Variational Approach to the Lane-Emden Equation

By the semi-inverse method, a variational principle is obtained for the Lane-Emden equation, which gives much numerical convenience when applying finite element methods or Ritz method.

A Variational Approach to the Burridge-Knopoff Equation

A variational principle is obtained for the Burridge-Knopoff model for earthquake faults, and this paper considers an analytic approach that does not require linearization or perturbation.

Variational Approach to the Thomas-Fermi Equation

By the semi-inverse method, a variational principle is obtained for the Thomas-Fermi equation, then the Ritz method is applied to solve an analytical solution, which is a much simpler and more efficient method.

Generalized rayleigh principle and its applications

In this paper, we mainly deal with cigenvalue problems of non-self-adjoint operator. To begin with, the generalized Rayleigh variational principle, the idea of which was due to Morse and Feshbach, is examined in detail and proved more strictly in mathematics. Then, other three equivalent formulations of it are presented. While applying them to approximate calculation we find the condition under which the above variational method can be identified as the same with Galerkin's one. After that we illustrate the generalized variational principle by considering the hydrodynamic stability of plane Poiseuille flow and Bénard convection. Finally, the Rayleigh quotient method is extended to the cases of non-self-adjoint matrix in order to determine its strong eigenvalne in linear algebra.

Research on the influence of fabrication parameters on the performance of buried ion-exchanged glass waveguides using the variational method

The variational method is proposed to analyze the influence of the fabrication parameters on the performance of buried K+-Na+ ion-exchanged Er3+-Yb3+ ions co-doped glass waveguide. The unknown parameters of the Hermite-Gaussian functions as the trial field distribution are determined based on the scalar variational principle. It is demonstrated that the results calculated in this paper agree with those measured in the experiment. The mode dimensions, the effective refractive index, and the overlap factor as the functions of the fabrication parameters are investigated. These results of the variational analysis are useful for the design and optimization of Er3+-Yb3+ ions co-doped waveguides.

Unified expressions of all integral variational principles

In terms of the quantitative causal principle, this paper obtains a general variational principle, gives unified expressions of the general, Hamilton, Voss, Holder, Maupertuis-Lagrange variational principles of integral style, the invariant quantities of the general, Voss, Holder, Maupertuis-Lagrange variational principles are given, finally the Noether conservation charges of the general, Voss, Holder, Maupertuis-Lagrange variational principles axe deduced, and the intrinsic relations among the invariant quantities and the Noether conservation charges of all the integral variational principles axe achieved.

Preliminary report on the energy balance for nonlinear oscillations

In this paper, a reliable technique for calculating angular frequencies of nonlinear oscillators is developed. The new algorithm offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. Some illustrative examples are given. (C) 2002 Published by Elsevier Science Ltd.

Computation of stress intensity factors by the sub-region mixed finite element method of lines

Based on the sub-region generalized variational principle, a sub-region mixed version of the newly-developed semi-analytical 'finite element method of lines' (FEMOL) is proposed in this paper for accurate and efficient computation of stress intensity factors (SIFs) of two-dimensional notches/cracks. The circular regions surrounding notch/crack tips are taken as the complementary energy region in which a number of leading terms of singular solutions for stresses are used, with the sought SIFs being among the unknown coefficients. The rest of the arbitrary domain is taken as the potential energy region in which FEMOL is applied to obtain approximate displacements. A mixed system of ordinary differential equations (ODEs) and algebraic equations is derived via the sub-region generalized variational principle. A singularity removal technique that eliminates the stress parameters from the mixed equation system eventually yields a standard FEMOL ODE system, the solution of which is no longer singular and is simply and efficiently obtained using a standard general-purpose ODE solver. A number of numerical examples, including bi-material notches/cracks in anti-plane and plane elasticity, are given to show the generally excellent performance of the proposed method.

Bending solution of high-order refined shear deformation-theory for rectangular composite plates

A new high-order refined shear deformation theory based on Reissner's mixed variational principle in conjunction with the state- space concept is used to determine the deflections and stresses for rectangular cross-ply composite plates. A zig-zag shaped function and Legendre polynomials are introduced to approximate the in-plane displacement distributions across the plate thickness. Numerical results are presented with different edge conditions, aspect ratios, lamination schemes and loadings. A comparison with the exact solutions obtained by Pagano and the results by Khdeir indicates that the present theory accurately estimates the in-plane responses.

Magnetohydrodynamics equilibrium of a self-confined elliptic plasma ball

A variational principle is applied to the problem of magnetohydrodynamics (MHD) equilibrium of a self-contained elliptical plasma ball, such as elliptical ball lightning. The principle is appropriate for an approximate solution of partial differential equations with arbitrary boundary shape. The method reduces the partial differential equation to a series of ordinary differential equations and is especially valuable for treating boundaries with nonlinear deformations. The calculations conclude that the pressure distribution and the poloidal current are more uniform in an oblate self-confined plasma ball than that of an elongated plasma ball. The ellipticity of the plasma ball is obviously restricted by its internal pressure, magnetic field, and ambient pressure. Qualitative evidence is presented for the absence of sighting of elongated ball lightning.

Application of the strain energy density criterion to ductile fracture

The strain energy density criterion due to Sih is used to predict fracture loads of two thin plates subjected to large elastic-plastic deformation. The prediction is achieved with a finite element analysis which is based on Hill's variational principle for incremental deformations capable of solving gross yielding problems involving arbitrary amounts of deformation. The computed results are in excellent agreement with those obtained in Sih's earlier analysis and with an experimental observation.

带压电陶瓷片梁的力学分析和二类变量广义变分原理

对于采用贴有压电陶瓷片作为作动元件的智能结构，在进行自适应控制时，往往要分析压电陶瓷片所引起的结构中的应力、应变和位移。对于带有压电陶瓷片梁的力学分析，文献中大多采用Euler-Bernoulli模型，即不考虑梁中的剪力，且假定梁沿厚度方向满足直法线假定。考虑到压电陶瓷片对梁的作用主要是通过粘贴层以剪力的形式传递到梁上，梁截面上的剪应力和剪应变一般很大，其影响不能忽略。本文采用Hellinger-Reissner二类变分广义余能原理，导出考虑梁截面上剪应力和剪应变影响的方程式，其中采用吉尔法求解非齐次常微分方程组。并将求得的解与相同条件的有限元解进行比较。结果证明该方法很有效。本文还对二类广义变分法进行了一般的讨论，发现，在使用二类广义变分法求解时，随着应力和位移所取项数的增加，结果有时反而变坏。并对二类广义变分法的使用提出了一些建议。

Solitary magnon excitations in a one-dimensional antiferromagnet with Dzyaloshinsky-Moriya interactions

We investigate solitary excitations in a model of a one-dimensional antiferromagnet including a single-ion anisotropy and a Dzyaloshinsky-Moriya antisymmetric exchange interaction term. We employ the Holstein-Primakoff transformation, the coherent state ansatz and the time variational principle. We obtain two partial differential equations of motion by using the method of multiple scales and applying perturbation theory. By so doing, we show that the motion of the coherent amplitude must satisfy the nonlinear Schrodinger equation. We give the single-soliton solution.

Extremum principle of crystal plasticity

An analytical method for determining slip shear rate under prescribed stress rate or prescribed strain rate has been presented on the basis of the incremental theory of crystal plasticity. The problem has been reduced to a quadric convex programming.In order to analyse the plastic response of crystals subjected to external load, two new extremum principles are proposed. They are equivalent to the boundary-value problem of crystal plasticity. By the new extremum principles, the slip shear rates are independent function which can be obtained from the variational equation.

Novel Investigation on Principle of Similarity for Microgravity Two-Phase Flow

根据两流体同心环状流线性稳定性分析的结果 ,对微重力气 /液两相流地面模拟实验所应遵循的相似准则进行了探讨 ,得到了一个新的重力无关性准则 ,即Bond数和环形区流体相的毛细数之比的绝对值不大于 1 .此外 ,微重力气 /液两相流模拟实验还必须满足两个条件 ,即流量比和气相表观Weber数应与所模拟的流动中对应数值相等 . In the present paper, the principle of similarity for two phase flows at microgravity is studied based on the results of the linear stability analysis of the two fluid concentric annular flow configuration. A new criterion of gravity independence, namely the absolute value of the ratio between the Bond number and the capillary number of the phase flowing in the annulus is no more than one, is achieved. It is also pointed out that the flowrate ratio and the gas superficial Weber number must have the same ...