Computation Formulas of Generalized Inverse Padé Approximants Using for Solution of Integral Equations

For the generalized inverse function-valued Padé approximants, its intact computation formulas are given. The explicit determinantal formulas for the denominator scalar polynomials and the numerator function-valued polynomials are first established. A useful existence condition is given by means of determinant form. Foundation item: the National Natural Science Foundation of China (19871054) Biography: Gu Chuan-qing (1955-), Professor, Doctor Director     

ORTHOGONAL POLYNOMIALS AND DETERMINANT FORMULAS OF FUNCTION-VALUED PADE-TYPE APPROXIMATION USING FOR SOLUTION OF INTEGRAL EQUATIONS

To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Pade-type approximation is denned. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Pade-type approximation are explicitly given.     

Orthogonal polynomials and determinant formulas of function-valued Padé-type approximation using for solution of integral equations

To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given. Project supported by the National Natural Science Foundation of China (No.10271074)     

黏弹性地基上梁的力学行为分析

 考虑地基土(或基础)的黏弹性性态，基于黏弹性力学的基本原 理，采用Fourier级数，建立了梁的力学分析模型，给出了Maxwell与 Kelvin地基(或基础)上梁的变形和内力表达式. 文末的工程实例表明， 所建立的力学模型正确，可用于对各种工程中的基础梁分析.     

An approach for obtaining approximate formulas for the Rayleigh wave velocity

In this paper, we introduce an approach for finding analytical approximate formulas for the Rayleigh wave velocity for isotropic elastic solids and anisotropic elastic media as well. The approach is based on the least-square principle. To demonstrate its application, we applied it in order to obtain an explanation for Bergmann’s approximation, the earliest known approximation of the Rayleigh wave velocity for isotropic elastic solids, and used it to establish a new approximation. By employing this approach, the best approximate polynomials of the second order of the cubic power and the quartic power in the interval [0, 1] were found. By using the best approximate polynomial of the second order of the cubic power, we derived an approximate formula for the Rayleigh wave speed in isotropic elastic solids which is slightly better than the one given recently by Rahman and Michelitsch by employing Lanczos’s approximation. Also by using this second order polynomial, analytical approximate expressions for orthotropic, incompressible and compressible elastic solids were found. For incompressible case, it is shown that the approximation is comparable with Rahman and Michelitsch’s approximation, while for the compressible case, it is shown that our approximate formulas are more accurate than Mozhaev’s ones. Remarkably, by using the best approximate polynomials of the second order of the cubic power and the quartic power in the interval [0, 1], we derived an approximate formula of the Rayleigh wave velocity in incompressible monoclinic materials, where the explicit exact formulas of the Rayleigh wave velocity so far are not available.     

Instability of Dual Eigenvalue Fourth-Order Systems

Investigations of the postbuckling behavior of an elastic structure at a twofold branching point generally involve a potential of the cubic type. However, when the cubic part vanishes identically (for example, when there is symmetry in both active coordinates), the potential becomes of the quartic type. Here, quartic potentials in normalized coordinates are considered and formulas for limit points and bifurcations on imperfect paths are given in terms of trigonometric polynomials. These are used in certain structural examples to show that a theorem of Ho is invalid unless extra conditions are placed on the potential. They are also used in a proof of the modified Ho theorem.     

正交各向异性平面问题应力强度因子的边界元分析

本文给出了正交各向异性平面弹性问题的边界元方程，导出了常单元离散化时求系数的解析式。作为数值算例，计算了正交各向异性板的应力强度因子。结果表明，本文所导出公式的正确性。     

EPSILON-ALGORITHM AND ETA-ALGORITHM OF GENERALIZED INVERSE FUNCTION-VALUED PAD APPROXIMANTS USING FOR SOLUTION OF INTEGRAL EQUATIONS

Two efficient recursive algorithms epsilon-algorithm and eta-algorithm are introduced to compute the generalized inverse function-valued Padé approximants. The approximants were used to accelerate the convergence of the power series with function-valued coefficients and to estimate characteristic value of the integral equations. Famous Wynn identities of the Padé approximants is also established by means of the connection of two algorithms. Foundation items: the National Natural Science Foundation of China (10271074) Biographies: LI Chun-jing (1958 −) GU Chuan-qing (1955 −)     

Transport properties of nonequilibrium polyatomic gas mixtures

It is shown that the well-known Hirschfelder-Euken correction to the thermal conductivity of a polyatomic gas mixture given by the first approximation in Sonine polynomials can be less than the corresponding exact value (for a Lorentz mixture of light and heavy molecules interacting in accordance with Coulomb's law) by a factor of 3.4. Fairly high accuracy is achieved in the second approximation in Sonine polynomials. Within the framework of the latter, similar corrections to the nonequilibrium heat and diffusion fluxes are found. On the basis of the generalized Chapman-Enskog method a more general case is studied. In this case some of the nonelastic collision integrals is also taken into account in calculating the transport coefficients. The transport coefficients are either represented in terms of the well-known formulas for fast and retarded internal molecular energy exchange or convenient approximate expressions are obtained.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 183–189, March–April, 1995.     

Efficient Approach to Description of Heat Transfer and Multicomponent Diffusion in Ionized Gases

The formulas for the heat fluxes of heavy components and electrons as well as the Stefan–Maxwell relations for the diffusion fluxes in amagnetic field are derived for amulticomponent two-temperature plasma with regard to the higher-order approximations in orthogonal expansions of the component distribution functions in Sonine polynomials. For the complex transport coefficients of heavy components and electrons exact formulas are obtained in the significantly simpler form as compared with the standard procedure of the Chapman–Enskog method with the minimum number of minimum-order matrix inversions.     

Solution of three-dimensional problems of elasticity theory using new formulas for harmonic polynomials

Approximate solutions of three-dimensional problems of elasticity theory are sought in the form of linear combinations of vector functions each of which satisfies a differential equation. The linear-combination coefficients are found by energy minimization of the difference between exact and approximate solutions. This can be realized in the first and second basic problems. Simple recursion relations and differentiation formulas for similar harmonic polynomials are obtained. The above-mentioned vector functions are constructed using these formulas and the Trefftz representation. The problem of a truncated pyramid is considered. Odessa University, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 4, pp. 11–18, April, 1999.     

两种各向异性材料界面周期裂纹的反平面问题

研究两种各向异性材料界面含周期裂纹的反平面剪切问题，运用复变函数方法，获得了封闭形式解答，并给出了应力强度因子公式。从本文解签的特殊情形，可直接导出均匀各向异性材料共线裂纹，两种各向同性材料界面裂纹的相应问题公式。     

Unsteady axisymmetric deformation of an elastic thick-walled sphere under the action of volume forces

This paper considers a homogeneous isotropic elastic body bounded by concentric spheres and acted upon by axisymmetric unsteady volume forces. Displacement fields are determined using series expansions in Legendre and Gegenbauer polynomials, Laplace transforms in time, and integral representations with kernels in the form of Green’s functions. Explicit formulas for the Green’s functions are constructed that allow accurate determination of the originals. Examples of the calculations are presented.     

岩体力学中流变与断裂的耦合作用

本文首先分析含Ｉ型裂纹岩石的流变断裂特性，提出了Ⅰ型裂纹流变断裂初度的三个阈值；然后应用断裂力学和粘塑性理论。得出了具有屈服、蠕变和Ⅱ型裂纹扩展等物理力学特性的岩体隧洞的衬砌与围岩应力的解析表达式。     

两种各向异性材料界面共线裂纹的反平面问题

本文研究两种各向异性材料界面共线裂纹的反平面剪切问题。利用复变函数方法，提出了一般问题公式和某些实际重要问题的封闭形式解。考察了裂纹尖端附近的应力分布并给出了应力强度因子公式。从本文解签的特殊情形，可以直接导出两种各向同性材料界面裂纹，均匀各向异性材料共线裂纹以及均匀各向同性材料共线裂纹的相应问题公式，其中包括已有的经典结果。     

尖端具有线性粘着力作用的加层空间的界面裂纹对稳态弹性波的散射

本文研究一类粘着型界面裂纹的弹性波散射问题．文中利用积分变换和积分方程方法推导了确定这类问题的奇异积分方程组．采用围道积分技术和切比雪夫多项式展开技术，得到了待定系数的非线性代数方程组．最后本文给出裂纹尖端粘着区的大小和界面应力的数值结果．     

环板在两种不同荷载共同作用下的塑性极限分析

本文针对外边界支承环板的塑性极限分析问题,应用奇异函数给出一种简便的分析方法,并分四种情况给出环板在两种不同荷载共同作用下的极限荷载的计算公式。     

黎曼位形空间中约束多体系统的动力学分析

在黎曼位形空间中研究了约束多体系统的动力学问题．通过对约束矩阵的奇异值分解和修正的Ｇｒａｍ Ｓｃｈｍｉｄｔ过程构造了系统流形的法向和切向子空间的正交归一化基，将系统的动力学方程沿这双基进行投影，得到了求系统动力学响应的新型公式，给出了其数值分析的一种方法，并举了算例．     

圆柱壳在侧向非对称冲击载荷下的塑性动力屈曲

采用塑性动力屈曲能量准则，对圆柱壳非均匀局部径向冲击下的塑性动力屈曲进行了研究。文中分别采用弹性的角弹簧和位移弹簧模拟非屈曲部分对屈曲部分的影响，推导了有关模态和临界速度的冲击公式，并与有关的实验结果进行了比较，分析了两种边界对塑性动力屈曲的影响。