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In order to eliminate the influence of the arbitrary initial state on the systems, open-loop and open-close-loop PDα-type fractional-order iterative learning control (FOILC) algorithms with initial state learning are proposed for a class of fractional-order linear continuous-time systems with an arbitrary initial state. In the sense of Lebesgue-p norm, the sufficient conditions for the convergence of PDα-type algorithms are disturbed in the iteration domain by taking advantage of the generalized Young inequality of convolution integral. The results demonstrate that under these novel algorithms, the convergences of the tracking error are can be guaranteed. Numerical simulations support the effectiveness and correctness of the proposed algorithms.

The high-order methods is difficultly applied in various elements. The development of a 3D solver by using the spectral difference method of unstructured grids via mixed elements is presented. A mixed tri-prism and tetrahedral grid is firstly refined using one-level h-refinement to generate a hexahedral grid while keeping the curvature of wall boundaries. The SD method designed for hexahedral elements can subsequently be applied for refining the unstructured grid. Through a series of numerical tests, the present method is high-order accurate for both inviscid and viscous flows is demonstrated; the results obtained for inviscid and viscous compressible flows compare well with other published results.

For the parallel solution of structural finite element problem with non-matching multi-domains, a nonmatched finite element tearing and interconnectiong (FETI) parallel algorithm is proposed based on L-FETI method by introducing the frame node force and modifying the frame displacement compatibility condition and the load balance condition. Based on the radial basis functions (RBF) interpolation technique, the data transfer of internal force and displacement between the neighboring subdomains has a unified matrix format and is easy to program by introducing a local coordinate system into the non-matching interfaces. Taking the finite element model for plate bending problem with four subdomains as an example, two kinds of multi-domains models, matching and non-matching meshes, are constructed respectively. The numerical results show that the out-of-plane deflection of the same nodes on the domain decomposition frame is in a good agreement, which shows that the present method is reasonable and effective for solving the parallel non-matching multi-domains model.

Based on the theory of linear elastic fracture mechanics, the relationships between material constants c3, c4 required in Abaqus and constants C, m in Paris formula are derived. Then extended finite element method (XFEM) of Abaqus software is used to is used to predict the crack propagation path and life of the plate with center inclined through crack and typical stiffened wing spar with initial crack under the constant amplitude fatigue load. The results show that the predicted crack propagation path is in good agreement with the experimental results, and the crack propagation life error is less than 6.3%. It also shows that this method can accurately predict the fatigue crack growth path and life of two-dimensional and three-dimensional complex structures under constant amplitude loads. This study can provide an effective way for damage tolerance analysis of structures and has certain engineering application value.

Firstly, the problem of group-air grouping is analyzed to introduce the aircraft attribute grouping model and aircraft fuel consumption grouping model. Then, SATC-ALO optimized by Chaos optimization algorithm and Tournament Selection strategy and SOM neural network are used to solve the formation grouping model. Finally, comparative experiments of similarity calculation method and formation grouping method were performed with 50 groups of data. The experimental results show that hybrid method is superior to Euclidean distance method. SATC-ALO algorithm has the highest grouping accuracyand meets the real-time requirements. However, the number of groups needs to be specified in advance. The accuracy of SOM neural network grouping is slightly lower than SATC-ALO algorithm, but the grouping time is lower than SATC-ALO algorithm, and there is no need to specify the number of groups. Both SOM neural network and SATC-ALO algorithm can perfectly solve the problem of group-air grouping and have practical application value.

This paper focuses on the studying on some flow problems of nonlinear based on the Element Free Galerkin method. First the Navier-Stokes equation is discretized with the Galerkin method. The inertial term in the equation is discretized with the method of the speed term and direct deduction respectively. And the penalty function method is used to deal with the pressure and the essential boundary condition in the equation, and the discretization of two-dimensional N-S equation based on the EFG method is established. Then the flow problem of stationary nonlinear is studied. The flow problem of water in the rectangular domain squeezed by the two plates distributed above and below the calculated domain is studied with the method of EFG. The accuracy of the direct linear alternating interation method is shown by contrast with the analytical solution. Then the flow problem of unsteady nonlinear is studied. The θ-weighted method is used to discrete the time term of the N-S equation and the unsteady nonlinear solution matrix of EFG is established. The flow problem of flow around the square column is studied with the method of EFG and the flows under a series of low Reynolds are stimulated.