含脱层单向铺设层合梁非线性后屈曲分析

NONLINEAR POST-BUCKLING ANALYSIS OF UNIDIRECTIONAL LAMINATED BEAMS WITH DELAMINATION

采用四分区模型,将含脱层单向铺设复合材料层合板梁分为4个子梁,根据复合材料层合理论,考虑后屈曲路径上位于脱层界面上、下子梁之间的局部受力与变形机制,建立了子梁之间接触力与变形之间的非线性定量关系。在此基础上,结合可伸长梁的几何非线性理论,推导出了计及接触效应的各子梁的非线性后屈曲控制方程。设定简支板梁的边界条件以及脱层前沿处各子梁之间力和位移的连续性条件,通过对控制方程和定解条件归一化,采用小参数摄动法求解,并根据梁的平衡微分方程的特点,解析其通解与特解的构造,获得了含脱层单向铺设层合梁受轴向压力作用的临界屈曲荷载及后屈曲平衡路径的理论解。通过对含脱层单向铺设的复合材料层合梁进行数值分析,综合讨论了脱层长度和深度等对层合板梁的临界屈曲载荷及接触性能的影响,并将所得的理论解与ABAQUS有限元分析得到的结果进行对比,结果表明二者高度吻合。研究发现梁的屈曲模态包含宏观的整体失效模态和界面的微观屈曲模态。梁的屈曲荷载和接触性能都是其固有属性,前者受梁的几何参数和材料参数的影响较显著,而后者则主要受脱层的位置和大小影响。

The unidirectional composite beam with buried delamination is divided into four sub-regions. Using the theory for composite laminates, the nonlinear relationship between the contact force and the deflections of the sub-regionsis established. The governing equations are derived by introducing the available contact effect into the geometric nonlinear theory of extensible beams. The four sub-regions are integrated into a whole beam by employing the continuity conditions at the delamination fronts. Assuming simply supported boundary conditions, the governing equations are solved through the perturbation approach. The analytical solutions of the buckling load and the post-buckling equilibrium path for the delaminated unidirectional composite beam are obtained by examining the composition of the differential equation of the beam and by analyzing the characteristics of its general and particular solutions. The effects of delamination length and depth on the critical buckling load and contact performance of the delaminated beam are discussed by numerical analysis. The theoretical solutions are compared with the results obtained from ABAQUS finite element analysis. The results show that the two solutions are in good agreement with each other. It is found that the buckling modes of the delaminated beam includes macroscopic failure modes and micro-buckling modes at the interfaces. Both the buckling load and contact performance are inherent properties of the delaminated beam. The former is affected by the geometric parameters and material properties of the beam, while the latter is mainly affected by the depth and length of the delamination.