【作者】 陈得良；

【导师】 傅衣铭；

【作者基本信息】 湖南大学 ， 固体力学， 2009， 博士

【摘要】 复合材料层合结构具有比强度高、比刚度大、抗疲劳和抗振性能好、热稳定性优良、材料性能可设计等一系列优点,因此,其在航空航天、汽车制造和化工装备等领域得到了日益广泛的应用。然而,由于复合材料制备工艺必然存在的不足和缺陷以及使用过程中不可避免的外来低能量冲击,使得复合材料层合结构极易产生脱层现象,脱层的存在和扩展将会使得结构的刚度和强度降低,非线性静、动力学行为发生改变,承载寿命降低。本文以具任意位置脱层复合材料层合圆板为研究对象,采用分区模型,基于复合材料力学、板壳理论、非线性力学的基础理论,建立脱层层合圆板的非线性静、动力学控制方程和定解条件,研究具脱层层合圆板的屈曲、后屈曲、脱层扩展以及非线性振动与非线性动力响应等问题,深入讨论了脱层尺寸、脱层位置以及材料参数等因素对脱层圆板非线性动、静力学行为的影响。本文的主要研究内容如下。基于Von-Kármán理论,采用三分区模型,应用Reissner变分原理,建立了考虑横向剪切变形效应的具脱层轴对称层合圆板的屈曲与后屈曲分析模型,并应用正交配点法对上述问题进行求解。详细讨论了脱层深度、脱层半径及铺层材料参数等对脱层圆板屈曲及后屈曲特性影响,并与有关文献的结果进行了比较。基于三分区模型和Von-Kármán理论,建立了考虑横向剪切变形的含椭圆脱层层合圆板的屈曲和后屈曲控制方程,采用改进的正交配点法,即在圆板的径向上采用Chebyshev多项式零点和在圆板的环向上采用等分角度交点作为配置点,对上述问题进行求解。讨论了椭圆脱层形状、脱层深度、铺设材料等因素对脱层层合圆板屈曲及后屈曲性能的影响。在考虑几何非线性的情况下,对具脱层轴对称层合圆板的非线性自由振动问题进行了研究。通过对未知变量在空间上采用Bessel函数离散,并应用Galerkin方法,得到了仅含时间函数的系统的非线性自由振动控制方程,最后采用谐波平衡法对此控制方程进行求解。讨论了脱层半径、脱层深度和横向剪切效应等因素对正交对称铺设轴对称层合圆板非线性幅频响应的影响。建立了在轴向压力和横向荷载共同作用下,考虑横向剪切变形效应和脱层界面处的接触效应的具任意脱层的正交对称铺设轴对称层合圆板的非线性动力响应分析模型。分析中,通过引入Heaviside阶跃函数将脱层上下两部分视为两串联的弹性体来计算接触力,对系统的运动控制方程进行了修正,从而有效地避免了脱层界面物理上不应出现的相互贯穿现象,然后,应用正交配点法和平均加速度法,求解了具脱层正交对称铺设轴对称层合圆板的非线性动力响应,数值算例表明层间接触效应对脱层结构的非线性动力学行为影响显著。采用四分区模型,基于可动边界变分原理,分别对横向荷载和径向面内压缩荷载作用下的具任意脱层轴对称层合圆板的脱层扩展行为进行了研究。分析中考虑了横向剪切变形效应和脱层界面处的接触效应,应用Griffith准则,导出了层合圆板脱层前缘各点处总能量释放率及其各型分量的表达式,最后,采用正交配点法对脱层前沿处的能量释放率进行了数值计算。讨论了脱层圆板在横向荷载和径向面内压缩荷载作用下,脱层半径、脱层深度、铺层材料等因素对层合圆板脱层扩展的影响,获得了一些有意义的结论。更多还原

【Abstract】 Composite laminates have been widely used in aerospace, automobile and chemical equipment, due to their high strength-to-weight and high stiffness-to-weight, favourable fatigue and vibration resistance, heat stability and designability of material performance. On the other hand, delamination inevitably, delaminated damage arises from manufacturing processes and hit of runway debris, for instance, low energy shock in assembling procedures. The existance of delamination and their further growth will drastically reduce the stiffness and residual strength and life of delaminated plates as well as their their dynamics characteristics. In the dissertation, the composite laminate circular plates with delamination are investigated. Employing the partition region model and appling the plate theory and nonlinear mechanics ,the nonlinear differential governing equations of delaminated circular plate are built. The static buckling , postbuckling, nonlinear free vibration, nonlinear dynamic response ,as well as the delamination growth of composite laminated circular plates with delamination are systematically studied. The effects of delamination size, delamination depth and ply materials on the static and dynamic characteristics of delaminated circular plates are investigated. The main research contents are given as follows.Based on the Von-Kármán plate theory, considering the effect of transverse shear deformation, the buckling and postbuckling model of axisymmetric laminated circular plate with delamination are studied by applying the Reissner variational principle. The orthogonal point collocation method is adopted tosolve the system governing equations. Then ,the influences of delamination depth and radius as well as ply material character on the buckling and postbuckling are discussed in detail. The numerical results are compared with available data.According to the Von-Kármán plate theory and the three dissociate regions model, considering the effect of transverse shear deformation, the post and postbuckling governing equations for the axisymmetric laminated cicular plates with elliptic delamination are derived. By using the modified orthogonal point collocation method, that the crossing points of zero points of Chebyshev polynomial on circular radius and circumferential sectrix curve are taken as collocation points, the governing equations are solved. Then, the effects of elliptical delamination size, delamination depth and material properties on buckling and post-buckling of the laminated circular plates are discussed.Under consideration of geometric nonlinearity, the nonlinear vibration of ortho-symmetric plies axisymmetric circular plate with delamination are investigated. Adopting Bessel function on the space, the dimensionless differential motion equations are got with Galerkin method. The harmonic Balance method is used to solve the equations. Then, amplitude-frequency curves of axisymmetric laminated circular plate in different radius and various depth of delamination sa well as the transverse shear deformation are presentedBased on the Von-Kármán plate theory, employing the three region model, and considering the effect of transverse shear as well as contact between the delaminated surfaces, the nonlinear governing equations of delaminated circular plate with ortho-symmetric plies are obstained. Firstly ,the contact force is derived by regarding the sub-laminate and super-laminate of delamination as two springs connected in serials by Heaviside jumping function. Then, the governing equation of transverse motion is modified by the contact force. The dynamic responses of axisymmetric delaminated circular plate are analyzed by using the orthogonal point collocation method, and the effect of contact on the nonlinear dynamic response of delaminated plates is discussed.By using movable boundary variational principle, and the four dissociated region model, considering the transverse shear deformation and contact effect, the delamination growth of composites laminated circular plate subjected to transverse and radial load is studied repectively. At the same time, according to the Griffith criterion, the formulas of total energy release rate and its individual mode components along the delamination front are obtained. In calculation, the influences of delamination radius and depths, and material properties on energy release rate and its individual components under radial and transverse loads are discussed respectively.更多还原