铁电体表面效应的唯象理论及其与横场Ising模型的关系

分析了铁电体横场Ising模型与Landau唯象理论的关系,得出了有表面的铁电体的Landau自由能表达式,指出原有的表达式中面积分部分仅含与极化平方成正比的项只在特殊情况下成立,一般情况下还应包含与极化四次方成正比的项.利用所得出的自由能表达式,计算了铁电薄膜自发极化和Curie温度与厚度的关系,使原先用唯象理论不能理解的一些实验现象得到了解释     

多元复合函数求导链式法则证明的注记

"当自变量增量趋向于0时,中间变量增量可能取到0"是多元复合函数求导链式法则证明过程中的主要困难.本文通过补充定义的方法克服该难点,在外层函数可微、内层函数可导这一最弱条件下严格化了证明.     

加肋双曲冷却塔动力响应的渐近分析法——摄动有限元解

加肋壳体与光滑面壳相比,一般它具有较好的动力特性与较好的稳定性.本文通过对作者关于加肋双曲冷却塔自由振动及阵风响应计算结果的文献[1,2]的综合分析,认为目前工程中一般仅加几根环肋的双曲冷却塔,可以把肋的质量、刚度矩阵作为在原光滑塔壳的质量、刚度矩阵基础上的一个增量矩阵,从而可采用一般的奇异渐近分析法来统一求解.文中我们首先给出了轴对称环向加强肋及非轴对称一般加强肋的质量、刚度矩阵,并根据渐近分析原理给出了由于肋的刚度、质量矩阵所引起的塔固有频率、塔振型的一般增量表达式.由此增量表达式,我们还进一步给出了使最小基频达到最大值的加肋位置参数和加肋截面尺寸(肋的宽高比)参数并对实际工程中的双曲冷却塔给出了具体的数值结果. 其次,在阵风响应的分析中,本文用渐近方法也相应给出了由于肋的刚度、质量矩阵所引起的响应增量及阵风响应因子增量的计算表达式. 渐近分析结果同一般数值结果的比较表明,对塔的固有频率前者能给出较精确的结果,而对塔的振型一般误差较大.针对这一情形,文中还建议了一种修正了的振型计算法.     

有限变形热粘弹性本构关系的内变量理论 *

基于非平衡态热力学理论 ,提出了一个新的有限变形热粘弹性本构关系 .在定容比热为常数的条件下 ,给出了热学效应和力学效应之间具有解耦形式的自由能表达式 .通过对固体高聚物细观变形机制的分析 ,引进了相应的内变量 ,并在此基础上建立了计及温度效应的有限变形粘弹性本构关系的内变量理论 .此外 ,还推导了参考构形中分子网络具有随机取向分布时本构关系的具体表达式 .讨论了温度变化对松弛时间的影响 .将自由能展开为内变量二次式的粘弹性本构理论仅仅是一种线性化近似 .     

含Cauchy核奇异积分高精度求积公式

用分离奇异性方法构造了具有高代数精度的含Cauchy核奇异积分的Gauss-Kronrod求积公式,给出了计算求积系数的简洁方法和表达式,导出了求积公式余项表达式.对求积公式在计算机上用Matlab编程进行了数值实验,数值实验结果与理论分析一致.     

非临界Liouville弦模型中单圈自由能的计算

该文采用路径积分方法计算了非临界Liouville弦模型中单圈自由能,结果表明D=27时的临界温度与共形物质场的中心荷有关, 并获得了自由能的渐近表达式.     

动脉中血液脉动流的一种分析方法

动脉中的血液流动被分解为平衡状态(相当于平均压定常流状态)和叠加在平衡状态上的周期脉动流,利用Fung的血管应变能密度函数分析血管壁在平衡状态下的应力-应变关系,确定相对于平衡状态血管作微小变形所对应的周向弹性模量和轴向弹性模量,并建立在脉动压力作用下相应的管壁运动方程,与线性化Navier-Stokes方程联立,求得血液流动速度和血管壁位移的分析表达式,详细讨论血管壁周向和轴向弹性性质差异对脉博波、血液脉动流特性以及血管壁运动的影响.     

关于热冲击弹性问题的自由能及变分原理

在讨论耦合热弹性问题的变分原理的一些著作中,以弹性应变e_ij和温度变化值θ为状态参数的自由能φ(e_ij,θ)为自由能的这一表达式只适用于|θ|<0(绝对参考温度)的情况.在热冲击弹性问题中,温度变化值θ很大,甚至可以大过T₀同时,材料常数(λ,μ,γ,c等)随θ而发生变化,不再保持为常数.就这种情况,本文导出自由能的表达式.(0.1)式则为其特殊情况.将自由能的这一表达式引入变分原理,其欧拉方程将成为非线性.为了线性化,将热冲击作用的时间过程划分为若干足够小的时间元△t_k(△t_k=t_k-t_k-1,k=1,2,…,n).在△t_k中,温度变化θ_k很小,材料常数由t_k-1瞬时的温度场T_k-1=T_{x1,x2,x3,tk-1}确定,自由能φ_k可近似地采用(0.1)式的形式,从而得到变分原理的分段近似表达.     

求m阶递推数列通项公式的两种方法

利用分析中的解析函数方法和代数中的矩阵方法,得到了m阶常系数齐次线性递推数列通项公式的解析表达式,是对已有结果的完善和推广.     

水合物沉积物的力学本构模型及参数离散元计算

为有效描述水合物沉积物在不同水合物饱和度与围压情况下的力学行为,该文基于广义Hooke(胡克)定律建立了水合物沉积物的应力 应变关系方程和弹性模量弱化方程;基于三轴压缩试验确定了水合物沉积物的软化系数和软化指数,基于颗粒流程序（PFC3D）开发了水合物沉积物初始弹性模量的离散元算法（DEM）.利用建立的应力 应变关系方程、弹性模量弱化方程和初始弹性模量DEM,数值模拟了水合物沉积物在6种不同水合物饱和度与围压情况下的力学行为.数值模拟结果与三轴压缩试验结果的对比表明,建立的应力 应变关系方程、弹性模量弱化方程和初始弹性模量DEM,能有效预测水合物沉积物的力学行为,可为水合物井筒设计与安全开采提供理论基础和计算方法.     

Reflection of magneto-thermoelastic waves with two relaxation times and temperature dependent elastic moduli

The model of the equations of generalized magneto-thermoelasticity with two relaxation times in an isotropic elastic medium under the effect of reference temperature on the modulus of elasticity is established. The modulus of elasticity is taken as a linear function of reference temperature. Reflection of magneto-thermoelastic waves under generalized thermoelasticity theory is employed to study the reflection of plane harmonic waves from a semi-infinite elastic solid in a vacuum. The expressions for the reflection coefficients, which are the relations of the amplitudes of the reflected waves to the amplitude of the incident waves, are obtained. Similarly, the reflection coefficients ratios variations with the angle of incident under different conditions are shown graphically. A comparison is made with the results predicted by the coupled theory and with the case where the modulus of elasticity is independent of temperature.     

Relation between the temperature and deformation dependences of the modulus of elasticity

An analysis of the temperature and deformation dependences of the modulus of elasticity and the rate of stress relaxation has revealed the existence of a strain-temperature analogy. It is suggested that the physical significance of this analogy is associated with the change of volume. The experimental expression of the temperature and deformation dependences of the modulus in terms of change of volume leads to coincidence of the curves in the region above T_g, which confirms the correctness of the conclusion that the temperature-strain equivalence may be associated with the volume changes in that region.     

带球形空腔的广义热弹性无限大材料的弹性模量和传热系数与材料参考温度的相关性

利用具某一松弛时间的广义热弹性方程求解了带球形空腔的无限大材料问题．该材料的弹性模量和传热系数是可变的．空腔的内表面没有力作用,但有热冲击作用．利用Laplace变换求得直接逼近解．数值求解了Laplace逆变换．给出了温度、位移和应力的分布图．     

Effect of fillers on the structure and properties of cured resins

The elastic (modulus of elasticity and equilibrium high-elastic modulus) and thermal (volume coefficients of thermal expansion below and above the glass transition temperature) properties of compositions based on ÉD-5 epoxy resin cured with polyethylenepolyamine have been investigated. Quartz powder and aluminoborosilicate glass powder were employed as fillers at concentrations from 0 to 0.413. The thermal expansion coefficients of the compositions were studied in a dilatometer, in which the specimen is free of mechanical loads. The Young's modulus at 25°C and the equilibrium high-elastic modulus at 125°C of the compositions were determined in the compression regime in an instrument based on the IZV-2 optical length gage. The thermal expansion coefficients of the polymer matrix were calculated with allowance for the elastic properties of the resin and the filler. It is shown that, as the filler concentration increases, the thermal and elastic properties of the resin in the filled system change. This can be interpreted as a change in the properties of the resin as it approaches the surface of the filler particles. Increased interaction between the filler surface and the epoxy resin tends to stiffen the polymer network.Scientific Research Institute of Precision Technology, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1018–1022, November–December, 1969.     

Compression tests on composite tubes

The possibility of determining the modulus of elasticity, Poisson's ratio, and compressive strength across the fibers of a unidirectional composite by means of compression tests on cross-wound tubes is examined. By analyzing the Leknitskii [3] solution for the case of a transversely isotropic cylinder it is shown that only the modulus of elasticity can be reliably determined in this way. The conclusions are confirmed by experimental data obtained by testing glass-reinforced plastic tubes.     

Phenomenological theory of surface effects in ferroelectrics and its relationship with transverse Ising model

The relationship between the transverse field Ising model and the Landau phenomenological theory for ferroelectrics is analyzed, and the Landau free energy expression for ferroelectrics having surfaces is derived. It is pointed out that the traditional expression in which the surface integral has only a term of the square polarization is valid only for special cases, in general a term of the polarization to the four should be included as well. By use of the newly derived free energy expression, the thickness-dependence of the spontaneous polarization and Curie temperature of ferroelectric films is calculated; thereby some experimental results incompatible with the traditional phenomenological theory are successfully explained.     

纳米晶体弹性模量的模拟研究

通过分子动力学(MD)方法模拟纳米晶体(1～3nm)的结构,并对模拟的结果进行了X射线衍射的点阵常数、结合能及弹性模量等模拟计算.结果表明纳米晶体无论是晶界和晶粒都与传统的粗晶粒晶体材料没有根本的区别,只是由于晶粒尺寸变小以及晶界的体积分数等的作用而导致诸如弹性模量大幅度减少等一系列不同性能.     

Wave Dispersion Decoupling in Micropolar Thermoelasticity

For a system of field equations of micropolar thermoelasticity we derive a propagation condition for thermoelastic disturbance in a form of monochromatic plane wave in deformation, micro rotation and temperature. The corresponding dispersion relation is given in an explicit form, together with dependence of characteristic coefficients on principal material constants forming the constitutive tensor of isothermal macro and micro elasticity, phenomenological heat conductivity and coupled macroscopic thermoelasticity. It is shown that due to the centro–symmetric nature of microelasticity and particular form of temperature coupling in a free energy function, the separation between the optical and acoustical branch of dispersion relation is inherent. For such systems dispersion relations due to the micropolar fields on one side and macroscopic thermoelastic fields on the other side are completely independent without any cross–coupling. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of some dynamic characteristics of forming bone callus by the induced vibration method

Conclusions 1. Upon maturation, bone callus not only goes through a series of morphological chantes but also changes in mechanical properties. This is true primarily for an increase in the elasticity modulus.2. The specific energy of dispersion and loss modulus have maxima which occur after 25 to 30 days. This behavior is apparently related to the fact that bone callus at this period has the nature of spongy bone tissue. For compact bone tissue, on the other hand, these values are equal to zero.3. The area of the hysteresis loop is almost completely independent of the frequency upon cyclic stressing.4. The elasticity modulus is proportional to the x-ray density of the samples, which thus may serve as an objective criterion of the degree of maturity of callus.Smolensk State Medical Institute. Translated from Mekhanika Polimerov, No. 5, pp. 896–900, September–October, 1977.     

Vibration using for the longitudinal elasticity modulus determination

Longitudinal elasticity modulus, E, is a material specific feature, which,. in general, is establish on the pieces by longitudinal stress. This procedure is possible to apply to the compact material but not to the sintered power parts (or porous material test pieces). For sintered parts, the establishing of Young's modulus, in this paper, it is proposed by transmition of mechanical vibrations along to the test pieces. The test pieces of compact or porous material were strained at longitudinal vibrations. It was establish the linkage between vibration and density, respective between the density and the value of the longitudinal elasticity modulus. Using the test pieces of compact material we realized the methodology to obtain the longitudinal elasticity modulus regarding the compact material, and in this way can be establish the possibility to measure with a good result the longitudinal elasticity modulus for the pieces of sintered powders or of porous material. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)