The required reinforcement force to prevent instability and the yield acceleration of reinforced slopes are computed under seismic loading by applying the kinematic approach of limit analysis in conjunction with the p...The required reinforcement force to prevent instability and the yield acceleration of reinforced slopes are computed under seismic loading by applying the kinematic approach of limit analysis in conjunction with the pseudo-dynamic method for a wide range of soil cohesion, friction angle, dilation angle and horizontal and vertical seismic coefficients. Each parameter threatening the stability of the slope enhances the magnitude of the required reinforcement force and vice versa. Moreover, the yield acceleration increases with the increase in soil shear strength parameters but decreases with the increase in the slope angle. The comparison of the present work with some of the available solutions in the literatures shows a reasonable agreement.展开更多
Stochastic bifurcations of the SD （smooth and discontinuous） oscillator with additive and/or multiplicative bounded noises are studied by the generalized cell mapping method using digraph analysis algorithm. From th...Stochastic bifurcations of the SD （smooth and discontinuous） oscillator with additive and/or multiplicative bounded noises are studied by the generalized cell mapping method using digraph analysis algorithm. From the global viewpoint, stochastic bifur- cation can be described as a sudden change in shape and size of a random attractor as the system parameter valies. The evolu- tionary process of stochastic bifurcation in the SD oscillator is shown in detail. Meanwhile, we show the phenomenon that un- der stochastic excitation the shape and size of random attractor and random saddle change along with the direction of unstable manifold. A plane stochastic bifurcation diagram is included.展开更多
An analytical method is proposed to find geometric structures of stable,unstable and center manifolds of the collinear Lagrange points.In a transformed space,where the linearized equations are in Jordan canonical form...An analytical method is proposed to find geometric structures of stable,unstable and center manifolds of the collinear Lagrange points.In a transformed space,where the linearized equations are in Jordan canonical form,these invariant manifolds can be approximated arbitrarily closely as Taylor series around Lagrange points.These invariant manifolds are represented by algebraic equations containing the state variables only without the help of time.Thus the so-called geometric structure of these invariant manifolds is obtained.The stable,unstable and center manifolds are tangent to the stable,unstable and center eigenspaces,respectively.As an example of applicability,the invariant manifolds of L 1 point of the Sun-Earth system are considered.The stable and unstable manifolds are symmetric about the line from the Sun to the Earth,and they both reach near the Earth,so that the low energy transfer trajectory can be found based on the stable and unstable manifolds.The periodic or quasi-periodic orbits,which are chosen as nominal arrival orbits,can be obtained based on the center manifold.展开更多
An efficient iterative algorithm is presented for the numerical solution of viscous incompressible Navier-Stokes equations based on Taylor-Galerkin like split and pressure correction method in this paper. Taylor-Hood ...An efficient iterative algorithm is presented for the numerical solution of viscous incompressible Navier-Stokes equations based on Taylor-Galerkin like split and pressure correction method in this paper. Taylor-Hood element is introduced to overcome the numerical difficulties arising from the fluid incompressibility. In order to confirm the properties of the algorithm, the numerical simulation on plane Poisseuille flow problem and lid- driven cavity flow problem with different Reynolds numbers is presented. The numerical results indicate that the proposed iterative version can be effectively applied to the simulation of viscous incompressible flows. Moreover, the proposed iterative version has a better overall performance in maximum time step size allowed, under comparable convergence rate, stability and accuracy, than other tested versions in numerical solutions of the plane PoisseuiUe flow with different Reynolds numbers ranging from low to high viscosities.展开更多
文摘The required reinforcement force to prevent instability and the yield acceleration of reinforced slopes are computed under seismic loading by applying the kinematic approach of limit analysis in conjunction with the pseudo-dynamic method for a wide range of soil cohesion, friction angle, dilation angle and horizontal and vertical seismic coefficients. Each parameter threatening the stability of the slope enhances the magnitude of the required reinforcement force and vice versa. Moreover, the yield acceleration increases with the increase in soil shear strength parameters but decreases with the increase in the slope angle. The comparison of the present work with some of the available solutions in the literatures shows a reasonable agreement.
基金supported by the National Natural Science Foundation of China (Grant Nos.10932009 and 11172233)the Natural Science Foundation of Shaanxi Province (Grant No.2012JQ1004)the Northwestern Polytechnical University Foundation for Fundamental Research (Grant Nos.JC201266 and JC20110228)
文摘Stochastic bifurcations of the SD （smooth and discontinuous） oscillator with additive and/or multiplicative bounded noises are studied by the generalized cell mapping method using digraph analysis algorithm. From the global viewpoint, stochastic bifur- cation can be described as a sudden change in shape and size of a random attractor as the system parameter valies. The evolu- tionary process of stochastic bifurcation in the SD oscillator is shown in detail. Meanwhile, we show the phenomenon that un- der stochastic excitation the shape and size of random attractor and random saddle change along with the direction of unstable manifold. A plane stochastic bifurcation diagram is included.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10832004 and 11102006)the FanZhou Foundation (Grant No. 20110502)
文摘An analytical method is proposed to find geometric structures of stable,unstable and center manifolds of the collinear Lagrange points.In a transformed space,where the linearized equations are in Jordan canonical form,these invariant manifolds can be approximated arbitrarily closely as Taylor series around Lagrange points.These invariant manifolds are represented by algebraic equations containing the state variables only without the help of time.Thus the so-called geometric structure of these invariant manifolds is obtained.The stable,unstable and center manifolds are tangent to the stable,unstable and center eigenspaces,respectively.As an example of applicability,the invariant manifolds of L 1 point of the Sun-Earth system are considered.The stable and unstable manifolds are symmetric about the line from the Sun to the Earth,and they both reach near the Earth,so that the low energy transfer trajectory can be found based on the stable and unstable manifolds.The periodic or quasi-periodic orbits,which are chosen as nominal arrival orbits,can be obtained based on the center manifold.
基金the National Natural Science Foundation of China (No. 50778111)the Key Project of Fund of Science and Technology Development of Shanghai(No. 07JC14023)the Doctoral Disciplinary Special Research Project of Chinese Ministry of Education(No. 200802480056)
文摘An efficient iterative algorithm is presented for the numerical solution of viscous incompressible Navier-Stokes equations based on Taylor-Galerkin like split and pressure correction method in this paper. Taylor-Hood element is introduced to overcome the numerical difficulties arising from the fluid incompressibility. In order to confirm the properties of the algorithm, the numerical simulation on plane Poisseuille flow problem and lid- driven cavity flow problem with different Reynolds numbers is presented. The numerical results indicate that the proposed iterative version can be effectively applied to the simulation of viscous incompressible flows. Moreover, the proposed iterative version has a better overall performance in maximum time step size allowed, under comparable convergence rate, stability and accuracy, than other tested versions in numerical solutions of the plane PoisseuiUe flow with different Reynolds numbers ranging from low to high viscosities.
