The Effects Of The Geometrical Imperfections On The Mechanical Properties Of Arch Structures

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.