For a composite laminated plate, it has been found that classical laminate theory (CLT) can not always predict the final cured shape correctly and geometric nonlinearity must be considered. For composite laminated shells, experiments show that the cured shape depends on stacking sequence, radius, thickness, and size. This paper investigates the cured shape of several cross-ply composite shells. The cured shape of a cross-ply shell is generally cylindrical. A model is established to predict the cured shape. The model is based on the Rayleigh-Ritz energy method and considers geometric nonlinearity. Modeling and experiment show that, for certain stacking sequences, the generator of the cured shape may be orthogonal to the original generator, while other stacking sequences can lead to deeper or shallower cured shapes. The predictions of the model are very close to the results of FEM analysis and experiment. This model can be used as a guide in the manufacture of unsymmetric cross-ply laminates.

A robust multi-objective wing design optimization procedure using CFD is presented in this work. Instead of directly applying CFD to wing design optimization, a Kriging aerodynamic model that approximates CFD result is proposed to save computational cost. By introducing 6σ robust approach as a sub-objective function, multiobjective wing design problems can be solved with aerodynamic robustness. Non-Uniform Rational B-Spline curves (NURBS) are introduced to depict the wing geometry in design optimization process. The most important parameters of the wing geometry can then be screened by design of experiment and treated as design variables due to the local variation property of NURBS. Under this formulation, a multi-objective genetic algorithm based on nondominated sorting is employed to handle multiple flight conditions in wing design. The optimum wing geometry is selected according to trade-off among design objects on the non-dominated front. To validate the proposed approach, two robust design optimization cases are studied for ONERA-M6-Wing. It turns out that the drag coefficient is insensitive to Mach number between Ma0.8-Ma0.9 after robust optimization. The result also verifies the effectiveness of our method in boosting performance and robustness of multiple flight conditions: the lift curve slope (Ma0.3) of optimum wing and the 6σ objective function of transonic drag (Ma0.8-Ma0.9) increase by 11.9% and 25.4%, respectively. Observations in the optimization cases are concluded as follows: 1) For wing aerodynamic design problems, the multi-objective robust optimization can both improve the performance at different flight conditions and provide robustness. 2) The Kriging aerodynamic model derived from CFD result can satisfy the precision requirement of wing design. 3) Even though the optimization result is subject to the weights of the 6σ function in sub-object, the influence is not comparable to the trade-off among design objects. 4) The optimum solution obtained by proposed approach is superior to gradient based optimization method, while the computational cost is acceptable.

Tests are conducted using stitched laminates in order to calculate the unnotched failure stress and the compression after impact (CAI) strength of the stitched laminates. Unnotched laminates, laminates with a hole, and laminates with impact damage are used in the tests. All the specimens are made of two different types of layup sequence of laminates with three different stitching directions - 0, 45, and 90. In this paper, an FEM model is developed using the MSC PATRAN software to predict the CAI strength of stitched laminates. Two failure criteria are applied to the model to predict the CAI strength, the point stress criterion (PS) and the fiber breakage in damage zone (FD) criterion. The influence of the moduli retention ratio (Mr) is investigated. The predicted CAI strengths show a good agreement when compared with the test results.

In order to improve airfoil performance under different flight conditions and to make the performance insensitive to off-design condition at the same time, a multi-objective optimization approach considering robust design has been developed and applied to airfoil design. Non-uniform rational B-spline (NURBS) representation is adopted in airfoil design process, control points and related weights around airfoil are used as design variables. Two airfoil representation cases show that the NURBS method can get airfoil geometry with max geometry error less than 0.0019. By using six-sigma robust approach in multi-objective airfoil design, each sub-objective function of the problem has robustness property. By adopting multi-objective genetic algorithm that is based on non-dominated sorting, a set of non-dominated airfoil solutions with robustness can be obtained in the design. The optimum robust airfoil can be traded off and selected in these non-dominated solutions by design tendency. By using the above methods, a multi-objective robust optimization was conducted for NASA SC0712 airfoil. After performing robust airfoil optimization, the mean value of drag coefficient at Ma0.7−0.8 and the mean value of lift coefficient at post stall regime (Ma0.3) have been improved by 12.2% and 25.4%. By comparing the aerodynamic force coefficients of optimization result, it shows that: different from single robust airfoil design which just improves the property of drag divergence at Ma0.7−0.8, multi-objective robust design can improve both the drag divergence property at Ma0.7− 0.8 and stall property at low speed. The design cases show that the multi-objective robust design method makes the airfoil performance robust under different off-design conditions. robust design, multi-objective optimization, NURBS, Pareto front, airfoil Citation:Liang Y, Cheng X Q, Li Z N, et al. Multi-objective robust airfoil optimization based on non-uniform rational B-spline (NURBS) representation. Sci

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