【作者】 杨金花；

【导师】 傅衣铭；

【作者基本信息】 湖南大学 ， 固体力学， 2006， 博士

【摘要】 脱层是复合材料层合结构中常见的一种损伤。脱层的出现及其进一步扩展可降低结构的强度和刚度,从而改变结构的静、动力学性能。本论文以具环向贯穿脱层的纤维增强复合材料层合圆柱壳为研究对象,系统地探讨了脱层壳的屈曲、后屈曲、动力稳定性、非线性自由振动、非线性动力响应及脱层扩展等问题。本论文的研究成果具有重要的学术价值,也具有重要的工程应用意义。其主要研究工作如下。基于Donnell薄壳理论和相邻平衡准则,建立了含环向贯穿脱层复合材料层合圆柱壳屈曲问题的解析分析模型,探求了一种有效的解析求解方法。算例中,给出了脱层壳的三种不同屈曲模态,具体讨论了脱层大小、深度、位置以及复合材料纤维铺层方式等因素对脱层圆柱壳屈曲载荷的影响,并与有关文献的结果进行了比较。根据非线性弹性理论,建立了用应力函数和挠度表示的具脱层正交铺设圆柱壳的后屈曲控制方程及相应的定解条件,且应用Koiter初始后屈曲理论并借助小参数摄动法,寻求了控制方程的渐近解。算例中,给出了挠度随轴向载荷变化的响应曲线和挠度随轴向坐标变化的后屈曲变形曲线。基于瑞利-里兹方法,建立了含环向贯穿脱层复合材料层合圆柱壳的动力稳定性分析模型。首先,引入Heaviside单位阶跃函数,假定一种适合于脱层壳动力问题的位移模式,推导出脱层壳的总能量方程;然后,将位移函数近似地表示为双三角级数的形式,且施加瑞利-里兹法,得到用于圆柱壳稳定性分析的Mathieu型参数振动方程;接着,采用Bolotin方法对其进行求解。算例中,讨论了脱层大小、脱层深度、铺设材料性质及外激励的大小等对复合材料脱层圆柱壳固有频率及主要动力不稳定区域的影响。在考虑几何非线性的情况下,对脱层圆柱壳的非线性自由振动问题进行了研究。通过对脱层壳的能量分析并应用瑞利-里兹法后,得到系统关于时间函数的非线性控制微分方程,接着,采用谐波平衡法对控制方程进行求解。算例中,讨论了不同脱层长度和深度等因素对轴对称脱层圆柱壳振动模态及非线性幅频响应曲线的影响。基于非线性弹性壳理论,建立了考虑脱层间接触效应的具脱层轴对称层合圆柱壳的非线性动力响应分析模型。首先,将脱层的上、下部分视为两串连弹簧,来计算接触力;然后,对系统的横向运动控制方程进行修正,从而有效地避免了脱层之间的相互贯穿。且综合利用有限差分法、Newton-Newmark法和迭代法对更多还原

【Abstract】 Delamination is a kind of common damage in composite laminated structures. The occurrence of delaminations and their further growth can weaken the stiffness and strength of structure, which will change the structural static and dynamic characteristics. In this dissertation, considering composite laminated cylindrical shells with throughout circumference delamination as the subjects investigated, the static buckling, postbuckling, dynamic stability, nonlinear free vibration, nonlinear dynamic response, as well as the delamination growth of composite laminated cylindrical shells are systematically studied. The research results have an important meaning not only in the academic research but also in the practical engineering. The main research contents are given as follows.Based on the Donnell thin shell theory and the adjacent equilibrium criterion, an analytic model for buckling problems of composite laminated cylindrical shells with throughout circumference delamination is established. And a valid analytic method is sought during solving process. In numerical calculations, three different buckling modals for delaminated shells are presented. Then, the influences of delamination lengths, depths and positions as well as laminate stacking sequences on the buckling loads of delaminated cylindrical shells are discussed in detail. The present results are compared with available data.According to the nonlinear elastic theory, the postbuckling governing equations of delaminated cross-ply cylindrical shells expressed by stress function and deflection are founded and the corresponding boundary conditions, the continuous conditions of displacements and the equilibrium conditions of forces are determined. By employing the Koiter theory and perturbation technique, the asymptotic solutions of governing equations are obtained subsequently. In numerical calculations, the load-deflection curves and the postbuckling deformation curves for delaminated cylindrical shells under axial compression are presented.Based on Rayleigh-Ritz method, an analytic model for dynamic stability of composite laminated cylindrical shells with throughout circumference delamination is established. Firstly, introducing the Heaviside unit step functions and supposing a displacement mode fitting for dynamic problem of delaminated shell, the total energy equation of delaminated cylindrical shell is derived. Then, using double trigonometric series to approximate displacement functions and applying Rayleigh-Ritz method, the Mathieu-type parametric vibrating equations of the system are obtained. And the更多还原