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181.
182.
Julien Dallot 《Journal of the mechanics and physics of solids》2008,56(2):561-580
The purpose of this paper is to determine , the overall homogenized Love-Kirchhoff strength domain of a rigid perfectly plastic multi-layered plate, and to study the relationship between the 3D and the homogenized Love-Kirchhoff plate limit analysis problems. In the Love-Kirchhoff model, the generalized stresses are the in-plane (membrane) and the out-of-plane (flexural) stress field resultants. The homogenization method proposed by Bourgeois [1997. Modélisation numérique des panneaux structuraux légers. Ph.D. Thesis, University Aix-Marseille] and Sab [2003. Yield design of thin periodic plates by a homogenization technique and an application to masonry wall. C. R. Méc. 331, 641-646] for in-plane periodic rigid perfectly plastic plates is justified using the asymptotic expansion method. For laminated plates, an explicit parametric representation of the yield surface is given thanks to the π-function (the plastic dissipation power density function) that describes the local strength domain at each point of the plate. This representation also provides a localization method for the determination of the 3D stress components corresponding to every generalized stress belonging to . For a laminated plate described with a yield function of the form , where σu is a positive even function of the out-of-plane coordinate x3 and is a convex function of the local stress σ, two effective constants and a normalization procedure are introduced. A symmetric sandwich plate consisting of two Von-Mises materials ( in the skins and in the core) is studied. It is found that, for small enough contrast ratios (), the normalized strength domain is close to the one corresponding to a homogeneous Von-Mises plate [Ilyushin, A.-A., 1956. Plasticité. Eyrolles, Paris]. 相似文献
183.
Nonlinear interactions and chaotic dynamics of suspended cables with three-to-one internal resonances 总被引:2,自引:0,他引:2
Nonlinear planar oscillations of suspended cables subjected to external excitations with three-to-one internal resonances are investigated. At first, the Galerkin method is used to discretize the governing nonlinear integral–partial-differential equation. Then, the method of multiple scales is applied to obtain the modulation equations in the case of primary resonance. The equilibrium solutions, the periodic solutions and chaotic solutions of the modulation equations are also investigated. The Newton–Raphson method and the pseudo-arclength path-following algorithm are used to obtain the frequency/force–response curves. The supercritical Hopf bifurcations are found in these curves. Choosing these bifurcations as the initial points and applying the shooting method and the pseudo-arclength path-following algorithm, the periodic solution branches are obtained. At the same time, the Floquet theory is used to determine the stability of the periodic solutions. Numerical simulations are used to illustrate the cascades of period-doubling bifurcations leading to chaos. At last, the nonlinear responses of the two-degree-of-freedom model are investigated. 相似文献
184.
185.
186.
In this paper a general technique for the analysis of nonlinear dynamical systems with periodic-quasiperiodic coefficients
is developed. For such systems the coefficients of the linear terms are periodic with frequency ω while the coefficients of
the nonlinear terms contain frequencies that are incommensurate with ω. No restrictions are placed on the size of the periodic
terms appearing in the linear part of system equation. Application of Lyapunov-Floquet transformation produces a dynamically
equivalent system in which the linear part is time-invariant and the time varying coefficients of the nonlinear terms are
quasiperiodic. Then a series of quasiperiodic near-identity transformations are applied to reduce the system equation to a
normal form. In the process a quasiperiodic homological equation and the corresponding ‘solvability condition’ are obtained.
Various resonance conditions are discussed and examples are included to show practical significance of the method. Results
obtained from the quasiperiodic time-dependent normal form theory are compared with the numerical solutions. A close agreement is found. 相似文献
187.
《Wave Motion》2018
We introduce a perfectly matched layer approach for finite element calculations of diffraction by metallic surface-relief gratings. We use a non-integrable absorbing function which allows us to use thin absorbing layers, which reduces the computational time when simulating this type of structure. In addition, we numerically determine the best choice of the absorbing layer parameters and show that they are independent of the wavelength. 相似文献
188.
This paper presents the beam-mode stability of a fluid-conveying periodic shell on an elastic foundation subjected to external loading. A transfer matrix (TM) method was developed to investigate the characteristics of steady-state waves in the system and the dynamic response of the periodic shell system. When subjected to external perturbations, including either a moving load or a stationary one, the shell may be subjected to instability for flow velocities exceeding a certain critical velocity. The system can also become unstable when a travelling load exceeds a certain critical value. The coupled effects of the speed of a moving load and the flow velocity of a fluid on the stability of the shell system were also investigated. A periodic structure was designed for such a shell system to enhance its dynamic stability. The periodic shell system produces innumerable velocity band gaps (VBGs), which could raise the critical velocity and extend the stable range for both the moving load and the flowing fluid. Finally, the formation mechanism of the VBGs was studied, as well as the effects of the thickness, length of the shell cells, Young׳s modulus and stiffness of the elastic foundation on modulating the VBGs. 相似文献
189.
Li Li 《Nonlinear dynamics》1996,9(3):223-247
In this paper a new method for solving for the periodic solution (limit cycle) of a strongly nonlinear system is suggested. Using this method not only the existence, stability and number of periodic solutions can be decided, but at the same time the approximate expressions for these periodic solutions can also be obtained. The proof of this method is given as well.The project is supported by the National Natural Science Foundation of China. 相似文献
190.
By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, the global exponential stability and periodicity are investigated for a class of delayed high-order Hopfield neural networks (HHNNs) with impulses, which are new and complement previously known results. Finally, an example with numerical simulation is given to show the effectiveness of the proposed method and results. The numerical simulation shows that our models can occur in many forms of complexities including periodic oscillation and the Gui chaotic strange attractor. 相似文献