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International Conference on Science and Technology of Heterogeneous Materials and Structures

作者： Zheng Yao Changliang Zheng Transportation Equipment and Ocean Engineering College Dalian Maritime University

This paper develops the Hamilton theory for the nonlocal linear elasticity originally proposed by Eringen[1].The energy density expression and variational principle for the differential form of the two dimensional nonlocal elastic theory are developed based on the symplectic theory and algorithm established in applied mechanics in recent *** associated LagTange function for the nonlocal dynamic problem is *** introducing the Hamilton function and dual variables,the variational principle is rewritten in the duality system,the dual equilibrium equations and relevant boundary conditions are derived from the variational equation in duality *** fundamental theory and computational algorithm are applied in dynamic problems of layered structures,and numerical experiments are carried out to demonstrate the validity of the theory and algorithm developed in this *** present study shows the potential of the symplectic-mathematical theory for nonlocal mechanics.

关键词： Nonlocal mechanics Hamilton theory Variational principle symplectic algorithm Layered structure

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Study on the finite element method of Hamiltonian system with chaos

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INTERNATIONAL JOURNAL OF MODERN PHYSICS C 2020年第11期31卷

作者： Tang, Qiong Liu, YangFan Zheng, Yujun Xu, ChengJie Hunan Univ Technol Coll Sci Zhuzhou 412007 Hunan Peoples R China Cent South Univ Sch Mat Sci & Engn Changsha 410083 Hunan Peoples R China Hunan Univ Sci & Engn Coll Sci Yongzhou 425199 Hunan Peoples R China Hunan Univ Technol Coll Sci Zhuzhou 412007 Hunan Peoples R China

By comparing with symplectic different methods, the quadratic element is an approximately symplectic method which can keep high accuracy approximate of symplectic structure for Hamiltonian chaos, and it is also energy conservative when there have chaos phenomenon. We use the quadratic finite element method to solve the Henon-Heiles system, and this method was never used before. Combining with Poincare section, when we increase the energy of the systems, KAM tori are broken and the motion from regular to chaotic. Without chaos, three kinds of methods to calculate the Poincare section point numbers are the same, and the numbers are different with chaos. In long-term calculation, the finite element method can better keep dynamic characteristics of conservative system with chaotic motion.

关键词： Hamiltonian systems chaos finite element methods symplectic algorithm Poincare section

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Birkhoffian symplectic algorithms derived from Hamiltonian symplectic algorithms

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Chinese Physics B 2016年第1期25卷 407-411页

作者：孔新雷吴惠彬梅凤翔 College of Science North China University of TechnologyBeijing 100144China School of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China School of Aerospace Engineering Beijing Institute of TechnologyBeijing 100081China

In this paper, we focus on the construction of structure preserving algorithms for Birkhoffian systems, based on existing symplectic schemes for the Hamiltonian equations. The key of the method is to seek an invertible transformation which drives the Birkhoffian equations reduce to the Hamiltonian equations. When there exists such a transformation, applying the corresponding inverse map to symplectic discretization of the Hamiltonian equations, then resulting difference schemes are verified to be Birkhoftian symplectic for the original Birkhoffian equations. To illustrate the operation process of the method, we construct several desirable algorithms for the linear damped oscillator and the single pendulum with linear dissipation respectively. All of them exhibit excellent numerical behavior, especially in preserving conserved quantities.

关键词： Birkhoffian equations Hamiltonian equations symplectic algorithm

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symplectic Simulations of Radial Diffusion of Fast Alpha Particles in the Presence of Low-Frequency Modes in Rippled Tokamaks

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JOURNAL OF FUSION ENERGY 2017年第1期36卷 40-47页

作者： Khan, Majid Schoepf, K. Goloborod'ko, V. Sheng, Zheng-Mao Zhejiang Univ Inst Fus Theory & Simulat Dept Phys Hangzhou 310027 Zhejiang Peoples R China Quaid I Azam Univ Islamabad Dept Phys Islamabad Pakistan Univ Innsbruck Inst Theoret Phys Assoc EURATOM OEAW Innsbruck Austria Ukrainian Acad Sci Inst Nucl Res Kiev Ukraine

The symplectic Hamiltonian guiding centre code which enables efficient calculation of charged particle trajectories and diffusion coefficients has been applied to fast ion motion in magnetically perturbed tokamak plasmas. Particularly fusion born alpha particle drift motion, in constant of motion space, is examined in the presence of low mode-number neoclassical tearing mode (NTM) perturbation in a toroidally rippled tokamak. The main focus of this study is to investigate the dependence of the radial diffusion coefficient of energetic ions on the perturbation strength and on the localization of the perturbation. The resonance between bounce motion and toroidal field ripples plays a significant role in this context. The presence of NTMs results in substantial enhancement of radial diffusion coefficient for passing particles. Depending on the strength and localization of the NTM it can cause enhancement or degradation of the radial ripple diffusion coefficient of trapped particles.

关键词： symplectic algorithm Toroidal field ripples Neoclassical tearing mode Radial diffusion coefficient Resonance interaction Tokamak

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RIDING QUALITY ANALYSIS FOR HIGH-SPEED TRAINS BASED ON PSEUDO-EXCITATION METHOD AND symplectic algorithm

RIDING QUALITY ANALYSIS FOR HIGH-SPEED TRAINS BASED ON PSEUD...

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铁道工程新技术：第二届铁道工程关键技术国际学术会议

作者： Pan XIANG~1,Yan ZHAO~1,Youwei ZHANG~1,Jiahao LIN~1,Aiqing TIAN~2 1 State Key Laboratory of Structural Analysis for Industrial Equipment,Department of Engineering Mechanics,Faculty of Vehicle Engineering and Mechanics,Dalian University of Technology,Dalian 116023 2 CSR Qingdao Sifang Locomotive & Rolling Stock Co.,Ltd.,Qingdao 266000

Riding quality estimation is an issue of most concern for both the manufacturers and operators,especially under the random excitations,of which the track irregularity is *** this paper the riding quality analysis method for high-speed trains due to track irregularity based on pseudo excitation method(PEM) and symplectic algorithm is presented,in which the coach was modelled as an elastic finite element *** mode superposition was adopted to reduce the order of the *** bogies and wheel sets are treated as rigid bodies connected in terms of primary and secondary *** track is treated as a Bernoulli-Euler beam connected to sleepers and the ballast and is regarded as an infinite periodic structure whose responses can be simply obtained by symplectic *** dynamic equations of the coupled vehicle-track system under the mixed modal coordinates,physical coordinates and wheel sets and symplectic coordinates are established based on the wheel-rail coupling *** types of track irregularities,***,alignment and superelevation irregularities,are applied simultaneously which are regarded as the superposition of pseudo harmonic irregularities by using PEM,which makes the random vibration analysis of the coupled system more efficiently and *** the numerical example,the riding quality of some Chinese high-speed trains due to track irregularity was calculated and investigated.

关键词： pseudo excitation method symplectic algorithm coupled vehicle-track system riding quality track irregularity random vibration finite element method(FEM)

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symplectic algorithms with mesh refinement for a hypersensitive optimal control problem

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2015年第11期92卷 2273-2289页

作者： Peng, Haijun Gao, Qiang Wu, Zhigang Zhong, Wanxie Dalian Univ Technol Dept Engn Mech State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Sch Aeronaut & Astronaut Dalian 116024 Peoples R China

A symplectic algorithm with nonuniform grids is proposed for solving the hypersensitive optimal control problem using the density function. The proposed method satisfies the first-order necessary conditions for the optimal control problem that can preserve the structure of the original Hamiltonian systems. Furthermore, the explicit Jacobi matrix with sparse symmetric character is derived to speed up the convergence rate of the resulting nonlinear equations. Numerical simulations highlight the features of the proposed method and show that the symplectic algorithm with nonuniform grids is more computationally efficient and accuracy compared with uniform grid implementations. Besides, the symplectic algorithm has obvious advantages on optimality and convergence accuracy compared with the direct collocation methods using the same density function for mesh refinement.

关键词： optimal control problem Hamiltonian system boundary-value problem hypersensitive problem symplectic algorithm

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Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method

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Applied Geophysics 2017年第2期14卷 258-269,323页

作者： Fang Gang Ba Jing Liu Xin-xin Zhu Kun Liu Guo-Chang The Key Laboratory of Gas Hydrate Ministry of Land and Resources Qingdao Institute of Marine Geology Qingdao 266071 China Laboratory for Marine Mineral Resources Qingdao National Laboratory for Marine Science and Technology Qingdao 266071 China School of Earth Sciences and Engineering Hohai University Nanjing 211100 China School of Geosciences China University of Petroleum （East China） Qingdao 266580 China State Key Laboratory of Petroleum Resources and Prospecting China University of Petroleum-Beijing Beijing 102249 China.

Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference （symplectic FFD） method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.

关键词： symplectic algorithm Fourier finite-difference Hamiltonian system seismic modeling anisotropic

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New way to construct high order Hamiltonian variational integrators

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Applied Mathematics and Mechanics(English Edition) 2016年第8期37卷 1041-1052页

作者： Minghui FU Kelang LU Weihua LI S. V. SHESHENIN School of Engineering Sun Yat-sen University Guangzhou 510275 China Guangdong Provincial Academy of Building Research Group Company Limited Guangzhou 510500 China College of Electromechanical Engineering Guangdong Polytechnic Normal University Guangzhou 510635 China Faculty of Mechanics and Mathematics Lomonosov Moscow State University Moscow 119992 Russia

This paper develops a new approach to construct variational integrators. A simplified unconventional Hamilton＇s variational principle corresponding to initial value problems is proposed, which is convenient for applications. The displacement and mo- mentum are approximated with the same Lagrange interpolation. After the numerical integration and variational operation, the original problems are expressed as algebraic equations with the displacement and momentum at the interpolation points as unknown variables. Some particular variational integrators are derived. An optimal scheme of choosing initial values for the Newton-Raphson method is presented for the nonlinear dynamic system. In addition, specific examples show that the proposed integrators are symplectic when the interpolation point coincides with the numerical integration point, and both are Gaussian quadrature points. Meanwhile, compared with the same order symplectic Runge-Kutta methods, although the accuracy of the two methods is almost the same, the proposed integrators are much simpler and less computationally expensive.

关键词： Hamiltonian system variational integrator symplectic algorithm unconventional Hamilton＇s variational principle nonlinear dynamics

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Multi-objective transfer to libration-point orbits via the mixed low-thrust and invariant-manifold approach

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NONLINEAR DYNAMICS 2014年第1-2期77卷 321-338页

作者： Peng, Haijun Chen, Biaosong Wu, Zhigang Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dept Engn Mech Dalian 116024 Peoples R China Dalian Univ Technol Sch Aeronaut & Astronaut State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China

The multi-objective optimization of transfer trajectories from an orbit near Earth to a periodic libration-point orbit in the Sun-Earth system using the mixed low-thrust and invariant-manifold approach is investigated in this paper. A two-objective optimization model is proposed based on the mixed low-thrust and invariant-manifold approach. The circular restricted three-body model (CRTBP) is utilized to represent the motion of a spacecraft in the gravitational field of the Sun and Earth. The transfer trajectory is broken down into several segments;both low-thrust propulsion and stable manifolds are utilized based on the CRTBP in different segments. The fuel cost, which is generated only by the low-thrust trajectory for transferring the spacecraft from an orbit near Earth to a stable manifold, is minimized. The total flight time, which includes the time during which the spacecraft is controlled by the low-thrust trajectory and the time during which the spacecraft is moving on the stable manifold, is also minimized. Using the nondominated sorting genetic algorithm for the resulting multi-objective optimization problem, highly promising Pareto-optimal solutions for the transfer of the spacecraft are found. Via numerical simulations, it is shown that tradeoffs between time of flight and fuel cost can be quickly evaluated using this approach. Furthermore, for the same time of flight, transfer trajectories based on the mixed-transfer method can save a larger amount of fuel than the low-thrust method alone.

关键词： Multi-objective optimization Nonlinear optimal control symplectic algorithm Circular restricted three-body problem Low-thrust transfer Invariant manifold

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Nonlocal Analytical Formulas for Plane Crack Elements and Semi-Analytical Element Method for Mode I Crack

Nonlocal Analytical Formulas for Plane Crack Elements and Se...

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2nd International Conference on Advances in Computational Modeling and Simulation (ACMS 2013)

作者： Zheng, Changliang Yao, Zheng Dalian Maritime Univ Transportat Equipment & Ocean Engn Coll Dalian 116026 Liaoning Peoples R China

ISBN: (纸本)9783037859063

This paper presents the series solutions in Hamiltonian form for plane sectorial domain of the nonlocal linear elasticity originally proposed by Eringen [1]. Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques were employed to obtain these solutions. These solutions can be used to develop a nonlocal analytical finite element for the model I crack in nonlocal fracture mechanics.

关键词： Nonlocal mechanics Hamilton theory Variational principle symplectic algorithm Plane fracture

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