Variational Asymptotic Equivalent Model And Mechanical Properties Analysis Of Woven Composite Plates

The woven composite plate is a kind of light and high strength structure,which is composed of interlaced fiber bundle and matrix.It has excellent mechanical properties and is widely used in aerospace,national defense industry,automobile,architecture and other fields.At present,the research on woven composite plate mainly focuses on tensile,bending,compression properties,damage,impact resistance and so on.However,due to the complex structure of woven composites,it is a great challenge to establish accurate numerical model of woven composite plate.In this paper,the equivalent model of woven composite plate is established based on the variational asymptotic method,which can greatly reduce the calculation time and the cost on the premise of sufficient accuracy.On this basis,the effects of fiber bundle spacing,width,thickness and ply direction on the mechanical properties of the woven composite plate are investigated.The main work and research results are as follows:（1）Based on the variational asymptotic method,the strain energy of the woven plate is derived from the energy functional,and the representative structural element（RSE）is analyzed by using variational asymptotic method.Based on the equivalent stiffness matrix extracted from the energy functional analysis,a two-dimensional equivalent model（2D-EPM）is established.The three-dimensional woven plate can be transformed into a two-dimensional plate/shell for analysis.According to the global macro response of 2D-EPM,the distribution of local stress,strain and displacement field within the unit cell was predicted by recovery relationship.（2）The accuracy and efficiency of 2D-EPM under different boundary and loading conditions are verified by the numerical example of plain woven plate.The static and dynamic analysis errors between 2D-EPM and three-dimensional finite element model（3D-FEM）are in the range of 0.83%-7.32%,but the computational efficiency is improved about 10 times.The variation trend of local stress and strain along the specified path in the Representative Structural Element（RSE）is consistent with the local distribution extracted by the three-dimensional model.The spacing and width of fiber bundles have a great influence on A₁₁and D₁₁,and the number of layers directly affects the overall stiffness of plain woven plate.With the increase of fiber bundle angle,the natural frequency of plain weave board gradually increases.The influence of fiber bundle width on the natural frequency of plain woven plate is opposite.（3）The accuracy and efficiency of 2D-EPM under different boundary and loading conditions are verified by the example of 3D woven plate with more complex cell structure.compared with 3D-FEM,the static and dynamic errors of the 2D-EPM are in the range of 0.12%-8.67%,the computational efficiency is improved about 20 times.The equivalent stiffness of 3D woven plate decreases with the increase of envelope width,while the influence of warp（weft）width on the equivalent stiffness is relatively small,mainly affecting A₁₁and D₁₁.The results show that the equivalent stiffness of plain woven plate is larger and the displacement of plain woven plate is smaller under the condition of equal size and equal volume fraction of fiber bundle,while the overall performance and torsion resistance of 3D woven plate are better when the layers are fixed by envelope lines.