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Elasto-viscoplastic consistent tangent operator concept-based implicit boundary element methods

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Science China(Technological Sciences) 2000年第2期43卷 154-164页

作者：刘勇梁利华 GlaucioH.Paulino Institute of Superplasticity and Plasticity Zhejiang University of Technology Hangzhou China Department of Civil and Env. Eng. University of California Davis USA Department of Mechanical Engineering Zhejiang University of Technology Hangzhou China

An elasto-viscoplastic consistent tangent operator (CTO) concept-based implicit algorithm for nonlinear boundary element methods is presented. Both kinematic and isotropic strain hardening are considered. The elasto-viscoplastic radial return algorithm (RRA) and the elasto-viscoplastic CTO and its related scheme are developed. In addition, the limit cases (e.g. elastoplastic problem) of vis-coplastic RRA and CTO are discussed. Finally, numerical examples, which are compared with the latest FEM results of Ibrahimbegovic et al. and ABAQUS results, are provided.

关键词： boundary element method elasto-viscoplasticity consistent tangent operator (CTO) implicit algorithm computational mechanics.

Numerical Validations of the tangent Linear Model for the Lorenz Equations

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Computer Modeling in Engineering & Sciences 2019年第7期120卷 83-104页

作者： Tengjin Zhao Jing Zhang Zhilin Li Zhiyue Zhang School of Mathematical Sciences Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex SystemsNanjing Normal UniversityNanjing210023China Department of Mathematics North Carolina State UniversityRaleighNC 27695-8205USA

The validity of the tangent linear model(TLM)is studied numerically using the example of the Lorenz equations in this paper.The relationship between the limit of the validity time of the TLM and initial perturbations for the Lorenz equations is investigated using the Monte Carlo sampling method.A new error function between the nonlinear and the linear evolution of the perturbations is proposed.Furthermore,numerical sensitivity analysis is carried to establish the relationship between parameters and the validity of the TLM,such as the initial perturbation,the prediction time,the time step size and so on,by the method of mathematical statistics.

关键词： Lorenz model tangent linear model nonlinear model Monte Carlo

Non-extendibility of tangent Bundles of Complex Projective Spaces and Quaternion Projective Spaces

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Chinese Science Bulletin 1993年第13期38卷 1057-1059页

作者：唐梓洲 Department of Mathematics Graduate School Academia Sinica Beijing 100039 PRC

1 Introduction Let K be a CW-complex and L be its subcomplex. A real (resp. complex) vector bundle over L is said to be extendible to K if it is equivalent to the restriction of a real (resp. complex) vector bundle over K. R. L. E. Schwarzenberger studied the non-extendibility of vector bundles over CP^n (resp. RP^n) to CP^m(resp. RP^m), m>n, where CP^n (resp. RP^n) is the complex (resp. real)

关键词： tangent bundle complex projective spaces quaternion projective spaces.

Investigation of the Mechanism of tangent Bifurcation in Current Mode Controlled Boost Converter

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Circuits and Systems 2011年第1期2卷 38-44页

作者： Ling-ling Xie Ren-xi Gong Kuang Wang Hao-ze Zhuo 不详

tangent bifurcation is a special bifurcation in nonlinear dynamic systems. The investigation of the mechanism of the tangent bifurcation in current mode controlled boost converters operating in continuous conduction mode (CCM) is performed. The one-dimensional discrete iterative map of the boost converter is derived. Based on the tangent bifurcation theorem, the conditions of producing the tangent bifurcation in CCM boost converters are deduced mathematically. The mechanism of the tangent bifurcation in CCM boost is exposed from the viewpoint of nonlinear dynamic systems. The tangent bifurcation in the boost converter is verified by numerical simulations such as discrete iterative maps, bifurcation map and Lyapunov exponent. The simulation results are in agreement with the theoretical analysis, thus validating the correctness of the theory.

关键词： tangent Bifurcation Discrete Iterative Map Boost Converter Continuous Current Mode (CCM)

Using tangent Boost along a Worldline and Its Associated Matrix in the Lie Algebra of the Lorentz Group

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Journal of Modern Physics 2017年第8期8卷 1190-1212页

作者： Michel Langlois Martin Meyer Jean-Marie Vigoureux IRRG Besan&Ccedil on France Laboratoire de Mathématiques Université de Franche-Comté Besan&Ccedil on Cedex France Institut UTINAM UMR CNRS 6213 Université de Franche-Comté Besan&Ccedil on Cedex France

In order to generalize the relativistic notion of boost to the case of non inertial particles and to general relativity, we look closer into the definition of the Lie group of Lorentz matrices and its Lie algebra and we study how this group acts on the Minskowski space. We thus define the notion of tangent boost along a worldline. This very general notion gives a useful tool both in special relativity (for non inertial particles or/and for non rectilinear coordinates) and in general relativity. We also introduce a matrix of the Lie algebra which, together with the tangent boost, gives the whole dynamical description of the considered system (acceleration and Thomas rotation). After studying the properties of Lie algebra matrices and their reduced forms, we show that the Lie group of special Lorentz matrices has four one-parameter subgroups. These tools lead us to introduce the Thomas rotation in a quite general way. At the end of the paper, we present some examples using these tools and we consider the case of an electron rotating on a circular orbit around an atom nucleus. We then discuss the twin paradox and we show that when the one who made a journey into space in a high-speed rocket returns home, he is not only younger than the twin who stayed on Earth but he is also disorientated because his gyroscope has turned with respect to earth referential frame.

关键词： Lie Group of Lorentz Matrices Lie Algebra tangent Boost along a Worldline Acceleration Special Relativity General Relativity Thomas Rotation Twin Paradox Inertial Particles Non Inertial Particles

On Tachibana and Vishnevskii Operators Associated with Certain Structures in the tangent Bundle

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Journal of Applied Mathematics and Physics 2018年第10期6卷 1968-1978页

作者： Lovejoy S. Das Mohammad Nazrul Islam Khan Department of Mathematics Kent State University Tuscarawas New Philadelphia OH USA Department of Computer Engineering College of Computer Qassim University Buraidah KSA

The aim of the present work is to study the complete, vertical and horizontal lifts using Tachibana and Visknnevskii operators along generalized almost r-contact structure in tangent bundle. We also prove certain theo... 详细信息

关键词： tangent Bundle Vertical Lift Complete Lift Lie Derivative Tachibana Operator Vishnevskii Operator

Nonlinear Dimensionality Reduction via Homeomorphic tangent Space and Compactness

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国际计算机前沿大会会议论文集 2017年第1期 132-133页

作者： Shaoqun Zhang Wanyun Xie Sichuan University Chengdu 610024China

This paper establishes the geometric framework of manifold learning.After summarizing the requirements of the classical manifold learning methods,we construct the smooth homeomorphism between the manifold and its tangent space.Then we propose a new algorithm via homeomorphic tangent space(LHTS).We also present another algorithm via compactness(CSLI)by analyzing the topological properties of manifolds.We illustrate our algorithm on the completed manifold and non-completed manifold.We also address several theoretical issues for further research and improvements.

关键词： Manifold learning Smooth homeomorphism Homeomorphic tangent space Compactness

Microwave strengthens decomposition of mixed rare earth concentrate: Microwave absorption characteristics

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Journal of Rare Earths 2019年第5期37卷 541-546页

作者： Yukun Huang Ting'an Zhang Zhihe Dou Guozhi Lv Guihong Han Weijun Peng School of Chemical Engineering and Energy Zhengzhou University Laboratory of Special Metallurgy and Process Engineering School of Metallurgy Northeastern University

The potential application of microwave heating technology for processing the mixed rare earth concentrate was systematically investigated by analyzing the microwave absorption characteristics in this study. The complex permittivity was measured through resonant cavity perturbation method. The variations of permittivity, the loss factor, loss tangent and the penetration depth with the increasing temperature were investigated numerically. The results indicate that the permittivity increases as the temperature increases, and temperature has a pivotal effect on it. The mixed concentrate is high loss material at the temperature range from 600 to 800℃ according to theoretical analyses of loss tangent and penetration depth. The results of phase transition analysis prove that the variation of microwave absorption characteristics of mixed concentrate is caused by the changes of crystal and lattice structures.The reflectivity, loss factor and penetration depth of the mixed concentrate were also calculated, and the results indicate that processing the mixed concentrate by microwave heating is of high feasibility and industrial potential.

关键词： Microwave processing Microwave absorption characteristics Dielectric constant Loss tangent Mixed rare earth concentrate

Combined influence of nonlinearity and dilation on slope stability evaluated by upper-bound limit analysis

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Journal of Central South University 2017年第7期24卷 1602-1611页

作者：唐高朋赵炼恒李亮陈静瑜 School of Civil Engineering Central South UniversityChangsha 410075China

The combined influence of nonlinearity and dilation on slope stability was evaluated using the upper-bound limit analysis theorem.The mechanism of slope collapse was analyzed by dividing it into arbitrary discrete soil blocks with the nonlinear Mohr–Coulomb failure criterion and nonassociated flow rule.The multipoint tangent(multi-tangent) technique was used to analyze the slope stability by linearizing the nonlinear failure criterion.A general expression for the slope safety factor was derived based on the virtual work principle and the strength reduction technique,and the global slope safety factor can be obtained by the optimization method of nonlinear sequential quadratic programming.The results show better agreement with previous research result when the nonlinear failure criterion reduces to a linear failure criterion or the non-associated flow rule reduces to an associated flow rule,which demonstrates the rationality of the presented method.Slope safety factors calculated by the multi-tangent inclined-slices technique were smaller than those obtained by the traditional single-tangent inclined-slices technique.The results show that the multi-tangent inclined-slices technique is a safe and effective method of slope stability limit analysis.The combined effect of nonlinearity and dilation on slope stability was analyzed,and the parameter analysis indicates that nonlinearity and dilation have significant influence on the result of slope stability analysis.

关键词： slope stability analysis nonlinear failure criterion non-associated flow rule multipoint tangent technique upper-bound limit analysis theorem