Ntourmas, Georgios
(2023)
Detailed sizing optimisation of industrial-scale composite aeronautical structures.
PhD thesis, University of Nottingham.
Abstract
Carbon fibre reinforced polymers have been increasingly used in the aerospace industry over the last decades, because they offer reduced weight and enhanced mechanical characteristics compared to classic metallic structures. However, their application is also linked with several challenges concerning their design and optimisation process. One of the most widely studied topics is the detailed sizing optimisation of variable stiffness composite structures. This task involves determining the optimal thickness and stiffness distribution across the structure and translating that into a manufacturable stacking sequence design. In this study, uni-directional carbon fibre laminae are assumed to be used during manufacturing and therefore the stiffness variation across the span of a composite component is a result of multiple interconnected constant stiffness zones called patches. The task of the detailed design of a composite structure involves the computation of discrete stacking sequences satisfying both mechanical constraints, such as stability and strength, but also design and manufacturing guidelines commonly employed in the aerospace industry. When dealing with industrial-scale structures this optimisation is commonly split up in one gradient and one non-gradient based stage, in order to tackle the challenges of the task. These challenges are associated with mixed continuous and discrete design variables and constraints and the high computational cost of the mechanical constraints. A two stage-optimisation process has also been developed in the framework of this thesis.
In the first, gradient-based optimisation stage of the process, generic stacks are employed to model the thickness and stiffness distribution of the structure. A generic stack is comprised of a collection of layers whose orientations are fixed \textit{a priori}, but thicknesses can vary independently enabling exploration of the design space. The result of this first stage is a continuous thickness and stiffness distribution. All mechanical constraints must be considered in the first stage and therefore the converged optimisation result satisfies these constraints. Before moving to the second stage of the optimisation, the total thickness of each patch is rounded up to the nearest number of manufacturable plies, which can be easily derived since the thickness of the pre-impregnated uni-directional tape that will be used during manufacturing is known. In the second stage of the optimisation, the thickness distribution of the structure remains constant and the task is to retrieve stacking sequences which fulfil a set of predefined composite design and manufacturing rules, with blending or continuity between neighbouring patches being one of the most crucial ones. The objective function of this optimisation is to minimise the absolute difference between the stiffness of the continuous design computed in the first stage and the stiffness of the discrete candidate design in the second stage. The problem of retrieving layered designs that meet all of the prescribed composite rules is formulated as two Mixed Integer Linear Programming instances which mainly differ in how the blending is treated. Using either of the two formulations, mathematical programming algorithms can be employed to solve the problem to global optimality.
For the two-stage process to be successful, all constraints from both stages should be fulfilled. The main challenge is retrieving stacking sequences which satisfy the mechanical constraints of the problem, since these are not explicitly considered in the second stage of the optimisation but rather depend on the quality of the achieved stiffness match. To that extent, introducing as many composite design and manufacturing rules as possible in the first stage of the optimisation is of crucial importance in order to bridge the information gap between the continuous and discrete solution. This can be challenging due to the discrete nature of these constraints and the need to implement them in a gradient-based framework. Fortunately, the design space of the generic stacks allows multiple composite rules to be accurately formulated, which is not the case for alternative stiffness parametrisation techniques.
Overall, when applied to an academic demonstrator and compared to relevant studies, the developed approach is able to retrieve a design with a lower structural mass, while also satisfying all mechanical constraints. What is more, this can be achieved in only one iteration of the two-stage process. This result is a combination of having accurately formulated blending constraints in the first stage of the optimisation and of using a problem formulation in the second stage which does not limit the design freedom and is solved using a deterministic optimisation algorithm able to provide a globally optimum solution. The two-stage process has also been applied to the design of the composite wing skins of a large-scale unmanned aircraft. Both the first and second stage of the optimisation can efficiently handle the computational complexity of large case studies. For the second stage of the optimisation, a decomposition technique has been developed in order to derive good quality solutions in a significantly reduced time frame. In the case of the large-scale aircraft, minor constraint violations occur when evaluating the discrete design. These can be conveniently handled by a repetition of the continuous optimisation, while keeping the discretised stacking sequences fixed. The optimiser can easily satisfy all remaining violations by a slight modification of the stiffness properties of other sub-components, such as the stringers, whose stiffness characteristics can be easily manipulated in the continuous domain. Overall, the weight penalty introduced between the continuous and discrete result which satisfies all constraints is approximately 2\,Kg.
Finally, the work of the thesis has been extended towards the field of design for manufacturing. Automatic Fibre Placement manufacturing processes have become the aerospace industry standard for the production of large-scale composite components. The aspect of the layup time required to manufacture a composite component is introduced as an objective function in the first stage of the detailed sizing process. The methodology developed is able to identify how the material is going to be laid on the tool. The method is applied to the skin of the aforementioned aircraft wing and a trade-off between the structural weight and layup time is observed. Results demonstrate that the bi-objective optimisation is a promising tool for reducing the structural mass, while keeping the layup time to acceptable levels by benefiting from a more detailed structural modelling.
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