反对称铺设复合材料层合板非线性后屈曲分析

Nonlinear post-buckling analysis of composite laminates with antisymmetric angle-ply

基于层合板壳理论,考虑反对称铺设层合板的拉弯耦合效应和后屈曲过程中的非线性几何变形,推导了由应力函数和挠度表示的复合材料层合板的后屈曲控制方程。引入无量纲参数对控制方程和边界条件进行无量纲化,以消除材料参数及几何尺寸对分析结果的影响。采用摄动法将无量纲的非线性控制方程及边界条件展开成一系列非齐次线性摄动方程组,分析各阶摄动方程的通解与特解的构造,并逐次求解,建立了反对称铺设复合材料层合板受单向均布压力作用的临界屈曲荷载及后屈曲平衡路径的理论解。进而运用ABAQUS软件对复合材料层合板在面内压缩载荷作用下的屈曲和后屈曲进行有限元分析,结果表明理论解与ABAQUS结果十分接近,验证了理论解的正确性。在此基础上进一步讨论了铺设角度、铺设层数和拉弯耦合效应等对层合板后屈曲性能的影响。研究发现层合板的屈曲载荷受铺设角度与层数的影响较为显著,而拉弯耦合效应使板的屈后强度大大降低。

Based on the theory for laminated plates and shells,governing equations for post-buckling of anti-symmetrical laminated composite plates are derived in terms of stress function and transverse deflection by considering the tension-bending coupling effect and the von-Kaman nonlinear geometric relation.By introducing the non-dimensional parameters,the nonlinear governing equations and the boundary conditions are nondimensionalized to eliminate the influence of the material properties and the geometric parameters.Perturbation approach is applied to expand the governing equations as well as the boundary conditions into a series equations of a small perturbation parameter.Analytical solutions of the critical buckling load and the post-buckling equilibrium path for anti-symmetric cross plied composite laminates with simply supported boundary conditions are obtained by examining the characteristics of the general and particular solutions.After that,the buckling and post-buckling of the composite laminates with antisymmetric angle-ply under in-plane compressive load are analyzed using ABAQUS software,and the results from ABAQUS are compared with the theoretical solutions.It shows that the two results are in very good agreement which verifies the accuracy and effectiveness of the proposed analytical approach.Using the established solutions,the influences of the orientation angle of the composite ply,the number of the composite ply and tension-bending coupling effect on the post-buckling performance of the laminate are discussed.It is found that the critical buckling load of the laminate plate is significantly affected by the orientation angle and the tension-bending coupling effect will greatly reduce the post-buckling load carry capability of the laminates.