薄板哈密顿含参变分原理

将薄板哈密顿变分原理及其泛函∏_H(w,M_x,Ψ_x,V_x)推广为含两个可选参数η₁和η₂的薄板哈密顿含参变分原理及其含参泛函∏_Hη1η2(w,M_x,Ψ_x,V_x).其推导过程为:首先将薄板Hellinger-Reissner变分原理及其泛函∏_HR(w,{M})推广为含可选参数的薄板Hellinger-Reissner含参变分原理及其含参泛函∏_HRη1(w,{M}).然后采用消元法(消去变量M_y和M_xy)和换元乘子法(增加变量Ψ_x和V_x)由含参泛函∏_HRη1(w,{M})导出含两个可选参数的薄板哈密顿含参泛函∏_Hη1η2(w,M_x,Ψ_x,V_x).含参变分原理是多种变分原理的组合形式,并使多种变分原理之间得到沟通和融合.通过对参数η₁和η₂的合理选取和赋值,可以得到含参泛函的多种退化形式,为建立多种有限元模型创造条件.     

Complementary variational principles for a class of biharmonic problems

Summary Maximum and minimum principles for certain plate bending problems are derived in a unified manner from the canonical theory of complementary variational principles for multiple operator equations. The minimum principle is known in the literature, but the maximum principle appears to be new. A new error bound for approximate variational solutions is also presented.     

广义变分原理在高速铁路无缝道岔结构分析中的应用

在继承现有试验成果的基础上,将广义变分原理应用于铁路无缝道岔结构体系的分析,提出了一种新的铁路无缝道岔计算理论。建立了较为完善的计算模型,在假设钢轨纵向位移函数的基础上,计算了无缝道岔结构体系各部分的能量,通过广义变分法建立了结构体系的平衡方程,编制了计算程序,分析了固定辙叉无缝道岔钢轨温度力与位移。为无缝道岔计算理论和设计方法的研究开辟一条新途径。     

Finite element method applied to analysis of flow over a spillway crest

Numerical analysis of fluid flow over a spillway is treated in the present paper. A variational principle is introduced for a flow with a free surface boundary under gravity, where the stream function and the profile of the free boundary are independent quantities subjected to variation. A new iteration method is formulated by the combined use of the variational principle and the finite element method. A numerical example based on the iterative method is illustrated. Results thus obtained show good agreement with those obtained from an empirical formula.     

A variational principle in optics

We derive a new variational principle in optics. We first formulate the principle for paraxial waves and then generalize it to arbitrary waves. The new principle, unlike the Fermat principle, concerns both the phase and the intensity of the wave. In particular, the principle provides a method for finding the ray mapping between two surfaces in space from information on the wave's intensity there. We show how to apply the new principle to the problem of phase reconstruction from intensity measurements.     

Variational principles for generalized thermodiffusion theory in pyroelectricity

The universal thermodynamic variational principle proposed in the previous papers for nonlinear dielectrics and thermopiezoelectricity is extended to the thermodiffusion theory in pyroelectricity, and it is used as a fundamental physical principle to derive the simple complete governing equations of the generalized thermo-electro-diffuso-elastic theory in this paper. In the generalized thermo-electro-diffuso-elastic theory it is assumed that the variation of temperature needs the extra heat which introduces the inertial entropy, and the variation of chemical potential also needs the extra heat which introduces the inertial concentration, etc. The electro-chemical Gibbs function variational principle, the electric Gibbs function variational principle and the internal energy variational principle are derived in this paper.     

Certain integral and differential types of variational principles in nonlinear piezoelectricity

Various forms of variational principles are developed and used to generate, as Euler-Lagrange equations, the fundamental differential equations of nonlinear piezoelectricity. First, Hamilton's principle is rigorously applied to the motion of an electroelastic solid with small piezoelectric coupling, and an associated variational principle is readily derived. Then, by use of the dislocation potentials and Lagrange undetermined multipliers (Friedrich's transformation), the variational principle is augmented for the motion of a piezoelectric solid region with an internal surface of discontinuity. To incorporate the constraints into the two-field variational principle, Friedrich's transformation is again applied, and a unified variational principle is systematically established. This unified variational principle is shown to produce the fundamental equations of an electroelastic solid with small piezoelectric coupling.     

Variational principles for the equations of porous piezoelectric ceramics

The governing equations of a porous piezoelectric continuum are presented in variational form, though they were well established in differential form. Hamilton's principle is applied to the motions of a regular region of the continuum, and a three-field variational principle is obtained with some constraint conditions. By removing the constraint conditions that are usually undesirable in computation through an involutory transformation, a unified variational principle is presented for the region with a fixed internal surface of discontinuity. The unified principle leads, as its Euler-Lagrange equations, to all the governing equations of the region, including the jump conditions but excluding the initial conditions. Certain special cases and reciprocal variational principles are recorded, and they are shown to recover some of the earlier ones.     

一种建立分区变分原理的新方法

提出了一种建立弹性理论分区变分原理的新方法。放松了分区交界面上位移、应力连续的条件,证明了弹性理论分区求解体系的微分形式与积分形式的等价关系。本文以微分形式为前提,利用这种等价关系,在统一的构架下,导出了分区广义虚功方程和弹性理论分区变分原理。变分原理是积分形式的一种表现形式。讨论了积分形式的物理含义,提出了广义虚函数的概念。广义虚函数具有任意性、虚拟性。     

Non-equilibrium thermodynamics and variational principles for fully coupled thermal–mechanical–chemical processes

In this paper, the chemical Gibbs function variational principle, the Helmholtz function variational principle and the internal energy variational principle based on irreversible thermodynamics are proposed for the thermal–chemical–mechanical fully coupling problems. The complete fully coupling governing equations, including the heat conduction, mass diffusion and chemical reactions, are derived from the variational principles. The convective effect can also be derived in the diffusion and energy equations from the variational principles naturally. Moreover, the concentrations and entropy jump conditions on the moving interface between the products due to chemical reactions and the matrix can be derived from the variational principles naturally. This work provides the basis for the analyses and computations of thermochemomechanical coupling problems.     

压电材料修正后的H-R混合变分原理及其层合板的精确法

将三维弹性体的Hellinger-Reissner(H-R)混合变分原理引入到具有机-电耦合效应的压电材料静力学问题中,建立了压电材料修正后的H-R混合变分原理,通过变分运算和分部积分得到了压电材料的状态向量方程.给出了四边简支的压电材料层合板静力学状态向量方程的精确求解方法,数值实例的结果证明了方法是正确性的.这里的理论和求解方法同样适应于纯弹性材料板和压电材料板混合的层合板静力学问题的分析.变分原理将有利于压电材料问题相应的半解析法或有限元法的推导.     

Computational structural mechanics and optimal control—the simulation of substructural chain theory to linear quadratic optimal control problems

The theory of optimal control and the theory of a substructural chain in static structural analysis are mutually simulated issues. From the minimum potential energy variational principle of the substructural chain, the generalized variational principle with two kinds of variables is derived first. By comparing that generalized variational principle with the variational principle in LQ control theory, the simulation relation is established. Based on that relation, the potential energy and mixed energy formulation of the algebraic Riccati equations are derived, then iterative algorithms are proposed which give the upper and lower bounds to the solution matrix. By using the solutions of the positive and negative co-ordinate algebraic Riccati equations, the canonical transformation matrices for the eigenproblems of the substructural chain and LQ control are constructed respectively, which reduce the eigenproblem to half-size. The properties of the solutions are analysed, which establishes the basis for expansion solutions.     

弹性膜结构静力学的各类变分原理

通过罗恩早已提出的一条简单而统一的新途径,系统地建立了弹性膜结构静力学的各类变分原理。首先给出膜结构静力学的广义虚功原理的表式,然后从该式出发,不仅能得到膜结构静力学的虚功原理,而且通过所给出的广义Legendre变换,还能系统地成对导出弹性膜结构静力学的3类变量、2类变量变分原理以及总势能驻值原理和总余能驻值原理的互补泛函。同时,通过这条新途径还能清楚地阐明这些原理的内在联系。     

The modeling and numerical analysis of wrinkled membranes

In this paper three fundamental issues regarding modeling and analysis of wrinkled membranes are addressed. First, a new membrane model with viable Young's modulus and Poisson's ratio is proposed, which physically characterizes stress relaxation phenomena in membrane wrinkling, and expresses taut, wrinkled and slack states of a membrane in a systematic manner. Second, a parametric variational principle is developed for the new membrane model. Third, by the variational principle, the original membrane problem is converted to a non‐linear complementarity problem in mathematical programming. A parametric finite element discretization and a smoothing Newton method are then used for numerical solution. The proposed membrane model and numerical method are capable of delivering convergent results for membranes with a mixture of wrinkled and slack regions, without iteration of membrane stresses. Three numerical examples are provided. Copyright © 2003 John Wiley & Sons, Ltd.     

An anisotropic elastic formulation for configurational forces in stress space

A new variational principle for an anisotropic elastic formulation in stress space is constructed, the Euler–Lagrange equations of which are the equations of compatibility (in terms of stress), the equilibrium equations and the traction boundary condition. Such a principle can be used to extend recently obtained configurational balance laws in stress space to the case of anisotropy.     

Lagrangian mechanics and variational integrators on two‐spheres

Euler–Lagrange equations and variational integrators are developed for Lagrangian mechanical systems evolving on a product of two‐spheres. The geometric structure of a product of two‐spheres is carefully considered in order to obtain global equations of motion. Both continuous equations of motion and variational integrators completely avoid the singularities and complexities introduced by local parameterizations or explicit constraints. We derive global expressions for the Euler–Lagrange equations on two‐spheres, which are more compact than existing equations written in terms of angles. Since the variational integrators are derived from Hamilton's principle, they preserve the geometric features of the dynamics such as symplecticity, momentum maps, or total energy, as well as the structure of the configuration manifold. Computational properties of the variational integrators are illustrated for several mechanical systems. In addition, Lie group variational integrators can be used to integrate Lagrangian flows on more general homogeneous spaces. This is achieved by lifting the discrete Hamilton's principle on homogeneous spaces to a discrete variational principle on the Lie group that is constrained by a discrete connection. Copyright © 2009 John Wiley & Sons, Ltd.     

板壳非线性分析的新理论新方法

提出了板壳非线性分析的新理论新方法.首先建立了下列几个新的本构关系:塑性应变向量增量与总应变向量增量的新关系,热塑性应变向量增量与总应变向量增量及温度应变向量增量的新关系,粘塑性应变向量增量与总应变向量增量的新关系,热粘塑性应变向量增量与总应变向量增量及温度应变向量增量的新关系.这些关系分别称为弹塑性应变增量理论、热弹塑性应变增量理论、弹粘塑性应变增量理论及热弹粘塑性应变增量理论,避开了屈服曲面、加载曲面、流动法则及复杂的非线性应力应变关系.其次建立了非线性样条无网格法,这种方法是以新的本构关系、几何非线性理论、变分原理、广义变分原理、加权残数法及样条离散化为基础建立的,避免了经典本构关系及有限元法带来的巨大困难及缺陷,不仅计算简便,而且精度高,收敛速度很快.建立了板壳非线性分析的统一格式,对板壳的几何非线性分析、材料非线性分析及双重非线性分析都适用.     

压电体的混合变分原理及叠层板的自由振动分析

建立了具有机一电耦合效应的压电材料修正后的Hellinger—Reissner(H—R)混合变分原理，并推导了压电材料的Hamilton正则方程，即压电材料自由振动的控制微分方程；根据矩阵分析理论给出了带有压电材料层的叠层矩形板自由振动的精确求解方法，文中没有引入任何位移模式或应力模式假设，实例分析得到了压电混合叠层板正逆效应两种情况自由振动的低阶频率，并与已有文献结果进行了比较。本文提出的压电材料修正后的H—R混合变分原理将有利于压电材料动力问题的有限元法或半解析法的推导。     

Electrochemical evaluation of the interaction between endocrine disrupter chemicals and estrogen receptor using 17,beta-estradiol labeled with daunomycin

A new electrochemical screening method for endocrine disrupting chemicals (EDCs) was developed. To evaluate the binding capacity of EDCs to the estrogen receptor (ER), 17beta-estradiol labeled with daunomycin as an electroactive compound was prepared. The electrochemical sensitivity of the prepared labeled estradiol (LE) was high, as compared with daunomycin. The interaction between LE and ER was observed by the decrease in the electrode response of LE, indicating the specific binding of LE with ER. The competitive reaction between LE and 17beta-estradiol for the limiting binding site on ER produced increases in the peak current of LE. The relative standard deviation at 1 x 10(-8) M 17beta-estradiol was about 10.0% (n = 7). The binding affinity between EDC and ER was also evaluated by comparison with 17beta-estradiol-ER interaction. Bisphenol A, p-nonylphenol and p,p'-DDT was used as a test compound. All test compounds demonstrated some ability to bind with ER. This electrochemical binding assay illustrates a new method for evaluating the binding capacity of EDCs to ER without the need for a separation procedure for the bound and free LE.