Explainable Artificial Intelligence to Investigate the Contribution of Design Variables to the Static Characteristics of Bistable Composite Laminates.

Material properties, geometrical dimensions, and environmental conditions can greatly influence the characteristics of bistable composite laminates. In the current work, to understand how each input feature contributes to the curvatures of the stable equilibrium shapes of bistable laminates and the snap-through force to change these configurations, the correlation between these inputs and outputs is studied using a novel explainable artificial intelligence (XAI) approach called SHapley Additive exPlanations (SHAP). SHAP is employed to explain the contribution and importance of the features influencing the curvatures and the snap-through force since XAI models change the data into a form that is more convenient for users to understand and interpret. The principle of minimum energy and the Rayleigh-Ritz method is applied to obtain the responses of the bistable laminates used as the input datasets in SHAP. SHAP effectively evaluates the importance of the input variables to the parameters. The results show that the transverse thermal expansion coefficient and moisture variation have the most impact on the model's output for the transverse curvatures and snap-through force. The eXtreme Gradient Boosting (XGBoost) and Finite Element (FM) methods are also employed to identify the feature importance and validate the theoretical approach, respectively.

Design for bird strike crashworthiness using a building block approach applied to the Flying-V aircraft.

The Flying-V aircraft concept promises better fuel-burn performance over conventional tube-and-wing configurations, integrating the passenger cabin and cargo volume into the lifting surface. However, the wing-fuselage and cockpit windows of the Flying-V are exposed to the flight direction, posing a new challenge to the design and certification of structures in terms of bird strikes. This study is a first step towards understanding the dynamic load path and contribution of each structural element on the bird strike resistance of the Flying-V leading-edge structures. The objective is to propose a building block approach to design the Flying-V's leading edge bird strike crashworthiness that complies with the EASA's certification CS25.631 using a 4lb bird impacted at a sea level cruising speed of 70 m/s. An additional requirement by the authors is to keep the structure within the elastic deformation during the impact of a 4lb bird to avoid the need for repairs in the Flying-V fuselage. Plasticity generated in the structure is regarded as damage and is used as a comparative parameter. At the highest building block level, a sensitivity analysis is performed to identify the effect of the thickness of each structural element on the plasticity and weight of the leading-edge structures. The trends are used to modify the baseline design and achieve a reduction of 80% of the plastic energy. The critical case of a 133 m/s impact of a 4lb bird at the cruise altitude of 37000 ft is also evaluated, and the results show penetration.

Lightweight Design of Variable-Stiffness Cylinders with Reduced Imperfection Sensitivity Enabled by Continuous Tow Shearing and Machine Learning.

The present study investigates how to apply continuous tow shearing (CTS) in a manufacturable design parameterization to obtain reduced imperfection sensitivity in lightweight, cylindrical shell designs. The asymptotic nonlinear method developed by Koiter is applied to predict the post-buckled stiffness, whose index is constrained to be positive in the optimal design, together with a minimum design load. The performance of three machine learning methods, namely, Support Vector Machine, Kriging, and Random Forest, are compared as drivers to the optimization towards lightweight designs. The new methodology consists of contributions in the areas of problem modeling, the selection of machine learning strategies, and an optimization formulation that results in optimal designs around the compromise frontier between mass and stiffness. The proposed ML-based framework proved to be able to solve the inverse problem for which a target design load is given as input, returning as output lightweight designs with reduced imperfection sensitivity. The results obtained are compatible with the existing literature where hoop-oriented reinforcements were added to obtain reduced imperfection sensitivity in composite cylinders.

Developing Equations for Free Vibration Parameters of Bistable Composite Plates Using Multi-Objective Genetic Programming.

For the last three decades, bistable composite laminates have gained publicity because of their outstanding features, including having two stable shapes and the ability to change these states. A common challenge regarding the analysis of these structures is the high computational cost of existing analytical methods to estimate their natural frequencies. In the current paper, a new methodology combining the Finite Element Method (FEM) and Multi-Objective Genetic Programming (MOGP) is proposed for the analysis of bistable composite structures, leading to some analytical relations derived to obtain the modal parameters of the shells. To achieve this aim, the data extracted from FEM, consisting of the ratio of the length to width (a/b) and the thickness (t) of the laminate, is split into Train and Validation, and Test, subsets. The former is used in MOGP, and four formulas are proposed for the prediction of the free vibration parameters of bistable laminates. The formulas are checked against the Test subset, and the statistical indices are calculated. An excellent performance is observed for all GP formulas, which indicates the reliability and accuracy of the predictions of these models. Parametric studies and sensitivity analyses are conducted to interpret the trend of input parameters in the GP models and the level of sensitivity of each natural frequency formula to the input parameters. These explicit mathematical expressions can be extended to the other bistable laminates to obtain their natural frequencies on the basis of their geometrical dimensions. The results are validated against the experimental data and verified against FEM outcomes.

Bondline Thickness Effects on Damage Tolerance of Adhesive Joints Subjected to Localized Impact Damages: Application to Leading Edge of Wind Turbine Blades.

The leading edges of wind turbine blades are adhesively bonded composite sections that are susceptible to impact loads during offshore installation. The impact loads can cause localized damages at the leading edges that necessitate damage tolerance assessment. However, owing to the complex material combinations together with varying bondline thicknesses along the leading edges, damage tolerance investigation of blades at full scale is challenging and costly. In the current paper, we design a coupon scale test procedure for investigating bondline thickness effects on damage tolerance of joints after being subjected to localized impact damages. Joints with bondline thicknesses (0.6 mm, 1.6 mm, and 2.6 mm) are subjected to varying level of impact energies (5 J, 10 J, and 15 J), and the dominant failure modes are identified together with analysis of impact kinematics. The damaged joints are further tested under tensile lap shear and their failure loads are compared to the intact values. The results show that for a given impact energy, the largest damage area was obtained for the thickest joint. In addition, the joints with the thinnest bondline thicknesses displayed the highest failure loads post impact, and therefore the greatest damage tolerance. For some of the thin joints, mechanical interlocking effects at the bondline interface increased the failure load of the joints by 20%. All in all, the coupon scale tests indicate no significant reduction in failure loads due to impact, hence contributing to the question of acceptable localized damage, i.e., damage tolerance with respect to static strength of the whole blade.