弹性系数

By integral transformation of basic equations, the stress and displacement expressions with unknown coefficients of elastic and viscoelastic materials were obtained in Laplace domain respectively, and introducing dislocation density functions, the singular integral equations were got according to the boundary conditions and interface connection conditions, further adopting Gauss integration and Gauss-Jacobi integration formula, the problem was reduced to algebraic equations, then it can be solved with the method of collocation dots in Laplace domain. Finally, the time response of dynamic stress intensity factor was calculated with the inverse Laplace integral transformation.

采用积分变换方法，得到Laplace域内弹性和粘弹性材料的应力和位移的含未知系数的表达式；引入位错密度函数，并通过边界条件和界面连接条件，导出反映裂纹尖端奇异性的奇异积分方程组，采用Gauss积分，并运用Gauss-Jacobi求积公式化奇异积分方程组为代数方程组，利用配点法进行求解；最后经过Laplace逆变换，求得动态应力强度因子的时间响应。

In this method, the equivalent elastic and elastic-plastic response spectra are ensured considering of structural inelasticity, the explicit expression of response spectra including Newmark-Hall deformation reduction factors is achieved.

该方法首先考虑结构的非弹性反应确定等效弹性反应谱和弹塑性反应谱，并建立了使用Newmark-Hall变形折减系数的能力谱的明确表达式。

The results show that the calculated elastic properties are close to the experimental results. The high value of Poisson's ratio and low value of elastic anisotropy ratio imply that the interatomic force in ZrCr2 is weakly directional.

结果表明：计算得到的ZrCr2 Laves相的弹性性质与实验结果相近，其泊松比和弹性各向异性系数大小说明ZrCr2 中原子键合的方向性并不强烈； ZrCr2 Laves相的内禀和外禀层错能分别为112 mJ/m2和98 mJ/m2。

In this project, we study the theory of higher order differential equations in Banach spaces and related topics. We solve an open problem put forward by two American Mathematicians and two Italian Mathematicians concerning wave equations with generalized Weztzell boundary conditions, introduce an existence family of operators from a Banach space $Y$ to $X$ for the Cauchy problem for higher order differential equations in a Banach space $X$, establish a sufficient and necessary condition ensuring $ACP_n$ possesses an exponentially bounded existence family, as well as some basic results in a quite general setting about the existence and continuous dependence on initial data of the solutions of $ACP_n$ and $IACP_n$. We set up quite a few multiplicative and additive perturbation theorems for existence families governing a wide class of higher order differential equations, regularized cosine operator families, regularized semigroups, and solution operators of Volterra integral equations, obtain classical and strict solutions having optimal regularity for the inhomogeneous nonautonomous heat equations with generalized Wentzell boundary conditions, gain novel existence and uniqueness theorems,which extend essentially the existing results, for mild and classical solutions of nonlocal Cauchy problems for semilinear evolution equations, present a new theorem with regard to the boundary feedback stabilization of a hybrid system composed of a viscoelastic thin plate with one part of its edge clamped and the rest-free part attached to a visocelastic rigid body. Also we obtain many other research results.

在本研究中，我们对Banach空间中的高阶算子微分方程的理论以及相关理论进行了深入研究，解决了由美国和意大利的四位数学家联合提出的一个关于广义Wentzell边界条件下的波动方程适定性的公开问题，恰当地定义了Banach空间中的高阶算子微分方程Cauchy问题的算子存在族及唯一族，建立了齐次和非齐次高阶算子微分方程Cauchy问题适定性的判别定理，获得了关于高阶退化算子微分方程的算子存在族、正则余弦算子族、正则算子半群、Volterra积分方程解算子族的乘积扰动和混合扰动定理，得到了关于以依赖于时间的二阶微分算子为系数的一大类非自治热方程非齐次情形下的时变广义Wentzell动力边值问题的古典解、严格解的最大正则性结果，获得了半线性发展方程非局部Cauchy问题广义解和经典解存在唯一的判别条件，从实质上推广了现有的相关结果；得到了一部分边缘固定而另一部分附在一粘弹性刚体上的薄板构成的混合粘弹性系统的边界反馈稳定化的新稳定化定理，还建立了一系列其他研究结果。

This paper clarifies the relationships between compliance coefficients and engineering elastic constants combined with orthotropic nature of wood, and twelve elastic constants of Betula platyphylla Suk.

该文结合木材的正交各向异性特征论述了木材的柔度系数与其工程弹性常数的关系，并采用电测法测试了白桦木材的12个弹性常数。

The complexity of elastic characteristics are influenced by rubber component shape factor, the variety of static-dynamic ratio, and the damping of the rubber component leads to the difficulties of rubber FEA in engineering applications.

橡胶元件的形状系数对其外在弹性特性影响的复杂性、动-静刚度比的多样性及黏弹性阻尼特性是其工程应用方面的难点。

Experimental results showed that a better test of the oscillator Harmonic Oscillator cycle and the quality is proportional to the square with, and spring stiffness coefficient is inversely proportional to the square root of the spring up within the limits of flexibility and oscillator unrelated to the amplitude, Guide and the tilting reading irrelevant; the amplitude does not exceed the elastic limit of spring, the rail mill Sassafras of small conditions, oscillator is a very good harmonic vibration model.

实验结果发现，较好的验证了弹簧振子的简谐振动周期与振子的质量的平方跟成正比，与弹簧的劲度系数的平方根成反比，在不超过弹簧的弹性限度内与振子的振幅无关，与导轨的倾斜读无关；在振幅不超过弹簧的弹性限度、导轨上的磨檫力很小的条件下，弹簧振子是一个很好的简谐振动模型。

Experimental results showed that a better test of the oscillator Harmonic Oscillator cycle and the quality is proportional to the square with, and spring stiffness coefficient is inversely proportional to the square root of the spring up within the limits of flexibility and oscillator unrelated to the amplitude, Guide and the tilting reading irrelevant; the amplitude does not exceed the elastic limit of spring, the rail mill Sassafras of small conditions, oscillator is a very good harmonic vibration model.

实验结果发现，较好的验证了弹簧振子的简谐振动周期与振子的质量的平方跟成正比，与弹簧的劲度系数的平方根成反比，在不超过弹簧的弹性限度内与振子的振幅无关，与导轨的倾斜读无关；在振幅不超过弹簧的弹性限度、导轨上的磨檫力很小的条件下，弹簧振子是1个很好的简谐振动模型。

First, based on the relations of stress and strain between the whole medium and its macroscopically isotropic constituents, an explicit relation between elastic matrices of the whole medium and its constituents was derived. Combining the explicit relation of elastic matrices with the strain's relation, two coefficient tensors were defined and analyzed to get a general relation between the hulk and shear modulus of the whole medium under the assumption that all the field variables are in a unified coordinate system. Secondly, combining these relations with the classical Hashin-Shtrikman elastic modulus bounds, four new expressions of elastic medium of the whole medium were obtained and compared with the original hounds. Last, these formulae were applied in the computation of effective elastic moduli of clean sandstone saturated with pore water.

首先基于整体介质与宏观各向同性组分满足的应力和应变组分关系，推导出整体介质弹性矩阵与组分弹性矩阵之间的显式关系，联合其应变关系，定义和分析了对应的两个系数张童，并据此导出了相关场变量位于统一坐标系时整体介质体积模量与剪切模量的关系；然后将经典的Hashin-Shtrikman弹性模量边界模型与上述关系式结合，得到4个新的整体介质弹性模量的估算公式，再与原始的Hashin-Shtrikman弹性模量边界进行了比较，最后针对饱和水纯净砂岩介质进行了试算。

Is it is it gain knowledge to tire and dry to exposed to state frictional force is it is it analyse to go on to commit road surface have to rub to use at first,lagging behind in forming frictional force elasticity on function,glueing and cutting function to analyse a little separately, state the building stones lamination and construct the influence that the depth resist slippery performance to the road surface;Is it is it set up tire sport model to transfer according to elasticity of tire to to slip,is it slip person who move adhere to relation of coefficient with road surface to establish.

首先运用摩擦学知识对轮胎与路面干燥接触状态下摩擦力构成进行分析，分别对构成摩擦力弹性滞后作用、粘着与微切削作用进行分析，说明石料纹理与构造深度对路面抗滑性能的影响；根据轮胎的弹性滑转建立轮胎运动模型，建立滑移值与路面附着系数的关系。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。