Fracture Mechanics for a Mode Ⅲ Crack in a Piezoelectromagnetic Material

Analytical solutions for a Griffith crack inside an infinite piezoelectromagnetic medium under combined mechanical-electrical-magnetic loadings are formulated using integral transform method. The singular stress, elec tric and magnetic fields in the piezoelectromagnetic material are obtained by the theory of linear piezoelectromagneticity. Fourier transforms are used to reduce the mixed boundary value problems of the crack, which is as sumed to be permeable, to dual integral equations. The solution of the dual integral equations is then expressed analytically. Expressions for strains, stresses, electric fields, electric displacements, magnetic fields and magnetic inductions in the vicinity of the crack tip are derived. Field intensity factors and energy release rate for piezoelectromagnetic material are obtained. The stresses, electric displacements and magnetic inductions at the crack tip show the traditional square root singularities; and the electric field intensity factor （EFIF） and the magnetic field intensity factor （MFIF） are always zero.     

Fracture Mechanics for a Mode Ⅲ Crack in a Piezoelectromagnetic Material

Analytical solutions for a Griffith crack inside an infinite piezoelectromagnetic medium under combined mechanical-electrical-magnetic loadings are formulated using integral transform method. The singular stress, electric and magnetic fields in the piezoelectromagnetic material are obtained by the theory of linear piezoelectromagneticity. Fourier transforms are used to reduce the mixed boundary value problems of the crack, which is assumed to be permeable, to dual integral equations. The solution of the dual integral equations is then expressed analytically. Expressions for strains, stresses, electric fields, electric displacements, magnetic fields and magnetic inductions in the vicinity of the crack tip are derived. Field intensity factors and energy release rate for piezoelectromagnetic material are obtained. The stresses, electric displacements and magnetic inductions at the crack tip show the traditional square root singularities; and the electric field intensity factor (EFIF) and the magnetic field intensity factor (MFIF) are always zero.     

断裂力学中奇异积分方程的数值求解方法

对断裂力学中奇异积分方程的数值求解技术进行了综述。重点论述了第一类和第二类Cauchy型奇异积分方程以及超奇异积分方程的数值解法。这些方法的主要思想都是通过将奇异积分方程中的未知函数表示为多项式形式连续函数与特定形式权函数的乘积,然后借助Cauchy主值积分定义与超奇异积分的有限部积分定义,将奇异积分方程的求解归结为求解一组线性代数方程。本文拟结合一些具体的数值算例,对奇异积分方程中未知函数的不同表达方式、特点进行了评述,并比较了各种算法的优缺点。最后,指出了求解奇异积分方程的数值解法研究的未来发展方向。     

ANTIPLANE MULTIPLE CURVED CRACK PROBLEM IN CIR-CULAR INCLUSION AND MATRIX MATERIAL

茫桑遥茫眨蹋粒? ＩＮＣＬＵＳＩＯＮ ＡＮＤ ＭＡＴＲＩＸ ＭＡＴＥＲＩＡＬTX＠陆建飞＠王建华＠沈为平ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｉｎｔｅｒａｃｔｉｏｎｂｅｔｗｅｅｎｃｉｒｃｕｌａｒｉｎｃｌｕｓｉｏｎａｎｄｔｈｅｃｒａｃｋｈａｖｅｂｅｅｎｓｔｕｄｉｅｄ?..     

SOLUTION OF MULTIPLE CURVED RIGID LINE AND ANTIPLANE CIRCULAR INCLUSION PROBLEM BY WEAKLY SINGULAR INTEGRAL EQUATION

IntroductionMany investigators have investigated rigid lineinclusion and elastic inclusion problem.Early inthe 60 s,there were investigations aboutthe ex-perimental respects[1,2 ] and theoretical re-spects[3,4] of the inclusion problem . Wang etal[5 ]discussed the elastic stress field near the rigidline tips carefully.They put forward three frac-ture models of rigid lines corresponding to thethree fracture models of cracks and they pro-posed to use stress singularity coefficient( SSC)to desc…     

The Stochastic Stability of a Viscoelastic Cable with Small Sag

In this paper, the almost sure stability of a viscoelastic cablesubjected to an initial stress on the uniform cross section is studied. The constitutive of the cable material is assumed to be the hereditary integral type, the relaxation kernels of which are represented by the sums of exponents. The initial stress and the damping coefficient to the environment and also relaxation kernel coefficients are a random wide-band stationary process. The partial differential-integral equation of motion is derived first. Then by applying Galerkins method, the governing equation is reduced to a set of second order differential integral equations. Based on the Liapunovs direct method, sufficient conditions for almost sure stability of viscoelstic cable are obtained.     

含有裂纹水泥混凝土路面的理论分析

以断裂力学理论为基础,将水泥混凝土路面视为Winkler地基上的弹性板,利用傅立叶积分变换,并引入位错密度函数,建立了奇异积分方程,推导出水泥混凝土路面表面存在裂纹时裂纹尖端应力强度因子的解析表达式,然后应用Lobatto-Chebyshev数值方法求解奇异积分方程,得到了应力强度因子的数值解.以实际路面为例,计算了裂...     

含裂纹水泥混凝土路面的解析算法

水泥混凝土路面在使用过程中出现裂纹是一种常见的损坏形式。以断裂力学理论为基础,对含裂纹水泥混凝土路面进行了理论分析。将水泥混凝土路面视为Winkler地基上的弹性板,利用傅立叶积分变换,并通过引入位错密度函数建立奇异积分方程,推导出水泥混凝土路面含有垂直裂纹时裂纹尖端的应力强度因子的解析表达式。然后,再应用Lobatto—Chebyshev法求解奇异积分方程,得到应力强度因子的数值解。为了说明问题,以实际路面为例,给出水泥混凝土路面内部存在裂纹时裂纹尖端应力强度因子的计算结果,并讨论了影响应力强度因子大小的因素。     

Steady state analysis of towed marine cables

Efficient numerical schemes were presented for the steady state solutions of towed marine cables. For most of towed systems, the steady state problem can be resolved into two-point boundary-value problem, or initial value problem in some special cases where the initial values are available directly. A new technique was proposed and attempted to solve the two-point boundary-value problem rather than the conventional shooting method due to its algorithm complexity and low efficiency. First, the boundary conditions are transformed into a set of nonlinear governing equations about the initial values, then bisection method is employed to solve these nonlinear equations with the aid of 4th order Runge-Kutta method. In common sense, non-uniform (sheared) current is assumed, which varies in magnitude and direction with depth. The schemes are validated through the DE Zoysa's example, then several numerical examples are also presented to illustrate the numerical schemes.     

Current Density Distribution in Gas Tungsten Arc Welding Process

IntroductionWeldingisacriticaltechnologyinbuildingnuclearreactors,shins,piPelinesandinatomobilemanufaCtuing.BatuPtil1noWtheearemanyproblemsinPractice,understandingthedeVlopmentoftheweldpoolduringweldingisofconsiderablePracticalsignificance.BecauseofthecomPlexityoftheprocessandtl1ePresenceofthebrightarc,directexPerimentalinvestigationsareextremelyexPensiveandoftenimPossibleorimPracticable,thensomemathematicalmethodsareadoptedtosett1PthetfansiellttemPerattirefieldandthefluidflowfieldofthew…     

梯形截面箱梁的约束扭转计算

本文介绍了用广义坐标法推导的梯形截面箱梁约束扭转计算的基本微分方程;在初参数方程的求解中,利用了初参数影响系数矩阵。     

子矩阵约束下三类矩阵方程的对称正交对称迭代解法

讨论了子矩阵约束下三类矩阵方程的对称正交对称迭代解,利用广义共轭梯度法构造了迭代算法,并证明了算法的有限终止性.该算法能自动判定解的情况:当矩阵方程(组)相容时,得到矩阵方程(组)的解;当矩阵方程(组)不相容时,得到矩阵方程(组)的最小二乘解.     

一类二阶常微分方程多重正解的存在性

由于物理学和力学中的许多问题最终可以归结为一类二阶常微分方程的边值问题,此类问题的解的存在性和多重性得到了许多学者的研究．通过将常微分方程转化为非线性积分方程,利用锥拉伸和锥压缩不动点定理和不动点指数讨论了一类二阶常微分方程的正解存在性问题,在一定条件下,得到了几个多重正解定理,同时证明了与此相关的主要引理．     

一类双曲方程解的存在唯一性

对在等离子体和一维波动方程中出现的具体有初始分布数据的一类双曲微分方程正问题，将其化成第二类Volterra积分方程后，用压缩映像原理给出了解的存在唯一性。     

行人交通流三参数基本关系式适用性研究

为研究交通流量、密度和速度基本关系式对行人交通流的适用性,采用类比和误差分析方法,建立了行人交通流基本关系式评价方法与步骤.采集了水平通道、楼梯等步行设施行人流量、密度和速度数据,并利用基本关系式进行密度换算,分析了密度实际观测值与基本关系式换算值之间的差异.研究结果表明:对于有固定边界步行设施上的行人交通流,在极低密度和极高密度时,用基本关系式换算参数的误差可高达20%~25%;使用基本关系式还会得到极高密度时行人交通仍能获得较高流量与速度的错误结论,并导致部分高密度交通流数据缺失;行人交通流三参数基本关系式并不严格成立,对于行人通行能力的理论研究,不应采用基本关系式进行参数换算.      

一类微分方程反问题解的存在唯一性

对在等离子体和一维波动方程中出现的具有初始分布数据的一类双曲微分方程反问题，用压缩映像原理给出了解的存在唯一性。     

车架结构动力学特性边界元法解析

为在设计阶段对车架结构进行高效的动力学建模解析,提出了基于边界元的区域分割单元合成方法。采用薄板元件的动态基本解,建立了板型构件的边界方程,运用区域分割单元合成法,推导出车架结构的动力学方程。边界元计算值相对于实验值的最大相对误差为5.0%,相对于有限元计算值的最大误差为5.9%,表明基于边界元的区域分割单元合成方法能够快速、准确地分析车架结构的动力学特性,在设计阶段可提高车架结构的建模精度和计算效率。     

Influences on the spatial directivity of acoustic vector sensor by finite cylinder baffle and future prospects about eliminating the effects

The directivity of acoustic vector sensor can be distorted by the sound diffraction wave of baffle. According to Helmholtz integral equation, the directivity of acoustic vector sensor under the condition of finite cylinder baffle is calculated by using boundary element method (BEM). Considering the problem of nearly singular integrals of BEM, the exponent parts of fundamental solutions are expanded in trigonometric functions. The singular and the nonsingular parts are separated: the nonsingular parts are calculated by Gaussian integral method; the singular parts are regularized by subsection integral method. Then the surface integrals are reduced into line integrals along the elements?? contour which can be calculated by Gaussian integral method. The sound diffraction field of a plane wave under the condition of finite cylinder baffle at different frequencies and incident angles is calculated, and the characteristics of directivity of pressure and vibration velocity at different frequencies are analyzed. The experimental data are treated and the errors between the experimental and theoretical results are analyzed. Finally, according to the research results about the influences on the directivity of acoustic vector sensor by baffle at present, some future prospects about eliminating the effects of sound diffraction field by baffle are presented.     

水下目标低频散射特性的波叠加解法

针对运用边界积分方程法研究低频散射特性时,存在的表面奇异积分和特征频率处解的非惟一性等问题,将波叠加法引入到水下目标低频散射研究中.对刚性球体的低频散射计算表明,该方法较边界积分方程法不仅消除了奇异解和多值问题,而且具有更高的计算速度和精度,适用的频率范围更宽,可用于水下目标低频散射问题的研究.分析表明影响其计算精度的因素主要是虚源空间位置、目标表面与虚源表面划分精细程度.     

一类拟线性双曲型方程的初值问题

基于双曲型线性偏微分算子理论，引入并研究了具有非零初始值的拟线性双曲型方程的定解问题．由速降函数空间上的傅立叶变换的内积得到了相应的希尔伯特空间和一个重要的估计式．在已知函数满足某些假设条件时，利用Schauder不动点定理证明了该初值问题解的存在性定理．