复合材料圆柱壳结构动响应及屈曲
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摘要
本文的研究工作围绕着复合材料加筋圆柱壳自由振动、非线性冲击响应、屈曲及后屈曲、以及脱层屈曲这些研究内容展开。通过理论分析、数值计算和试验研究对上述内容进行了系统的研究,并分析了各种参数如壳体参数、加筋结构参数、脱层参数对复合材料结构的影响,为复合材料加筋圆柱壳的设计提供了合适的分析方法和理论依据。本文的主要工作有如下几个方面:
首先,论文对复合材料加筋圆柱壳的自由振动,在轴向载荷作用下的非线性动力响应,以及在轴向压缩作用下的屈曲和后屈曲问题作了全面回顾和评述,特别对含有脱层损伤的复合材料圆柱壳在轴向载荷下的屈曲问题的研究进展以及这类结构的试验研究进行了综述和评论。
第二章对两端简支纵横加筋层合圆柱壳的自由振动进行了理论研究。根据Love’s壳体理论以及Rayleigh-Ritz能量法,导出结构的动力控制方程,求解了复合材料加筋圆柱壳的自由振动频率。讨论了壳体和加筋结构参数以及静水压力的变化对圆柱壳自由振动频率的影响。
第三章采用半解析方法,建立了简化离散的复合材料环向加筋-圆柱壳模型,求解了环向加筋圆柱壳在轴向冲击载荷作用下的动力响应问题。分析中考虑了加筋壳的大变形、剪切变形、转动惯量、以及加筋肋骨的拉伸,弯曲,剪切变形的影响,运用Hamilton变分原理导出了层合加筋圆柱壳的非线性的运动控制方程,运用伽辽金法对控制方程进行离散,采用数值方法求解,通过算例分析讨论了环向加筋数目及几何参数,壳体铺层角度、材料参数、铺层方式、铺层层数以及冲击载荷形式等对动力响应的影响。
第四章基于一阶剪切理论推导了复合材料加筋圆柱壳在轴向压力作用下的广义Donnell型方程。采用摄动技术,给出了全局渐近摄动解,运用奇异摄动技术详细分析了该圆柱壳端部边界层方程和奇异摄动解。求解了角铺层及对称正交铺层圆柱壳在轴压下的屈曲载荷和后屈曲路径。揭示了复合加筋圆柱壳结构的后屈曲过程中模态跳跃、屈曲多次分支等现象。
第五章研究对象是含有环向贯穿脱层复合材料圆柱壳。建立了屈曲分析模型,基于一阶剪切理论得到了脱层壳屈曲微分方程以及相应的边界条件、位移连续条件和力平衡条件.然后采用分离变量法及状态空间法对方程求解,讨论了壳体参数、脱层长度、深度、位置以及纤维铺层方向对脱层圆柱壳屈曲载荷的影响。
文章的最后对复合材料圆柱壳的自由振动模态,轴压屈曲及后屈曲两个方面进行了系列化的试验研究。试验研究结果表明:复合材料圆柱壳在自由悬挂下测得的振动模态和理论计算相比很接近;而静压破坏试验结果和理论计算结果有较大的出入。最后分析了产生这些误差的原因。
Free vibration, nonlinear dynamic response, buckling and postbuckling, delaminarion buckling of composite circular cylindrical shells with stringer and ring stiffeners have been investigated theoretically, numerically, experimentally in this paper. The effects of the shells and stiffener parameters, delaminarion parameters on the stiffened composite shells are discussed. The aim is to provide appropriate analytical methods and theoretical basis for design of stiffened composite shells. The major work in this paper is as follows:
At the beginning, the advances in the research of free vibration, nonlinear dynamic response under axial impact load, buckling and postbuckling under axial compression of the stiffened composite shells are reviewed comprehensively. The main comments are systematically remark on the delaminarion buckling. Research background and involved elementary theory of this thesis are emphatically expatiated.
The second part of paper is about the analytical solution for the free vibration of simply supported composite circular cylindrical shells with stringer and ring stiffeners. Using the Love’s theory and the Rayleigh-Ritz energy method, the frequency equations can be deduced, which can be solved. The effects of shells and orthogonal stiffeners parameters such as the shell thickness-to-radius radio, the shell length-to-radius radio, the stiffener’s height, lamination angle and forms on the frequencies are studied. In addition, the effect of hydrostatic pressure is also discussed.
The third part presents a simple and efficient semi-analytic method to solve the nonlinear dynamic response of composite circular cylindrical shells with circumferential stiffeners under axial impact load. Applying the discrete stiffened shells model, Based on the composite shell's shear deformation theory, the motion equations of stiffened shells is deduced using Hamilton’s variation principle. The deformation of the shells and the load are expanded in double series. The motion equations expressed by deflection are obtained with the Galerkin method, and numerically solved by R-kutta approach. Examples are given for the nonlinear dynamic response of stiffened composite shells under axial impact. The effects of the stiffener geometric parameters, lamination angle, lamination forms, the numbers of lamination layers on the dynamic response of stiffened composite circular cylindrical shells are discussed.
In the forth part, the generalized Donnell-type equations governing large deflection of laminated cross-ply circular cylindrical shells based on first-order shear deformation theory are presented. An asymptotic series solution is constructed by the perturbation technique for postbuckling behavior of the cylindrical shell under axial compression. The boundary layer solutions are also designed to match with the out-of-plane boundary conditions by singular perturbation approach, and then determined the critical buckling loads and postbuckling equilibrium paths. The effect s of the stiffener and shell geometric parameters, lamination angle, lamination forms, initial imperfection on the buckling and postbuckling behavior of the shells are discussed.
The fifth chapter analyzed the buckling behavior of composite circular cylindrical shells with throughout circumference delamination by using the first first-order shear deformation theory. And establish the buckling model by spaning the entire circumference is divided into multiple sublaminates shell. The deformations are expanded in double series.
The variational principle is applied to obtain the governing equations, boundary conditions, the continuous conditions of displacements, the equilibrium conditions of the force and moment. The influences of the shell geometric parameters, lamination angle, lamination forms, length and depth of delamination on buckling load are analyzed.
The final part offered an experiment of free vibration, buckling and postbuckling under axial compression of composite circular cylindrical shells with or without delamination. The effects of lamination angle, length and range of delamination on buckling load, postbuckling behavior and the final damage form are discussed. The comparison between the experiment outcome and the numerical results indicates that those frequency results of the composite circular cylindrical shells are in good agreement with each other. However, the result of the crush experiment is inconsistent with the theoretical outcome. At last, the reasons for those discriminations are presented.
首先,论文对复合材料加筋圆柱壳的自由振动,在轴向载荷作用下的非线性动力响应,以及在轴向压缩作用下的屈曲和后屈曲问题作了全面回顾和评述,特别对含有脱层损伤的复合材料圆柱壳在轴向载荷下的屈曲问题的研究进展以及这类结构的试验研究进行了综述和评论。
第二章对两端简支纵横加筋层合圆柱壳的自由振动进行了理论研究。根据Love’s壳体理论以及Rayleigh-Ritz能量法,导出结构的动力控制方程,求解了复合材料加筋圆柱壳的自由振动频率。讨论了壳体和加筋结构参数以及静水压力的变化对圆柱壳自由振动频率的影响。
第三章采用半解析方法,建立了简化离散的复合材料环向加筋-圆柱壳模型,求解了环向加筋圆柱壳在轴向冲击载荷作用下的动力响应问题。分析中考虑了加筋壳的大变形、剪切变形、转动惯量、以及加筋肋骨的拉伸,弯曲,剪切变形的影响,运用Hamilton变分原理导出了层合加筋圆柱壳的非线性的运动控制方程,运用伽辽金法对控制方程进行离散,采用数值方法求解,通过算例分析讨论了环向加筋数目及几何参数,壳体铺层角度、材料参数、铺层方式、铺层层数以及冲击载荷形式等对动力响应的影响。
第四章基于一阶剪切理论推导了复合材料加筋圆柱壳在轴向压力作用下的广义Donnell型方程。采用摄动技术,给出了全局渐近摄动解,运用奇异摄动技术详细分析了该圆柱壳端部边界层方程和奇异摄动解。求解了角铺层及对称正交铺层圆柱壳在轴压下的屈曲载荷和后屈曲路径。揭示了复合加筋圆柱壳结构的后屈曲过程中模态跳跃、屈曲多次分支等现象。
第五章研究对象是含有环向贯穿脱层复合材料圆柱壳。建立了屈曲分析模型,基于一阶剪切理论得到了脱层壳屈曲微分方程以及相应的边界条件、位移连续条件和力平衡条件.然后采用分离变量法及状态空间法对方程求解,讨论了壳体参数、脱层长度、深度、位置以及纤维铺层方向对脱层圆柱壳屈曲载荷的影响。
文章的最后对复合材料圆柱壳的自由振动模态,轴压屈曲及后屈曲两个方面进行了系列化的试验研究。试验研究结果表明:复合材料圆柱壳在自由悬挂下测得的振动模态和理论计算相比很接近;而静压破坏试验结果和理论计算结果有较大的出入。最后分析了产生这些误差的原因。
Free vibration, nonlinear dynamic response, buckling and postbuckling, delaminarion buckling of composite circular cylindrical shells with stringer and ring stiffeners have been investigated theoretically, numerically, experimentally in this paper. The effects of the shells and stiffener parameters, delaminarion parameters on the stiffened composite shells are discussed. The aim is to provide appropriate analytical methods and theoretical basis for design of stiffened composite shells. The major work in this paper is as follows:
At the beginning, the advances in the research of free vibration, nonlinear dynamic response under axial impact load, buckling and postbuckling under axial compression of the stiffened composite shells are reviewed comprehensively. The main comments are systematically remark on the delaminarion buckling. Research background and involved elementary theory of this thesis are emphatically expatiated.
The second part of paper is about the analytical solution for the free vibration of simply supported composite circular cylindrical shells with stringer and ring stiffeners. Using the Love’s theory and the Rayleigh-Ritz energy method, the frequency equations can be deduced, which can be solved. The effects of shells and orthogonal stiffeners parameters such as the shell thickness-to-radius radio, the shell length-to-radius radio, the stiffener’s height, lamination angle and forms on the frequencies are studied. In addition, the effect of hydrostatic pressure is also discussed.
The third part presents a simple and efficient semi-analytic method to solve the nonlinear dynamic response of composite circular cylindrical shells with circumferential stiffeners under axial impact load. Applying the discrete stiffened shells model, Based on the composite shell's shear deformation theory, the motion equations of stiffened shells is deduced using Hamilton’s variation principle. The deformation of the shells and the load are expanded in double series. The motion equations expressed by deflection are obtained with the Galerkin method, and numerically solved by R-kutta approach. Examples are given for the nonlinear dynamic response of stiffened composite shells under axial impact. The effects of the stiffener geometric parameters, lamination angle, lamination forms, the numbers of lamination layers on the dynamic response of stiffened composite circular cylindrical shells are discussed.
In the forth part, the generalized Donnell-type equations governing large deflection of laminated cross-ply circular cylindrical shells based on first-order shear deformation theory are presented. An asymptotic series solution is constructed by the perturbation technique for postbuckling behavior of the cylindrical shell under axial compression. The boundary layer solutions are also designed to match with the out-of-plane boundary conditions by singular perturbation approach, and then determined the critical buckling loads and postbuckling equilibrium paths. The effect s of the stiffener and shell geometric parameters, lamination angle, lamination forms, initial imperfection on the buckling and postbuckling behavior of the shells are discussed.
The fifth chapter analyzed the buckling behavior of composite circular cylindrical shells with throughout circumference delamination by using the first first-order shear deformation theory. And establish the buckling model by spaning the entire circumference is divided into multiple sublaminates shell. The deformations are expanded in double series.
The variational principle is applied to obtain the governing equations, boundary conditions, the continuous conditions of displacements, the equilibrium conditions of the force and moment. The influences of the shell geometric parameters, lamination angle, lamination forms, length and depth of delamination on buckling load are analyzed.
The final part offered an experiment of free vibration, buckling and postbuckling under axial compression of composite circular cylindrical shells with or without delamination. The effects of lamination angle, length and range of delamination on buckling load, postbuckling behavior and the final damage form are discussed. The comparison between the experiment outcome and the numerical results indicates that those frequency results of the composite circular cylindrical shells are in good agreement with each other. However, the result of the crush experiment is inconsistent with the theoretical outcome. At last, the reasons for those discriminations are presented.
引文
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