Lay-up Optimisation of Fibre Metal Laminates: Development of a Design Methodology for Wing Structures

Abstract

The lower wing skin is one of the primary structures of an aircraft. To further improve the fatigue and damage tolerance (F&DT) performance of the lower wing, fibre metal laminates (FML) are proposed as a new material solution. FML consist of thin metal layers bonded with layers of fibre composites. This concept has potentially a large design freedom and its layups could be tailored for specific applications by varying the number, thickness, orientation, and material type of the metal and fibre constituents. This study has been performed to explore the possibilities of lay-up optimisation for FML and to apply the concept of FML to a wing structure. This research aimed to develop a design optimisation methodology for FML that satisfies F&DT criteria. The optimisation methodology should reveal the contribution of individual criteria to the obtained solutions. Furthermore, the method will be used to design a lower wing skin consisting of FML where F&DT and additional compatibility criteria are met. As a result, an analytical model is developed that comprises all the functionality to design a wing structure consisting of FML lower panels and aluminium upper panels. The lay-up solutions are obtained by evaluating the laminates for fatigue crack initiation (FCI), fatigue crack propagation (FCP) and residual strength (RS). These properties are obtained by means of prediction methods, which are implemented into a genetic algorithm optimisation environment. The scientific contribution is delivered by developing a method to reverse the prediction methods to find the lay-ups that satisfy the required property instead of determining the properties of a given lay-up. The lay-up solutions are defined by three parameters: thickness of metal layers, number of metal layers and the grade of a laminate. The amount and orientation of the fibre plies are defined in this grade. With the optimisation method, the lowest weight solution in the design space is determined by generating solutions based on crossover and mutation operators and ranking the satisfying solutions based on their weight. The method considers the optimisation of flat-plates and wing cross-sections. For cross-section optimisation, only the numbers of metal layers along the cross-section are optimised to comply with manufacturing constraints. Additionally, a thickness step constraint is introduced to prevent stress concentrations between elements and to force a distributed thickness along the cross-section. As a final step, the cross-section optimisation is linked to a wing design module that is now capable of dimensioning an aircraft wing structure with the lower panel consisting of FML and the upper panel of aluminium. The thickness of the aluminium skin is defined as variable for the upper skin and evaluated using buckling criteria. As output, a complete optimised cross-section is obtained. To further improve the computation time and to simply the optimisation routine, a regression analysis is performed on the prediction methods for FCI, FCP and RS to obtain approximations for these methods. These approximate functions replace the prediction methods with high correlation and with assurance that the same solutions are obtained as output. The functions are replaceable with other functions representing different criteria to have a generic design method. The influence of optimisation settings, approximations and different design criteria are extensively investigated. The output of the design method depends on the accuracy of the prediction methods and the accuracy of the performed regression, because a small difference in prediction influences the obtained optimal and near optimal design solutions. Further, genetic algorithm proved to be a robust method when optimising single elements or flat-plates when the settings are well-defined. In case of cross-section optimisation, due to the increasing size of the design space the method proved to be inefficient sometimes with the case that once in a while satisfying solutions were not obtained or were stuck at local minima. This problem is solved by defining an initial input to the procedure and increasing or decreasing the upper and lower boundary of the design space. A convergence loop for genetic algorithm is implemented to automate this process in this design method. In conclusion, the method has the ability to compare and evaluate material configurations, to investigate the influence of various design criteria on the lay-up solutions and to optimise the wing material for minimised weight for different sets of load cases and wing geometries.