有限变形和应变近似分析

本文基于Ｃａｕｃｈｙ平均转动的新近成果，给出一种变形和应变的近似分析方法，在此基础上讨论了Ｇｒｅｅｎ应变的近似表达式及其误差计，这些近似表达式在求解非线性力学问题中是常采用的，文中关于Ｇｒｅｅｎ应变常用近表达式的误差估计是严格基于小应变－中等或大转动变形的明确定义而获得的。     

二维介质参数的大扰动反演方法

对非均匀介质参数反演问题进行了研究，并提出了用于反演二维介质参数的广义射线近似方法．利用参考场量和扰动变量对声波方程中的介质参数进行处理，并利用Ｇｒｅｅｎ函数理论得到扰动参数比的积分方程．基于非均匀介质中波函数的局部理论和射线理论，引入了全波场的广义射线近似形式，通过定义介质参数函数，把反演目标归结为其第一类Ｆｒｅｄｈｏｌｍ积分方程．利用积分变换方法得到二维介质的介质参数函数，从而得到介质参数，在Ｂｏｒｎ近似方法中，反演的介质参数扰动不能超过２０％，但是在本文中介绍的方法能够有效地反演其扰动比不超过５０％的变化情况     

SH波散射与界面圆孔附近的动应力集中

建立了求解含有界面圆孔的二种不同弹性组合介质中ＳＨ波的散射和界面圆孔附近的动应力集中问题的Ｇｒｅｅｎ函数法给出了一个具有半圆形缺口的弹性半空间水平表面上任意一点承受时间谐和的出平面线源荷载作用时位移函数的基本解取基本解作为Ｇｒｅｅｎ函数，建立起问题的定解积分方程最后给出了界面圆孔的动应力集中的算例和结果，并讨论了不同介质参数的组合对动应力集中的影响     

半无限弹性空间域内点加振格林函数的计算

本文给出了满足全部自由面边界条件的半无限弹性空间域内点加振的Ｇｒｅｅｎ函数，利用变形的Ｈａｎｋｅｌ函数，在复数域内进行无限积分的有限化，从而使Ｇｒｅｅｎ函数的计算变得比较简单和方便。     

介质参数反演的广义射线近似方法

在对无粘性介质参数反演问题进行的研究中，引入一种全波场广义射线近似形式，提出一种新的反演参数的方法，文中，首先对由弹性波动方程演变成的声波方程进行分析，引入背景场量和扰动量，并结合Ｇｒｅｅｎ函数理论，得到了介质参数的积分方程；然后结合前人对非均匀介质中波函数局部理论的定性分析，引入一种全波场广度射线近似形式，把问题归结为一个第一类Ｆｒｅｄｈｏｌｍ积分方程；最后对半空间问题层状介质模型进行了反演，算     

柔韧扁球壳在静载荷作用下的非线性振动

本文研究了均布静载荷作用下柔韧扁球壳的非线性自由振动问题,其静力边值问题采用线性解,在此平衡构型的基础上,通过引入Ｇｒｅｅｎ函数,将动力协调方程及对应的边界条件转化为等的积分方程,并把摄动变分法于动力平衡方程的变分形式,得出其非线性固有频率和振幅间的二次近似特征关系。     

对内爆炸荷载下地下竖井的动力响应一文的看法的附注

1.变分方程的坐标函数（或基函数）要求是完备的,否则原问题的泛函收敛性得不到保证,这在一般的数学或力学教科书中均有论述。翟文在径向选取的位移基函数e-n（n-1）（n=1.1,）不是完备的,所以原问题解的收敛性得不到保证。而且很难对各种已给初始数据（几何形状,几何尺寸,荷载形式等）求出预先指定精度的变分近似解来,因此,翟文所建议的方法很难说是合理的。     

变水深坝—库系统耦振分析的边界元—有限元混合法

常用的混合元法解变水深坝－库系统的耦振，需要对变水深部分的流场进行域离散，计算工作量大，该文利用Ｆｒｉｅｄｍａｎ的算子函数理论，构造了势流问题在无限长带形域中的Ｇｒｅｅｎ函数，从而使流场的边界元剖分只限于变水深区域的边界，关于坝体仍采用有限元离散，最后借助所导出的有限元－边界元格式对坝－库系统的实例作了数值计算，结果证明了它的有效性。     

孔边裂纹对SH波的散射及其动应力强度因子

采用Ｇｒｅｅｎ函数法研究任意有限长度的孔边裂纹对ＳＨ波的散射和裂纹尖端场动应力强度因子的求解．取含有半圆形缺口的弹性半空间水平表面上任意一点承受时间谐和的出平面线源荷载作用时位移函数的基本解作为Ｇｒｅｅｎ函数,采用裂纹“切割”方法并根据连接条件建立起问题的定解积分方程,得到动应力强度因子的封闭解答．最后给出了孔边裂纹动应力强度因子的算例和结果,并讨论了圆孔的存在对动应力强度因子的影响     

粘弹性大变形动力响应的有限元分析

本文基于Ｔｏｔａｌ Ｌａｇｒａｎｇｉａｎ增量叠加方法，采用Ｋｉｒｃｈｈｏｆｆ应力增量和Ｇｒｅｅｎ应变增量表示的动力虚功方程和Ｋｉｒｃｈｈｏｆｆ应力－Ｇｒｅｅｎ应变的单积分型本构关系，导出粘弹性大变形的动力变分方程。依此采用Ｎｅｗｍａｒｋ法和八节点轴对称等参数元与二十节点三维等参数元编制了轴对称及三维问题的动力响应计算程序，典型例题的计算结果表明分析符合结构的物理性质。     

Green’s functions of an exponentially graded transversely isotropic half-space

By virtue of a complete set of displacement potential functions and Hankel transform, the analytical expressions of Green’s function of an exponentially graded elastic transversely isotropic half-space is presented. The given solution is analytically in exact agreement with the existing solution for a homogeneous transversely isotropic half-space. Employing a robust asymptotic decomposition technique, the Green’s function is decomposed to the closed-form Green’s function corresponding to the homogeneous transversely isotropic half-space and grading term with strong decaying integrands. This representation is very useful for numerical methods which are based on boundary-integral formulations such as boundary-element method since the numerically evaluated part is not responsible for the singularity. The high accuracy of the proposed numerical scheme is confirmed by some numerical examples.     

集中力作用下的两相饱和介质位移场Green函数

以复模两相饱和介质Biot动力学方程为基础,根据该方程D'Alembert解的Fourier变换所属的Homholtz方程特性,由Biot方程解的相容性条件及δ函数性质较好地解决了快、慢纵波位势的耦合问题.较为简便地得到了两相饱和介质在集中力作用下低频(ω＜ωc)时的频域和时域的Green函数.     

三维粘弹性层状半空间埋置集中荷载动力格林函数求解—修正刚度矩阵法

针对三维粘弹性层状半空间埋置集中荷载作用下动力响应问题,在柱面坐标下,结合径向Hankel积分变换,提出了一种新的求解方法—修正刚度矩阵法。方法基于位势函数理论,将三维问题分解为平面内反应(P-SV波型)和平面外反应（SH波型）两个二维问题的叠加;借鉴结构力学中超静定结构的位移法原理,首先固定荷载所在层的上下界面,通过对波动方程的特解和齐次解叠加得到“固端”反力。进而放松两“固端约束”,利用直接刚度法求得各层面位移,荷载作用层内反应另需叠加上该“固定层”内解,并将特解部分积分（直达波）由全空间解析解代替,解决了当接收点和源点作用水平面接近时的积分收敛问题。算例分析表明,对于低频（可退化为静力状态）和高频问题,本文方法均具有很高的计算效率和精度。     

SH波对内含裂纹衬砌结构的散射及动应力集中

当衬砌结构内含裂纹时 ,采用Green函数的方法 ,研究了SH波对裂纹的散射及其动应力集中 ,构造了在含有半圆形衬砌的弹性半空间上 ,在水平面上任一点承受时间谐和出平面线源载荷作用时的位移函数作为Green函数 ;推导了SH波对衬砌内有裂纹的散射定解积分方程组 ,进而求得裂纹尖端的动应力因子 ,重点讨论了衬砌及周围介质对裂纹尖端动应力因子的影响 ,给出了介质参数变化对裂纹尖端动应力因子的影响曲线 ,为工程设计提供了依据。     

Stokes flow with injection in a plane duct

Summary In this paper flow at low Reynolds number is studied in a plane duct with injection along its boundaries, by determining the Green function for the Stokes equation in the strip: in this way it is possible to calculate the fluid-dynamic field for any distribution of injection. To obtain the bi-harmonic function that governs this problem we write the stream function in terms of two harmonic functions f and g, represent these functions using the relevant Green function and write the integral equations that determine f and g. The solution is obtained by means of the Fourier transform technique. An asymptotic representation of this solution is also given.

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Sommario In questo lavoro si studia il campo fluidodinamico determinato) dall'apporto di fluido in un condotto in cui scorre un fluido a piccoli numeri di Reynolds, determinando la funzione di Green per l'equazione di Stokes nella striscia: in tal modo si può calcolare il campo fluidodinamico per una qualsiasi distribuzione di iniezione. Per determinare la funzione biarmonica con derivata longitudinale infinita in alcuni punti della frontiera che governa questo problema, si scrive l'incognita in termini di funzioni armoniche, si utilizza la funzione di Green per rappresentare tali funzioni ausiliarie e si scrivono le equazioni integrali che le determinano. La soluzione di queste equazioni integrali viene ottenuta mediante la trasformata di Fourier. I risultati vengono presentati sia in forma numerica che con serie asintotiche.

     

On constructing a Green’s function for a semi-infinite beam with boundary damping

The main aim of this paper is to contribute to the construction of Green’s functions for initial boundary value problems for fourth order partial differential equations. In this paper, we consider a transversely vibrating homogeneous semi-infinite beam with classical boundary conditions such as pinned, sliding, clamped or with a non-classical boundary conditions such as dampers. This problem is of important interest in the context of the foundation of exact solutions for semi-infinite beams with boundary damping. The Green’s functions are explicitly given by using the method of Laplace transforms. The analytical results are validated by references and numerical methods. It is shown how the general solution for a semi-infinite beam equation with boundary damping can be constructed by the Green’s function method, and how damping properties can be obtained.     

Fundamental formulation for transformation toughening

In this paper, the transformation toughening problem is addressed in the framework of plane strain. The fundamental solution for a transformed strain nucleus located in an infinite plane is derived first. With this solution, the transformed inclusion problems are formulated by a Green’s function method, and the interaction of a crack tip with a single transformation source is found. On the basis of this solution, the fundamental formulations for toughening arising from martensitic and ferroelastic transformation are formulated also using the Green’s function method. Finally, some examples are provided to demonstrate the validity and relevance of the fundamental formulations proposed in the paper.     

基于DDA的弹性力学全高阶多项式位移逼近方法及其实例验证

基于维尔斯特拉斯多项式函数的逼近定理,通过DDA高阶全多项式位移函数条件下的弹性力学推导,提出了一个逼近弹性力学连续位移函数真解的全多项式位移函数逼近方法。该方法采用完整的高阶多项式位移函数,以不同阶次条件下的多项式系数为未知数,以单纯形积分为解析积分方法,通过建立和求解平衡方程,逐步逼近弹性体真解。在对单纯形积分计算过程研究的基础上,给出了三维空间单纯形计算图解法,该图解法诠释了三维空间单纯形积分公式中各变量间的逻辑关系及计算过程的图形表达。基于上述方法,编写了相应计算程序,并以一个三维简支梁受均布荷载及一个四周固定的弹性薄板受集中力作用两算例为实例,验证了所提方法的可行性。实例计算结果表明,随着逼近函数阶次的提高,数值方法获得的多项式函数计算值均单调地逐步逼近解析解。在文中所用的6阶多项式函数逼近中,简支梁实例位移计算误差小于0.2%,弹性薄板实例位移误差小于0.91%,并且,两算例与解析解位移差值都在微m级。     

Analysis of scattering waves in an elastic layered medium by means of the complete eigenfunction expansion form of the Green’s function

A scattering problem due to an object and a plane incident wave in an elastic layered half space is presented in this paper. The complete eigenfunction expansion form of the Green’s function developed by the author and the boundary integral equation method are introduced into the analysis. First, the complete eigenfunction expansion form of the Green’s function is investigated for its application to the scattering problem. A comprehensive explanation is also given for the fact that the complex Rayleigh wave modes exhibit standing waves. Next, a method for the analysis of scattering waves by means of the Green’s function is presented. The advantage of the present method is that the formulation itself is independent of the number of layers and the scattering waves can be decomposed into the modes for the spectra defined for the layered medium. Several numerical calculations are performed to examine the efficiency of the present method as well as the properties of the scattering waves. According to the numerical results, the complete eigenfunction expansion form of the Green’s function provides accurate values for application to a boundary element analysis. The spectral structure and radiation patterns of the scattering wave are presented and investigated. The differences in directionality can be found from the radiation patterns of the scattering waves decomposed into the modes for the spectra.     

GREEN QUASIFUNCTION METHOD FOR FREE VIBRATION OF SIMPLY-SUPPORTED TRAPEZOIDAL SHALLOW SPHERICAL SHELL ON WINKLER FOUNDATION

The idea of Green quasifunction method is clarified in detail by considering a free vibration problem of simply-supported trapezoidal shallow spherical shell on Winkler foundation.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of simply-supported trapezoidal shallow spherical shell on Winkler foundation is reduced to two simultaneous Fredholm integral equations of the second kind by Green formula.There are multiple choices for the normalized boundary equation.Based on a chosen normalized boundary equation, the irregularity of the kernel of integral equations is avoided.Finally, natural frequency is obtained by the condition that there exists a nontrivial solution in the numerically discrete algebraic equations derived from the integral equations.Numerical results show high accuracy of the Green quasifunction method.