New Analysis Methods Of Dynamic Characteristics Of Laminated And Braided Composites

Firstly, the analysis methods of the inherent characteristics and dynamic responses of composite laminated plates and beams are briefly presented. Then the developments of predicting mechanical properties of 3D braided composites are reviewed in detail, the geometric models of unit cell of 3D braided composites are classified. Based on this, the following jobs are mainly included in this dissertation:(1) Based on the semi-inverse method of elasticity, the 2D composite beams are considered as the plane stress problem, and in this model the thickness effect are taken into consideration. The thickness effect means that the transverse deflection varies in thick direction. According to this idea, the formulations of analytic inherent frequencies and modal functions of laminated beams with simply-supported ends are derived, which can satisfy the stress and displacement boundary conditions as well as the interlaminar continuous conditions. The analytic solutions of inherent frequencies and modal functions of laminated beams are obtained, which can serve as a basis for evaluating other approximate analysis methods of inherent characteristics of laminated beams. The results obtained in this dissertation are compared with those of other typical theories, and the usages of these approximate theories are discussed briefly.(2) Using the obtained inherent frequencies and modal functions, the impact responses of laminated beam with simply-supported ends are deduced using IMSM (Indirect Modal Superposition Method). It can be concluded from comparison of the obtained results of impact problems with those of Timoshenko beam that Timoshenko beam theory is precise enough to analyze long beams, but the case is not so for short beams, so the thickness effects must be taken into account in analyzing the impact responses of short beams. From the numerical results of laminated beams, it's shown that the internal stress and strain states are complicated, which are closely related to the material properties and ply sequences of each layer, therefore the intricate changes of the interlaminar stress out of plane may be one of the main reasons of delamination. In order to study the internal dynamic responses of laminated beams, it's not enough to consider the shear and warping deformation only, usually, if the thickness effects are not taken into account, the internal stress states can not be analyzed precisely.(3) After summing up the existed works, a new geometric model of unit cell of 3D 4-step braided composites is proposed, in which the 3D geometric configuration of the yarn and the mutual effects of the yarn and the matrix are both reflected and the corresponding finite element model of the unit cell can be built easily. In the finite element model, the yarn and matrix are meshed by using solid hexahedral elements with eight nodes simultaneously. As a result, not only can the complicated stress be reflected, but one material in one element and the displacement continuity of the yarn/matrix interface are satisfied. Moreover, through controlling the mesh density, the displacement continuity of interior cells, interior and boundary cells, interior and corner cells can also be satisfied. Using this finite element model, the material macroscopic elastic constants of four different braiding angles are obtained, and the comparison of the present result with that of other theoretical and experimental methods shows that the proposed geometric model and finite element model are comparatively reasonable.(4) On the basis of energy principle and eigenvector expansions, the eigen-elements of the unit cells of 3D textile composites (3D orthogonal woven composites and 3D 4-step braided composites) are constructed, and the eigen-elements can relate the microstructure and macrostructure of the composites. After comparing the elements of the eign-element stiffness matrix to thoes of the stiffness matrix obtained using the conventional homogenization method, it can be demonstrated that the eigen-element stiffness matrix can reflect the material and geometric configuration in detail, while the stiffness matrix obtained by the conventional homogenization method can not. In order to evaluate the eigen-element method, the inherent frequencies of 3D orthogonal woven composites and 3D 4-step braided composites are computed by the eigen-element method,conventional homogenization method and ordinary finite element method respectively. After comparing the results by different methods, it is found that the eigen-element method is more precise than the conventional homogenization method with the same number of elements, and the amount of computational work reduces greatly compared with the ordinary finite element method with the same precision. The impact results of the cantilever beam show that the eigen-element method can also deal with the concentrated mass and springs.(5) Finally, the wave propagation characteristics of rod made of non-uniform materials are studied, especially, the wave propagation characteristics on the two material interfaces, and the energy distribution characteristics of the rod are obtained, which can serve as a guide to the analysis of the wave propagation properties of textile composites. In order to further validate the eigen-element method, the expressions of the impact responses of two kinds of textile composites (3D orthogonal woven composites and 3D 4-step braided composites) with two kinds of boundary conditions are obtained using DMSM (Direct Modal Superposition Method), the wave propagation characteristics of textile composite beams are investigated preliminarily. The comparisons of the results by eigen-element method with those of the conventional homogenization method and ordinary finite element method reveal that the eigen-element method can reflect the wave propagation characteristics of the structures with non-uniform materials, and the computational precision of eigen-element method is better than that of the conventional homogenization method.