【作者】 易壮鹏；

【导师】 赵跃宇；

【作者基本信息】 湖南大学 ， 桥梁与隧道工程， 2007， 博士

【摘要】 本文就几何缺陷对拱结构静力、动力和稳定性能的影响展开了全面而深入的研究,全文共分七章。第一章绪论对拱结构中几何缺陷影响的研究进行了综合评述;第二章主要对拱结构中任意分布的几何缺陷进行了随机描述;第三章从虚功原理和广义变分原理出发研究了径向均布荷载和集中荷载作用下铰支、固支和弹性支撑三种边界条件下圆弧拱存在几何缺陷时的稳定性能;第四章分析了大跨度拱桥在考虑几何缺陷时的稳定性能;第五章从运动稳定理论出发研究了存在几何缺陷的拱结构的动力稳定性能;第六章对含几何缺陷浅拱的动力跳跃特性进行了分析和研究;第七章研究了含几何缺陷浅拱的内共振、分岔和混沌等非线性动力学行为。最后是结论和展望。1.本文首次对拱结构中任意分布的几何缺陷进行了随机描述,得到了按出现可能性大小排列的缺陷分布方式及其大小。将拱结构的节点坐标偏离视为随机变量,由随机理论得到拱的支撑边界确定而节点坐标偏差保持随机情况下结构的条件相关矩阵,对其进行特征值求解得到的特征向量和特征值即可作为缺陷的分布方式与缺陷幅值标准差。这种求解拱结构随机几何缺陷的方法同样适用于其它结构中随机分布几何缺陷的分布方式及大小的求解。2.本文首次利用虚功原理和广义变分原理推导了铰支、固支和弹性支撑三种边界条件与径向均布荷载和跨中集中荷载作用下含几何缺陷圆弧拱的计算公式。由拱截面任意一点的薄膜应变和弯曲应变中考虑几何缺陷影响,通过系统总能量的变分求得含缺陷拱的轴、径向平衡微分方程,并求得圆弧拱屈曲前和屈曲时作用荷载和轴向压力的关系以及径向位移的表达式。还以径向均布荷载作用固支圆弧拱为例对拱结构中拱轴线形偏差、荷载非完全均匀分布和端支座沉陷等一般缺陷进行了分析,得到了荷载和轴向压力关系以及径向位移的求解方法。3.本文从结构的两类稳定理论出发,对大跨度拱桥考虑几何缺陷时的稳定性能进行了分析。几何缺陷的分布方式采用一致和随机两种模拟方式,对各种缺陷分布下拱桥结构的线弹性、弹性大变形和弹塑性大变形的稳定安全系数进行了分析计算。分析了大跨度拱桥在考虑几何非线性、材料非线性和初始几何缺陷情况下的极限承载能力,探讨了几何缺陷的分布方式和缺陷大小对非线性稳定性能的影响程度,得出了缺陷的最不利方式以及保证稳定性的缺陷幅值范围。4.本文从运动稳定理论出发提出了一种通过Lyapunov指数对含几何缺陷结构动力稳定性进行判别的方法。该方法中每一荷载步均考虑结构的几何、材料非线性,通过周期荷载和其它一般动力荷载作用下几何缺陷对拱结构影响的计算分析,验证了这种方法的可行性,可为动力荷载作用下结构的动力稳定性能进行判定。5.本文就几何缺陷对阶跃和脉冲荷载作用下正弦浅拱的动力跳跃特性进行了系统的研究,用从系统总能量出发在相平面内建立Lyapunov判定函数的解析方法得到浅拱不发生动力跳跃的充分条件,还采用基于Galerkin离散和龙格-库塔法的半解析方法研究了浅拱发生跳跃时的动力屈曲特性。首次就几何缺陷对粘弹性浅拱的动力稳定性能影响进行了分析,得到了含几何缺陷粘弹性浅拱的动力临界荷载和屈曲特点。6.本文首次利用多尺度摄动法和Melnikov函数积分法对含几何缺陷的浅拱进行了非线性动力学分析。建立了任意线形浅拱在任意分布荷载作用下的非线性动力模型,以含二阶谐波缺陷的正弦浅拱为例对缺陷浅拱的内共振模式与条件进行了分析,探讨了各种分岔类型并对各种分岔条件进行了数值模拟,通过混沌出现条件的解析预测,得到了分岔时的混沌性质以及产生混沌的参数条件。更多还原

【Abstract】 An all-round and deep research on the effects of the geometrical imperfections on the static and dynamic properties, stability of arch structures has been made in this paper. The dissertation consists of 7 chapters. The first one presents a comprehensive study of the effects of the geometrical imperfections on mechanical properties of arch. In chapter 2 stochastic description of the arbitrary geometrical imperfection in arch has been made. The stabilizations of arc arch, where the geometrical imperfection exist, on radial uniform load and concentrated load with hinged, fixed and elastic three types boundary conditions are determined from the basic principle of virtual work and generalized variation in chapter 3. In chapter 4 the stabilities of long-span arch bridge considering geometrical imperfection are investigated from the stability theory of arch structure. In chapter 5 the focus is placed on the dynamic stability of imperfect arch on the basis of Lyapunov motion stability theory. The dynamic snap-through of shallow arch with geometrical imperfection has been studied in chapter 6. In chapter 7 the internal resonance, bifurcation and chaos of imperfection arch have been analysis. Lastly, the conclusion and prospect are presented. 1.For the first time, the stochastic description of arch structure with arbitrary geometrical imperfection is made, and the distribution mode and magnitude of stochastic imperfection are obtained. Geometrical imperfections are interpreted as spatially fluctuating structural properties with respect to a perfect geometry. To obtain the conditional covariance matrix the boundary conditions are assumed to be deterministic while the structure itself which is exponential correlation remains stochastically. Then the shapes and amplitudes of geometrical imperfection can be determined through the decomposition of the correlation matrix.2. The computation formula of stabilization for arc arch with geometrical imperfection on radial uniform load and concentrated load are determined, where there are hinged, fixed and elastic support three boundary conditions, from virtual work and generalized variation. In the formula the effects on geometrical imperfection are considered from the membrane strain and bending strain of arbitrary point in cross section of arch. The differential equilibrium equations are obtained from the variation of the total energy of arch system, and then the relation between of load and axial forces and the expression of radial displacement can be determined.3 . The stabilities of long span arch bridge considering the geometrical imperfections are investigated. The distributions of imperfections are simulated from both the style of coherence and stochastic. The stability factors of arch bridge on the condition of linear, large displacement elasticity and large displacement elastic- plasticity with various imperfections are calculated. The limit carrying capacities of long span arch bridges when considering the geometrical imperfection are analysis. And the influences of the distribution modes and amplitudes of imperfections on the nonlinear stability are discussed; furthermore the worst distribution mode imperfection and the imperfection amplitude for the safe of stability are determined.4.A new discrimination criterion for the dynamic stability of imperfection arch is established on the basis of Lyapunov motion stability theory. To obtain the conditional covariance matrix the boundary conditions are assumed to be deterministic while the structure itself, whose node coordinate deviations are exponential correlation, remains stochastically. The top Lyapunov exponents, which can take both geometrical and material nonlinearities into account, are used to distinguish the dynamic stability.5.The dynamic snap-through of shallow arches with geometrical imperfection on the time-step and impulsive load are investigated systematically. And the dynamic equation, which is derived from d’Alembert principle and Euler-Bernoulli assumption, was used to obtain the equilibrium configurations by the Galerkin method. Appling the energy approach and the Lyapunov function in the phase space, the stability of critical points and the sufficient condition against dynamic snap-though of shallow arch are determined. The dynamic critical load and buckling characteristic of viscoelastic shallow arch with geometrical imperfection are researched for the first time.6.The nonlinear dynamics of shallow arch with geometrical imperfection were studied by using the multi-scale perturbation and Melnikov method. The nonlinear dynamic model arbitrary shape shallow arch on arbitrary distribution load is founded, and the sinusoidal shallow arch with second harmonic imperfection is taken as example to investigate the pattern and condition of internal resonance. And the types and conditions of bifurcations are investigated numerically. The chaos features and structural parameter for chaos of imperfection shallow arch are discussed.更多还原