The aim of this paper is to extend the semi-uniform ergodic theorem and semi-uniform sub-additive ergodic theorem to skew-product quasi-flows. Furthermore, more strict inequalities about these two theorems are establi...The aim of this paper is to extend the semi-uniform ergodic theorem and semi-uniform sub-additive ergodic theorem to skew-product quasi-flows. Furthermore, more strict inequalities about these two theorems are established. By making use of these results, it is feasible to get uniform estimation of the Lyapunov exponent of some special systems even under non-uniform hypotheses展开更多
In this paper,the proposed is a quasi-flow constitutive model with strain-rate sen- sitivity for elastic plastic large deformation.The model is based on the Quasi-flow Corner theory, and is suitable for the sheet meta...In this paper,the proposed is a quasi-flow constitutive model with strain-rate sen- sitivity for elastic plastic large deformation.The model is based on the Quasi-flow Corner theory, and is suitable for the sheet metal forming process simulation with a variable punch machine velocity. Uniaxial tensile tests and deep-drawing tests of a circular blank with square punch are carried out and numerically simulated.The consistency between the experimental and the numerically simulated results shows the validity of the present new constitutive model.展开更多
Flange earrings of strong anisotropic sheet metals in deep-drawing process are numerically analyzed by the elastic-plastic large deformation finite element formulation based on a discrete Kirchhoff triangle plate shel...Flange earrings of strong anisotropic sheet metals in deep-drawing process are numerically analyzed by the elastic-plastic large deformation finite element formulation based on a discrete Kirchhoff triangle plate shell element model. A Barlat-Lian anisotropic yield function and a quasi-flow corner theory are used in the present formulation. The numerical results are compared with the experimental ones of cylindrical cup drawing process. The focus of the present researches is on the numerical analysis and the constraining scheme of the flange earring of circular sheets with strong anisotropy in square cup drawing process.展开更多
A quasi -flow corner theory on lalge plastic deformation if ductile metals is proposed in this paper. From orthogonal rule of plastic flow, the theory introduces a 'modulus rethtced function' and a corne...A quasi -flow corner theory on lalge plastic deformation if ductile metals is proposed in this paper. From orthogonal rule of plastic flow, the theory introduces a 'modulus rethtced function' and a corner effect of yield surface into the constilulive model of elastic-plastic large deformation . Thereby, the smooth and continuous transitions from orthogonal constitutive model to non-orthogonal one, and from plastic loading to elastic unloading are realized. In addition, the theory makes it possible to connect general anisotropic yield functions with corner hardening effect. The comparison between numerical simulation and experimental observation for the uniaxial tensile instability and shear band deformation of anisotropic sheet metals shows the validity of the present quasi-flow corner theory.展开更多
In this paper, for a discontinuous skew-product transformation with the integrable observation function, we obtain uniform ergodic theorem and semi-uniform ergodic theorem. The main assumptions are that discontinuity ...In this paper, for a discontinuous skew-product transformation with the integrable observation function, we obtain uniform ergodic theorem and semi-uniform ergodic theorem. The main assumptions are that discontinuity sets of transformation and observation function are ignorable in some measure-theoretical sense. The theorems extend the classical results which have been established for continuous transformations and continuous observation functions.展开更多
In this paper, we show that for an eventually strongly monotone skew-product semiflow τ, the strict ordering on Ec （the set consisting of continuous equilibria of τ） implies the strong one.
non-autonomous finite-delay functional differential equations without any monotone conditions assumed.A minimal set is constructed in terms of which necessary and sufficient conditions for a continuous equilibrium to ...non-autonomous finite-delay functional differential equations without any monotone conditions assumed.A minimal set is constructed in terms of which necessary and sufficient conditions for a continuous equilibrium to exist are also obtained.Several illustrative examples are employed to demonstrate our results.展开更多
In the paper, the author addresses the Lyapunov characteristic spectrum of an ergodic autonomous ordinary differential system on a complete riemannian manifold of finite dimension such as the d-dimensional euclidean s...In the paper, the author addresses the Lyapunov characteristic spectrum of an ergodic autonomous ordinary differential system on a complete riemannian manifold of finite dimension such as the d-dimensional euclidean space ? d , not necessarily compact, by Liaowise spectral theorems that give integral expressions of Lyapunov exponents. In the context of smooth linear skew-product flows with Polish driving systems, the results are still valid. This paper seems to be an interesting contribution to the stability theory of ordinary differential systems with non-compact phase spaces.展开更多
文摘The aim of this paper is to extend the semi-uniform ergodic theorem and semi-uniform sub-additive ergodic theorem to skew-product quasi-flows. Furthermore, more strict inequalities about these two theorems are established. By making use of these results, it is feasible to get uniform estimation of the Lyapunov exponent of some special systems even under non-uniform hypotheses
基金The project supported by the Scientific Foundation of National Outstanding Youth of China (10125208),the National Natural Science Foundation of China (19832020),and the National Education Committee of China
文摘In this paper,the proposed is a quasi-flow constitutive model with strain-rate sen- sitivity for elastic plastic large deformation.The model is based on the Quasi-flow Corner theory, and is suitable for the sheet metal forming process simulation with a variable punch machine velocity. Uniaxial tensile tests and deep-drawing tests of a circular blank with square punch are carried out and numerically simulated.The consistency between the experimental and the numerically simulated results shows the validity of the present new constitutive model.
基金The project supported by the National Natural Science Foundation of China (19832020)Provincial Natural Science Foundation of Jilin, China (200000519)
文摘Flange earrings of strong anisotropic sheet metals in deep-drawing process are numerically analyzed by the elastic-plastic large deformation finite element formulation based on a discrete Kirchhoff triangle plate shell element model. A Barlat-Lian anisotropic yield function and a quasi-flow corner theory are used in the present formulation. The numerical results are compared with the experimental ones of cylindrical cup drawing process. The focus of the present researches is on the numerical analysis and the constraining scheme of the flange earring of circular sheets with strong anisotropy in square cup drawing process.
文摘A quasi -flow corner theory on lalge plastic deformation if ductile metals is proposed in this paper. From orthogonal rule of plastic flow, the theory introduces a 'modulus rethtced function' and a corner effect of yield surface into the constilulive model of elastic-plastic large deformation . Thereby, the smooth and continuous transitions from orthogonal constitutive model to non-orthogonal one, and from plastic loading to elastic unloading are realized. In addition, the theory makes it possible to connect general anisotropic yield functions with corner hardening effect. The comparison between numerical simulation and experimental observation for the uniaxial tensile instability and shear band deformation of anisotropic sheet metals shows the validity of the present quasi-flow corner theory.
基金Supported by National Natural Science Foundation of China(NSFC)(Grant Nos.11671382 and 11301512)Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(Grant No.2008DP173182)+1 种基金CAS Key Project of Frontier Sciences(Grant No.QYZDJ-SSW-JSC003)National Center for Mathematics and Interdisciplinary Sciences。
文摘In this paper, for a discontinuous skew-product transformation with the integrable observation function, we obtain uniform ergodic theorem and semi-uniform ergodic theorem. The main assumptions are that discontinuity sets of transformation and observation function are ignorable in some measure-theoretical sense. The theorems extend the classical results which have been established for continuous transformations and continuous observation functions.
基金Partially supported by the National Basic Research Program of China,973 Project (No. 2005CB321902)the Key Lab of Random Complex Structures and Data Science,CAS
文摘In this paper, we show that for an eventually strongly monotone skew-product semiflow τ, the strict ordering on Ec （the set consisting of continuous equilibria of τ） implies the strong one.
基金supported by the Key Lab of Random Complex Structures and Data Science,CAS(Grant No.2008DP173182)the National Basic Research Program of China (973 Project)(Grant No.2005CB321902)
文摘non-autonomous finite-delay functional differential equations without any monotone conditions assumed.A minimal set is constructed in terms of which necessary and sufficient conditions for a continuous equilibrium to exist are also obtained.Several illustrative examples are employed to demonstrate our results.
基金supported by the National Natural Science Foundation of China (Grant No. 10671088)the Major State Basic Research Development Program of China (Grant No. 2006CB805903)
文摘In the paper, the author addresses the Lyapunov characteristic spectrum of an ergodic autonomous ordinary differential system on a complete riemannian manifold of finite dimension such as the d-dimensional euclidean space ? d , not necessarily compact, by Liaowise spectral theorems that give integral expressions of Lyapunov exponents. In the context of smooth linear skew-product flows with Polish driving systems, the results are still valid. This paper seems to be an interesting contribution to the stability theory of ordinary differential systems with non-compact phase spaces.
