Integration of an Equilibrium System in an Enhanced Theory of Bending of Elastic Plates

The complete integral of the system of partial differential equations governing the equilibrium bending of elastic plates with transverse shear deformation and transverse normal strain is constructed by means of complex variable methods. The process helps to elucidate the physical meaning of certain analytic constraints imposed on the asymptotic behavior of the solutions and shows that in the case of an infinite plate, any analytic solution has finite energy if and only if the bending and twisting moments, the transverse shear force, the displacements in vertical planes, and two other characteristic quantities vanish at infinity. An example is discussed to illustrate the theory.     

Two-Dimensional Magnetoelastic Problem for a Multiply Connected Piezomagnetic Body

A general method based on complex variable theory is proposed to determine the magnetic and elastic fields of a piezomagnetic body. This method is used to derive the basic relations for complex potentials in the two-dimensional problem of magnetoelasticity, their general representations for a multiply connected domain, expressions for stresses, displacements, vectors of magnetic field intensity and magnetic flux density, and magnetic field potential. A closed-form solution is obtained for a body with an elliptic (circular) hole or crack subjected at infinity to the action of a constant magnetoelastic field. Numerical results for a piezomagnetic plate with a circular hole are presented __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 64–74, October 2005.     

Finite dimensional dynamics for evolutionary equations

We suggest a new method for studying finite dimensional dynamics for evolutionary differential equations. We illustrate this method for the case of the KdV equation. As a side result we give constructive solutions of the boundary problem for the Schrodinger equations whose potentials are solutions of stationary KdV equations and their higher generalizations.     

单层平面索网幕墙结构的风振响应分析及实用抗风设计方法

单层平面索网玻璃幕墙结构是广泛应用于大型公共建筑中的一种新型结构形式,由于其具有柔性大、质量轻、阻尼小、自振频率低的特点,属风敏感结构。由于单索幕墙具有较高的几何非线性,本文采用基于随机振动理论的模态叠加频域方法进行了单索幕墙结构的风振响应分析。将模态叠加频域方法的计算结果和非线性时程分析方法的精确计算结果进行了比较,证明了该方法的准确性。并且本文通过分析各阶模态对单索幕墙结构风振响应的贡献,得到脉动风荷载下结构的振动以第一阶模态为主的结论。根据该结论本文采用频域方法推导了单索幕墙结构的位移均方差和索内力均方差的实用计算公式,同时考虑单索幕墙的结构特点提出了基于结构响应的单索幕墙结构实用抗风设计方法。     

Boundary contour analysis for surface stress recovery in 2-D elasticity and Stokes flow

Summary A variant of the boundary element method, called the boundary contour method, offers a further reduction in dimensionality. Consequently, boundary contour analysis of 2-D problems does not require any numerical integration at all. In a boundary contour analysis, boundary stresses can be accurately computed using the approach proposed in Ref. [1]. However, due to singularity, this approach can be used only to calculate boundary stresses at points that do not lie at an end of a boundary element. Herein, it is shown that a technique based on the displacement/velocity shape functions can overcome this drawback. Further, the approach is much simpler to apply, requires less computational effort, and provides competitive accuracy. Numerical solutions and convergence study for some well-known problems in linear elasticity and Stokes flow are presented to show the effectiveness of the proposed approach. This research was supported in part by the 2004 Ralph E. Powe Junior Faculty Enhancement Award from Oak Ridge Associated Universities and by the University of South Alabama Research Council.     

Self-similar approximants of the permeability in heterogeneous porous media from moment equation expansions

We use a mathematical technique, the self-similar functional renormalization, to construct formulas for the average conductivity that apply for large heterogeneity, based on perturbative expansions in powers of a small parameter, usually the log-variance of the local conductivity. Using perturbation expansions up to third order and fourth order in obtained from the moment equation approach, we construct the general functional dependence of the scalar hydraulic conductivity in the regime where is of order 1 and larger than 1. Comparison with available numerical simulations show that the proposed method provides reasonable improvements over available expansions.     

微分求积方法对于桩基大变形分析的应用

本文基于大变形的理论,采用弧坐标首先建立了具有初始位移的桩基的非线性数学模型,一组强非线性的微分-积分方程,其中,地基的抗力采用了Winkeler模型;其次,引入变数变换将微分-积分方程转化为一组非线性微分方程,并用微分求积方法离散了方程组,得到一组离散化的非线性代数方程;最后用Newton-Raphson迭代方法对离散化方程进行了求解,得到了桩基变形前后的构形、弯矩和剪力.计算中选取了两种不同类型的初始位移,并考察了它们对桩基大变形力学行为的影响.     

半平面多边缘裂纹反平面问题的奇异积分方程

利用复变函数和奇异积分方程方法,求解弹性范围内半平面多边缘裂纹的反平面问题．提出了满足半平面边界自由的由分布位错密度表示的单边缘裂纹的基本解,此基本解由主要部分和辅助部分组成．将半平面多边缘裂纹问题看作是许多单边缘裂纹问题的叠加,建立了一组Cauchy型奇异积分方程．然后,利用半开型积分法则求解该奇异积分方程,得到了裂纹端处的应力强度因子．最后,给出了几个数值算例．     

A NEW CYCLIC J-INTEGRAL FOR LOW-CYCLE FATIGUE CRACK GROWTH

The constitutive equation under the low-cycle fatigue (LCF) was discussed, and a two-dimensional (2-D) model for simulating fatigue crack extension was put forward in order to propose a new cyclic J-integral. The definition, primary characteristics, physical interpretations and numerical evaluation of the new parameter were investigated in detail. Moreover, the new cyclic J-integral for LCF behaviors was validated by the compact tension (CT) specimens. Results show that the calculated values of the new parameter can correlate well with LCF crack growth rate, during constant-amplitude loading. In addition, the phenomenon of fatigue retardation was explained through the viewpoint of energy based on the concept of the new parameter.