应力

G. Lekhnitskii and the Hankel integral transformation are used, And thereby a solution of the Stress field and displacement field of an embedded penny-shaped crack lying in a transverely isotropic plane under the action of the uniform tension stress at the far end perpendicular to the crack surface is obtained.

本文利用对于横观各向同性体轴对称变形时应力函数解法的基本方程，并应用Hankel积分变换，求解了位于横观各向同性平面内的埋藏圆片裂纹在垂直于裂纹面远处均匀拉应力作用下的应力场和位移场，获得了与各向同性材料相同的应力强度因子，不同于各向同性材料的应力场和应变能释放率裂。

Results show that gas release in gassy sand will cause the additive deformation of tunnel and additive stress of the shield segment, and make important impacts on the global displacement of tunnel but little influences on the stress of shield segments and the relative displacement of tunnel. It is inclined to arouse the differential settlement and cracks on the tunnel so as to cause hazardousness. Re-accumulating of the gas can also produce additional stress and the additive resilience, but it can be ignored in practical engineering because the influence degree is small. The shallow gas in reservoirs is appropriate to be discharged before construction of the subway tunnel.

研究结果表明：气体释放将引起隧道产生附加变形和管片附加应力，浅层气体释放对地铁隧道结构应力和结构相对变形影响较小，而对隧道整体位移影响较大，易引起不均匀沉降，导致隧道裂缝或断裂，进而引发危险；气体重新回聚时，隧道产生的附加应力和回弹位移量较小，工程中可不予考虑；地铁隧道施工前，宜对浅层气体进行预先排放。

For analyzing the state of one C point,one small positive parallel hexahedron is taken out from the point.

A y 图1 - 5 (1)为了分析一点的应力状态，在这一点从物体内取出一个微小的正平行六面体，各面上的应力沿坐标轴的分量称为应力分量。

This paper studies the stress of gravity dam heel with careful numerical simulation, and analyses the effect of the variety of the elastic modulus of homogeneous or non-homogeneous foundations on the principal tensile stresses of gravity dam heel. The conclusions are as follows:① When the elastic modulus of homogeneous dam base and variated element in the critical place is changed with the same the fluctuation, the effect on the dam heel stresses caused by the latter is much more prominent than the former one.

本文通过精细网格模拟研究了重力坝坝踵应力情况，就均质坝基和非均质坝基弹模变化对坝踵主拉应力的影响，得出了如下结论：①均质坝基弹模与非均质坝基敏感区域的变异单元弹模变化相同的幅度，非均质情况引起的坝踵应力的变化远大于均质情况。

A hyperbolic sine relationship is found to correlate well the flow stress with the strain rate, and an Arrhenius relationship with the temperature. The strain hardening coefficient n and deformation activation energy Q are evaluated by linear regression analysis. And the flow stress constitutive equation of the alloy during hot compression is obtained.

应变速率和流变应力之间满足指数关系，温度和流变应力之间满足Arrhenius关系，通过线性回归分析计算出该材料的应变硬化指数n以及变形激活能Q，获得该铝合金高温条件下的流变应力本构方程。

The results indicate that its dynamic stress-strain curve is hyperbolic type. The dynamic strain of LCES decreases with increasing confining pressure, cement content, curing ages and cyclic loading frequency when it is subjected to the same dynamic stress. At the same dynamic strain, the dynamic secant elastic modulus E_(sec of LCES increases and the damping ratio decreases with increasing confining pressure, cement content, curing ages and cyclic loading frequency. The curves ofσ_d～ε_d,E_～ε_d and D～ε_d with different EPS content intersect respectively, the trend of LCES deformation characteristic is inversely proportional to EPS content near the intersection. The value of dynamic strain at the intersection is about 0.5%~3.0%, the magnitude of which is related to the mixing proportions and confining pressure.

试验结果表明，LCES的动应力应变骨干曲线形态符合双曲线；在相同的动应力作用下，LCES产生的动应变随着固结压力、水泥掺量、试样养护龄期和振动频率的增大而减小；在动应变相同的情况下，随着固结压力、水泥掺量、试样养护龄期和振动频率的增大，LCES的动模量增大而阻尼比减小；随着加载次数的增大，LCES的动模量在开始阶段显著降低，然后趋于稳定，但当加载次数达到几百次时，动模量又有增大的趋势；不同EPS掺入比的LCES的动应力应变骨干曲线、动模量随应变变化曲线和阻尼比随应变变化曲线都发生了相交，交点前后EPS掺入比的大小对LCES动力变形特性的影响趋势是截然相反的，交点处的动应变值一般在0.5％～3.0％范围内变化，其大小与LCES的配比以及固结压力有关。

3M i τi = 2 a i bi 3M i k = Ga i b i3 由后一式得 Gka i b i3 Mi = 3 60 Also Gk M =∑Mi = 3 i a i bi3 ∑ So we have: M a i b i3 = M 3 ∑ a ibi i Consequently we have:τ 3 Mb i = a i b i3 ∑ 3M k = G ∑ a i b i3 It is noticeable that: the shear stress of the midpoint of the long side of the narrow rectangle is considerably precise.

而 故有 Gk M =∑Mi = 3 M i a i bi3 ∑ a i b i3 = M 3 ∑ a ibi 从而有τ i 3 Mb i = a i b i3 ∑ 3M G ∑ a i b i3 k =值得注意的是：由上述公式给出的狭矩形长边中点的剪应力已相当精确，然而，由于应力集中的存在，两个狭矩形的连接处，可能存在远大于此的局部剪应力。

The error of SIF is discussed too. Then an index to estimate error of SIF is advised. The analysis shows it is a feasible and correct parameter.Size effect, Numerical analysis, Statistical theory, Energy theory, Fractal theory

8在对应力强度因子的计算方法进行评述的基础上，对应力强度因子的计算误差进行了分析，提出了一个使用有限元方法求解应力强度因子的误差指标参数。

By solving the frequency equation,the relationship between initial stress and phase velocity is obtained.

通过求解考虑初应力时的耦合波动方程，得到了管道壁中应力波传播时相速度和初应力的关系，并进行了实例计算。

On the base of the analysis, the following standpoints are presented definitely. There is no such a so-called zone with low density near the inwall of the lining. Upon the explosion terminates, the mortar would lose characteristics of the fluid. The compression strength of the lining layer formed by explosion is higher than that of a reference block tested.

在假定材料服从Tresca屈服准则或Coulomb屈服准则的条件下，得到了圆形井筒和球形腔体最大扩张压力p〓的计算公式；衬砌材料塑性区应力σ〓、σ〓和土体塑性区的应力σ〓、σ〓的计算公式；土体弹性区的应力σ〓、σ〓和径向位移u〓的计算公式；衬砌材料与土体交界面半径R〓以及土体中弹塑性区交界面半径R〓的计算公式。

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。