into the objective function to avoid fibre knots and intersections. Furthermore, the NURBS control point coordinates are creatively set as design variables. Considering all fibre intersection possibilities, hybrid elements are used in finite element analysis to further improve design efficiency. The method of moving asymptotes is subsequently applied to update the control points’ coordinates, guided by the sensitivity of the objective function. A significant advantage of this method is the direct derivation of the NURBS-expressed fibre path, eliminating the need for post-processing. Furthermore, compared with element densities or level set functions used in previous studies, the proposed method significantly reduces the number of design variables to improve optimisation efficiency. The project is the first to report using NURBS curves to express fibres and optimise their paths to meet manufacturing constraints. The key finding was that the intersection of fibres can cause thickness variations in the composite panel and excessive curvature can cause stress concentrations and ultimately degrade product performance. Adjusting fibre paths through post-processing can avoid intersections, but the calculation is complex and causes the fibres to deviate from the optimal distribution. This work introduces a fictitious repulsion energy to make the fibres evenly distributed and ensure the continuity of the objective function. This research aims to improve the practicality of optimisation algorithms for fibre-reinforced composites, ensuring that elegant configurations can be produced directly without post-processing. The brief of the three topics included in this thesis are listed as follows: The first research topic introduces a nodal-based evolutionary design optimisation algorithm for frame structures, utilizing the Delaunay triangulation of distributed nodes within the design domain. This method expands the solution space and reduces design variables by allowing free movement of non-loading and non-boundary nodes. The algorithm updates nodal coordinates and member thickness using the Method of Moving Asymptotes (MMA), informed by the objective function's sensitivity, which combines compliance and volume. The second research topic extended the previous method to fibre optimisation of composite materials. This research considers the intersection of fibres with rectangular elements in finite analysis to determine mechanical responses accurately. The optimisation framework involves shifting truss network nodes, with node coordinates as design variables updated using the MMA solver, guided by a sensitivity analysis smoothed by a radial basis function. Each iteration includes path adjustments for twist prevention and gap control through polynomial interpolation. Numerical examples show the method's efficiency in generating optimised fibre paths quickly, with significantly fewer design variables. This approach theoretically ensures a global minimum, achieving lower objective values than existing methods. The third research topic directly uses NURBS curves to describe fibres and optimise their paths. Mean compliance to prevent fibre knots and intersections. The p-norm method is applied for curvature constraints to mitigate sharp fibre turns. NURBS control point coordinates are innovatively used as design variables, and the hybrid element in the second research is used in FEA, thereby boosting design efficiency. Control points' coordinates are updated using the MMA solver, directed by the objective function's sensitivity. Numerical examples demonstrate this approach's effectiveness in a 2D VSC design. This method's significant advantage lies in directly deriving NURBS-expressed fibre paths, thus negating the need for post-processing and reducing the number of design variables compared to previous methods, enhancing overall optimisation efficiency. Compared with the previous method of using polynomial curve fitting, this work can obtain fibre paths without post-processing, and the NURBS curve is also conducive to using other CAD software. In summary, the research outcomes demonstrate that the proposed node-shifting optimisation methods can be combined with NURBS-expressed fibres to improve optimisation efficiency and effectiveness. The optimisation results meet the manufacturing constraints, can be directly exported to computer-aided design software, and then fabricated.