The present paper proposes a set of blending constraints expressed in lamination parameter space, applicable during the continuous optimisation of composite structures. Thicknesses and ply orientations of large composite structures are often locally optimised in response to unequal spatial load distribution. During this process, ensuring structural continuity is essential in order to achieve designs ready to be manufactured. Single step stacking sequence optimisations relying on evolutionary algorithms to enforce continuity, through the application of blending rules, are prone to the curse of dimensionality. By contrast, multi-step optimisation strategies including a continuous sub-step can optimise composite structures with reasonable computational effort. However, the discrepancies between continuous and discrete optimisation step result in performance loss during stacking sequence retrieval. By deriving and applying blending constraints during the continuous optimisation, this paper aim is to reduce the performance loss observed between optimisation levels. The first part of this paper is dedicated to the derivation of blending constraints. The proposed constraints are then successfully applied to a benchmark blending problem in the second part of this paper. Numerical results demonstrate the achievement of near-optimal easy-to-blend continuous designs in a matter of seconds.

In aircraft design, proper tailoring of composite anisotropic characteristics allows to achieve weight saving while maintaining good aeroelastic performance. To further improve the design, dynamic loads and manufacturing constraints should be integrated in the design process. The objective of this paper is to evaluate how the introduction of continuous blending constraints affects the optimum design and the retrieval of the final stacking sequence for a regional aircraft wing. The effect of the blending constraints on the optimum design (1) focuses on static and dynamic loading conditions and identifies the ones driving the optimization and (2) explores the potential weight saving due to the implementation of a manoeuvre load alleviation (MLA) strategy. Results show that while dynamic gust loads can be critical for wing design, in the case of a regional aircraft, their influence is minimal. Nevertheless, MLA strategies can reduce the impact of static loads on the final design in favour of gust loads, underlining the importance of considering such load-cases in the optimisation. In both cases, blending does not strongly affect the load criticality and retrieve a slightly heavier design. Finally, blending constraints confirmed their significant influence on the final discrete design and their capability to produce more manufacturable structures.

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Optimisation of Composite Structures -Enforcing the Feasibility of Lamination Parameter constraints with Computationally-efficient Maps AbstractComposite materials are increasingly used in high performance structural applications because of their high strength and stiffness to weight ratios together with their significant tailoring capabilities. The stiffness of a monolithic laminate can be expressed as a linear combination of material invariants, one thickness variable, and twelve lamination parameters, which is an efficient alternative to using fibre angles as design variables. However, feasibility constraints originating from the interdependency between lamination parameters must be satisfied to obtain laminates with realistic stiffness properties. Currently, enforcing these feasibility constraints is a computationally intensive task. In this paper we propose to use normalised design variables that inherently map (i.e. correspond) to feasible lamination parameters, effectively removing the need to evaluate feasibility constraints altogether. To this end, linear and B-spline maps of the feasible lamination parameter subspace are proposed and evaluated. Results of 2D and 4D benchmark analyses and optimisation studies suggest that the proposed methodology does successfully provide an efficient means of achieving feasible results at lower computational costs.

Optimizing the laminates of large composite structures is nowadays well-recognized as having significant benefits in the design of lightweight structural solutions. However, designs based on locally optimized laminates are prone to structural discontinuities and enforcing blending during the optimization is therefore crucial in order to achieve structurally continuous and ready-tomanufacture designs. Bi-step strategies, relying on a continuous gradient-based optimization of lamination parameters followed by a discrete stacking sequence optimization step during which blending is enforced, have been proposed in the literature. However, significant mismatch between continuous and discrete solutions were observed due to the discrepancies between both design spaces. The present paper highlights the capability of the continuous blending constraints, recently proposed by the authors, in reducing the discrepancies between discrete and continuous solutions. The paper also demonstrates that more realistic optimal continuous designs are achieved thanks to the application of the blending constraints during the aeroelastic optimization of a variable stiffness wing. Additionally, the proposed blending constraints have been applied to NASTRAN SOL 200 showing their ease of implementation in commercial software.