对“断裂力学中Westergaard应力函数小议”的意见

文[1]认为:“无穷远”边界条件的存在,Weste-rgaard 应力函数解出现了不确定性.并在应力函数中引进了任意常数m,求得了应力强度因子的不定解.本文要否定文[1]的观点.文[1]考察了双向均匀拉伸下的Griffith 裂纹(图1),取Westergaard 应力函数为     

对“断裂力学中Westergaard应力函数小议”的意见

<正> 文[1]认为:“无穷远”边界条件的存在,Weste-rgaard 应力函数解出现了不确定性.并在应力函数中引进了任意常数m,求得了应力强度因子的不定解.本文要否定文[1]的观点.文[1]考察了双向均匀拉伸下的Griffith 裂纹(图1),取Westergaard 应力函数为     

"关于刚体平面运动中动量矩定理的综合讨论"一文中的某些错误——与朱晨同志商榷

文[1]中有一些错误的推导和结论,现指出如下:1.错误及其来源文[1]在"对任意动点和任意相对定点的相对动量矩定理式"讨论中引用了文[2]中的(3)式,由于文[1]的某些符号规定不符合习惯,故把文[2]中正确的(3)式引用成文[1]中错误的(18)...     

关于“解决有限条法偶联问题的一个方法”一文的讨论

读了“解决有限条法偶联问题的一个方法”一文,发现该文存在一些错误,因而所提方法在理论上是不成立的。本文就此稍作讨论。 先将[1]中的主要公式抄录如下:     

关于“关于极限分析新上、下限定理中权因子的讨论”一文的讨论

文[1]探讨了极限分析法的一些问题,本文对文[1]提出下述商榷意见. 1.文[1]中所建立的新上限定理和新下限定理是错误的.今举例说明:设选取的σ_ij~*和ε_ij~o处处满足条件σ_ij~*ε_ij~o<0,则不论对于什么结构,也不论该结构承受什么样的外载,只要这些外载与某一参数成比例地增加,那么根据文[1],立即可以得出该结构的真实极限载荷值的上限值和下限值均等于零.这就是说,该任意结构不受外载时就会发生流动,显然这结论是有问题的. 2.根据文[2]的论证方法和所得结果,可以改正文[1]的错误.正如文[3]所述,文[4]存在着原则错误,因此,文[1]以文[4]为基础而建立的有关定理就不可能正     

对于“平面应力中临界应力强度因子的厚度效应”一文的意见

读了“平面…效应”一文(上海力学,3(3),69—74(1982))以后,发现其中有错误,兹指出如下。为了便于参考和查阅公式,本文中的复应力函数记号和专著[1]全同。又为说明“平面…效应”文的错误,下面我们也作出了类同的推导,最后说明错误产生的原因。由著作[2,页255—258中的式(b)、(j)、(k)、(l)],我们可得一种既平衡又协调的解答     

关于用变分法求平面问题的双三角级数解

文[1]给出过设位移为双三角级数用虚位移原理求解平面问题的两个例题。文[2]指出了[1]的错误,给出了一种正确解答。文[3]也对[1]作了讨论,找到若干种(见其表1、2)能使[1]的解答成立的特例。但[2]的解答带有"l+ ...     

强非线性振动系统的渐近解法

本文推广文[1]中方法于求解广泛一类强非线性振动系统,导出了适于近似定性分析和定量计算的简便公式。作为例子研究了修正的Vander Pol振子,最后给出数字Poincaré映射结果,从近似定性分析和定量计算两方面证明了本文求得的方法的有效性。     

关于壳体非线性应变分量的教学探讨

<正> 亮体非线性应变分量的研究十分重要,文[1]在这方面作了许多工作,但其在推导壳体非线性应变分量的一般公式时,对略去“微量”后是否会影响公式的一般性未作说明,因而文[2]给予补充,借助张量分析,得到了正交曲线坐标系下壳体非线性应变分量的表达式,使其更加完整,所得结果与文[3]完全相符.如学生对张量分析比较陌生,按这种分析方法讲解,就会使     

拉扭联合作用下实心圆杆的塑性屈服条件

文[1]对文[2]一书习题5.9关于拉扭联合作用下实心园杆的塑性屈服条件的公式...     

Theoretical solution for the cross-flow heat exchanger

The theory of the cross-flow heat exchanger first was treated by Nußelt [1, 2] on the base of heat balances for the two interacting fluids over an exchanging area element. This leads to a partial differential equation. But the solution was an infinite row which could not be expressed in a compact formula. In this paper it will be shown that a compact formula for the infinite row is possible. All temperatures of the interacting fluids, for example the local fluid temperatures and the mean outlet temperatures as well as the local temperature difference and the mean temperature difference over the complete exchanger are now being available in simple formulae which have the form of an infinite sum. The summation has to be stopped at a finite value with a negligible deviation. As all variables in the formulae are dimensionless, normalized diagrams are developed which are generally valid and give a good overview over a wide range of exchanger conditions.     

Crack propagation in a four-parameter piezoelectric medium

The simplified three-parameter formulation of a piezoelectric medium proposed by Gao et al. [Gao, H.J., Zhang, T.Y., Tong, P., 1997. Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J. Mech. Phys. Solids 45, 491–510] is extended to a four-parameter modified model in order to point out the features of a steadily propagating Griffith crack. It is assumed that the crack is electro-elastically free and the medium is subjected to a generalized electro-mechanical loading applied at infinity. The complete solution is provided under impermeable and permeable boundary conditions and results are presented in order to show the main dynamical features.     

Asymptotic behavior of the energy functional for a three-dimensional body with a rigid inclusion and a crack

A model of a three-dimensional elastic body containing a rigid inclusion and a crack located on the interface between the inclusion and the body is considered. Natural boundary conditions are imposed on the crack. A derivative of the energy functional with respect to the perturbation parameter is derived for an arbitrary, rather smooth perturbation of the domain, in particular, the Griffith formula is obtained.     

THE ASYMPTOTIC SOLUTION OF THE UNSTEADY PLANAR PARALLEL GAS FLOW FOR THE CASE THAT THE ADIABATIC INDEX NUMBER γ IS BIG

In ref I, under the condition that the components of velocity are only the functions of time and polar angle θ, Drornikov solved eqss. (1.1) (1.3) of the ideal gas unsteady planar parallel potential flow. It was pointed out in ref. [1] that in general cases, the evident solutions could not he obtained. Only for two especial cases, the evident solutions were obtained.In this paper, the author studies the same prohlein as that in ref. [1]. In the first section we obtain the evident solution of equations (1.1)-(1.3) under the condition that the sonic velocity is restricted by some complemental conditions. In the second section, we obtain the first-order approximate solutions of the fundamental equation for the case that γ>>1     

One-dimensional nonuniform temperature flow with heat transfer by convection

In ref. [1], V. E. Najenov studied the conditions that when the viscosity of the liquid is an exponential function of temperature, the pipe flow, having steady heat transfer, is one dimensional and with nonuniform temperature. For plane canal and circular pipe he still studied the velocity and the temperature fields.In this paper, the author presents two new methods for solving the same problem. The method as in ref. [1] may be regarded as the natural branch of the methods of this paper. One of our new methods only can solve the same problem as in ref. [1] and the complex degree of its computing process is nearly the same as that in ref. [1]. But the other can go beyond the studying scope of ref. [1], namely, for the case that the curvatures of circumference of the cross section of the pipe are not equivalent everywhere, the problem may also be solved.     

Global weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions

It is proved that under a physically realistic truncation of the collision kernel, the Boltzmann equation in the one-dimensional slab [0,1] with general diffusive boundary conditions at 0 and 1 has a global weak solution in the traditional sense. This solution satisfies the boundary conditions almost everywhere, and has, at worst, exponentially growing total energy.     

关于功率谱密度与风速谱的注记

探讨了随机过程中双边功率谱密度负频率引入的原因,实际的频谱函数应将负频率项与相应正频率项成对合并起来而直流分量保持不变,此即单边功率谱所表达的含义.对目前文献中给出的单边功率谱的表达式和单边功率谱与双边功率谱的关系式进行了修正,并对维纳-辛钦公式的变换形式也做了相应的修正,指出其修正前后在不同风速谱实际应用中的区别.算例证明了本文所给公式的正确性.     

材料参数对韧性材料高应变率拉伸碎裂过程的影响

Grady-Kipp将一个与断裂能量相关的内聚断裂模型引入Mott[1]的刚性卸载波分析,导出一个预测韧性材料在高速拉伸碎裂过程中产生碎片的平均尺度的计算公式[2]。为定量评估Grady-Kipp公式的适用程度,采用数值方法模拟了具有不同材料参数的一维弹塑性杆在高应变率拉伸过程中的碎裂现象。通过改变材料的断裂能 、密度 和应变率敏感系数c,模拟了杆在不同应变率 下的碎裂过程,研究了材料参数对碎裂时的碎片尺度、表观断裂应变和断口温升等的影响。通过对应变率和碎片尺寸进行无量纲化,证实Grady-Kipp公式在广泛的材料参数范围内能较好地预测碎裂过程中发生的碎片平均尺寸。     

层状介质中多个非共面硬币形裂纹弹性波散射问题研究

本文在[1]的基础上,利用 Hankel 积分变换,进一步研究了层状介质中多个非共面硬币形裂纹的弹性波散射问题。从所得结果来看,虽然层状介质中多个非共面硬币形裂纹的弹性波散射问题在形式上与多个非共面穿透形裂纹问题[1]有惊人的相似之处,但两者之间有着质的差异。     

Minimum Free Energies for Materials with Finite Memory

Finite memory viscoelastic materials are of interest because (a) they are not necessarily experimentally distinguishable from materials with infinite memory; and (b) the assumption of infinite memory can, in certain contexts, lead to results that run counter to physical intuition. An example of this - the quasi-static viscoelastic membrane in a frictional medium - is discussed. It is shown that, for a finite memory material, the singularity structure of the Fourier transform of the relaxation function derivative is quite different from the infinite memory case in the sense that it is an entire function with all its singularities being essential singularities at infinity. The formula for the minimum free energy [1] is still valid in this case. In contrast to the work function, this quantity, and all other functions of the minimal state, depend only on the values of the history over the period when the relaxation function derivative is nonzero. The factorization required to determine the form of the minimum free energy can be carried out explicitly for simple step-function choices of the relaxation function derivative. The two simplest cases are fully worked through and explicit formulae are given for all relevant quantities.