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Variational principles OF FLUID FULLFILLED ELASTIC SOLIDS

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Applied Mathematics and Mechanics(English Edition) 1999年第3期20卷 262-268页

作者：石志飞黄淑萍章梓茂 Northern Jiaotong University Beijing P R China

The generalized Variational principles of isothermal quasi-static fluid full-filled elastic solids are established by using variational Integral Method. Then by introducing constraints, several kinds of Variational principles are worked out, including five-field variable, four-field variable, three-field variable and two-field variable formulations. Some new Variational principles are presented besides the principles noted in the previous works. Based on Variational principles, finite element models can be set up.

关键词： fluid full-filled elastic solids variational integral method Variational principles generalized Variational principles

Dynamics of Nonholonomic Systems from Variational principles Embedded Variation Identity

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Dynamics of Nonholonomic Systems from Variational Principles...

THE Variational principles FOR PYROELECTRIC MEDIA

第十二届全国非线性振动暨第九届全国非线性动力学和运动稳...

作者： Yong-Xin Guo and Shi-Xing Liu Physics College, Liaoning University, Shenyang 110036, ChinaChang Liu Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China

Nondeterminacy of dynamics, i.e., the nonholonomic or the vakonomic, fundamental Variational principles, e.g. the Lagrange-d’Alembert or Hamiltonian, and variational operators, etc., of nonholonomic mechanical systems can be attributed to the non-uniqueness of ways how to realize nonholonomic constraints. Making use of a variation identity of nonholonomic constraints embedded into the Hamilton’s principle with the method of Lagrange undermined multipliers, three kinds of dynamics for the nonholonomic systems including the vakonomic and nonholonomic ones and a new one are obtained if the variation is respectively reduced to three conditional variations: vakonomic variation, Hlder’s variation and Suslov’s variation, defined by the identity. Therefore, different dynamics of nonholonomic systems can be derived from an integral variational principle, utilizing one way of embedding constraints into the principle, with different variations. It is verified that the similar embedding of the identity into the Lagrange-d’Alembert principle gives rise to the nonholonomic dynamics but fails to give the vakonomic one unless the constraints are integrable.

关键词： Nonholonomic systems Variational principles variation identity Chetaev’s condi- tion vakonomic dynamics ideal constraints

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Acta Mechanica Solida Sinica 1995年第4期8卷 303-313页

作者： Wang, XM Shen, YP XIAN JIAOTONG UNIV DEPT ENGN MECHXIAN 710049PEOPLES R CHINA

The pyroelectric medium is an important material in the application of smart materials and structures. It is necessary to systematically discuss ail kinds of Variational principles which play a very significant role in the fundamental theory of mechanics and numerical analysis method. This paper firstly gives the quasi-static and the dynamic Variational principles,then the principles for eigen problems. As a simple example, the principle was finally applied to derive the fundamental, equations for an anisotropic piezoelectric plate.

关键词： continuous mechanics pyroelectricity Variational principles smart material

STRUCTURAL FUNCTION THEORY OF GENERALIZED Variational principles FOR LINEAR ELASTIC MATERIALS WITH VOIDS

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Applied Mathematics and Mechanics(English Edition) 1991年第6期12卷 565-575页

作者：皮道华金莉华 Huazhong University of Science and Technology Wuhan

In this paper, we have obtained generalized Variational principles for linear elastic materials with voids from structural function theory. Correspondent relations between structural functions and generalized variatio... 详细信息

关键词： structural function void Variational principles

THE COMBINED ENERGY Variational principles IN LINEAR ELASTICITY

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Acta Mechanica Sinica 1985年第2期1卷 138-146页

作者： Xie Dingyi Wuhan Institute of Hydraulic and Electric Engineering Wuhan Institute of Hydraulic and Electric Engineering Wuhan China

In this paper, a new kind of mixed energy Variational principles in linear elasticity-thecombined energy Variational principles is presented. First, we define the conjugate body of an elasticbody, which is obtained by changing the boundary conditions of the elastic body. Next, we decomposethe conjugate body into two component-states, construct functionals of potential energy and com-plementary energy, respectively, for the component-states and define the additional hybrid energybetween the component-states. Thus the functionals of combined energy can be constructed. Threetypical combined energy Variational principles are demonstrated and the other forms of combinedenergy Variational principles are given. The application of the proposed principles to the calculation ofthin plates with complicated boundaries is shown.

关键词： conjugate body of an elastic body conjugate state component-state admissible combined state Variational principles elasticity.

Joint parameter and state estimation for stochastic uncertain system with multivariate skew t noises

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Chinese Journal of Aeronautics 2022年第5期35卷 69-86页

作者： Shuhui LI Zhihong DENG Xiaoxue FENG Ruxuan HE Feng PAN School of Automation Beijing Institute of TechnologyBeijing 100081China Kunming-BIT Industry Technology Research Institute INC Kunming 650106China

Due to the pulse interference, measurement outliers and artificial modeling errors, the multivariate skew t noise widely exists in the real environment. However, to date, little attention has been paid to the state estimation for systems in which the process noise and the measurement noise are both modeled as the heavy-tailed and skew non-Gaussian noise. In this paper, the multivariate skew t distribution is utilized to model the heavy-tailed and skew non-Gaussian noise. Then a probabilistic graphical form of the multivariate skew t distribution is given and proved. Based on the probabilistic graphical form, a hierarchical Gaussian state space model for stochastic uncertain systems is proposed, which transforms the estimation problem for systems with the heavy-tailed and skew non-Gaussian noises into the one with a hierarchical Gaussian state space model. Next, given the designed Gaussian state space model, the robust Bayesian filter and smoother based on the variational Bayesian inference are proposed to approximately estimate the system state and the unknown noise parameters. Furthermore, the complexity analysis together with the controllability and observability for stochastic uncertain systems with multivariate skew t noises is given. Finally,the simulation results of the target tracking scenario verify the validity of the proposed algorithms.

关键词： Estimation methods Non-Gaussian noise Target tracking Uncertain systems Variational principles

THE HYBRID PROBLEM OF FREE-SURFACE GRAVITY SPILLWAY FLOW TREATED BY Variational principles WITH VARIABLE DOMAIN: POTENTIAL fUNCTION FORMULATION

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Journal of Hydrodynamics 1992年第3期4卷 118-122页

作者： Liu Gao-lian Shanghai Institute of Applied Math.& Mechanics and Shanghai University of Technology Shanghai 200072,P.R.China

Making full use of functional variations with variable domain for handling both the free surface and unknown part of the dam wall,a family of Variational principles(VPs)for the hybrid(direct-inverse)problem of free surface spillway flow under gravity is formulated in terms of the potential function Φ.This theory offers new rational and versatile ways for dam de- sign and a sound theoretical basis for numerical solution,e.***.by the finite element method (FEM).

关键词： dam design finite element method free-surface gravity spillway flow Variational principles variable domain

Antiferromagnetism of Repulsively Interacting Fermions in a Harmonic Trap

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Chinese Physics Letters 2010年第8期27卷 65-68页

作者：祁建青王磊戴希 Beijing National Laboratory for Condensed Matter Physics and Institute of Physics Chinese Academy of Sciences Beijing 100190

We propose a real-space Gutzwiller variational approach and apply it to a system of repulsively interacting ultracold fermions with spin-1/2 trapped in an optical lattice with a harmonic confinement. Using the realspace Gutzwiller variational approach, we find that in a system with balanced spin-mixtures on a square lattice, antiferromagnetism either appears in a checkerboard pattern or forms a ring, and the antiferromagnetie order is stable in the regions where the particle density is close to one, which is consistent with the recent results obtained by the real-space dynamical mean-field theory approach. We also investigate the imbalanced case and find that the antiferromagnetic order is suppressed there.

关键词： ANTIFERROMAGNETISM FERMIONS HARMONIC oscillators RADIATION trapping Variational principles LATTICE theory MEAN field theory

Precision Calculations of Atomic Polarizabilities： A Relevant Physical Quantity in Modern Atomic Frequency Standard

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Chinese Physics Letters 2010年第6期27卷 78-81页

作者： GAO Xiang LI Jia-Ming Department of Physics Shanghai Jiao Tong University Shanghai 200240 Department of Physics and Key Laboratory of Atomic and Molecular Nanosciences of Ministry of Education Tsinghua University Beijing 100084

Electric dipole polarizabilities of atoms are very important in many different physical applications, such as the precision atomic frequency standard. Calculations of these properties are very important and challenging. We propose a calculation strategy to calculate the frequency dependent dipole polarizabilities with high precision variationally by using a set of high quality orbital bases where the electron correlations can be taken into account adequately. The static polarizabilitiez of the ground state of Na are calculated accurately by such a method and can be compared with precision experiment measurement directly. The calculation result is in excellent agreement with the available experimental measurements within about 0.1~, which demonstrates the validity of our strategy. Our calculation strategy has a wide usage, not only in polarizibilies, but also in other fields such as theoretical treatment of electron-atom scattering processes. Using the same orbital bases, we carry out precision calculation of Na- affinities. Our calculated affinity is in excellent agreement with precision laser spectroscopy measurements within 0. 1%.

关键词： PHYSICAL constants ATOMIC frequency standards DIPOLE moments POLARIZABILITY (Electricity) Variational principles ATOMIC orbitals SCATTERING (Physics) LASER spectroscopy