土木工程专业英语上册_翻译苏小卒_同济大学(考试手机专业版)(9)

As a result（因此）, the external virtual force P’ and internal virtual load u “ride along” by（乘上） and dL, respectively（分别地）, and therefore perform external virtual work of 1 on the body and internal virtual work of u dL on the element. Realizing that the external virtual work is equal to the internal virtual work done on all the elements of the body, we can write the virtual work equation as

1 = u dL （5-2）

因此，外部虚力P’和内部虚力u分别与 和dL“乘在一起”，因此在物体上形成外部虚功，在单元上形成内部虚功。了解到外部虚功等于对物体所有单元作的内部虚功，我们可以写出虚功方程

1 = u dL （5-2）

Where P’=1=external virtual unit load acting in the

direction of

u = internal virtual load acting on the element in = external displacement caused by the real loads dL = internal deformation of the element caused the direction of dL

by the real loads

By choosing P’ = 1, it can be seen that the solution for follows directly, since = u dL .

这里，P’等于1，也等于作用在 方向上的外部虚单位力；

u等于以dL方向作用在单元上的内部虚力； 等于真实荷载引起的外部位移； dL等于真实荷载引起的单元的内部变形。

可以看到通过选择P’=1能直接得到解，因为 = u dL 。

In a similar manner, if the rotational displacement（转动位移）or slope（转角）of the tangent at a point on a structure is to be determined, a virtual couple moment（力偶矩）M’ having a “unit” magnitude is applied at the point. As a consequence（因此）, this couple moment cause a virtual load in one of the element of the body. Assuming that the real loads deform

（使..变形）the element at amount dL, the rotation can be found from the virtual-work equation 1 = u dL . This method for applying the principle of virtual work is often referred to as the method of virtual forces（虚力法）, since a virtual force is applied resulting in the calculation of a real displacement. The equation of virtual work in this case represents a compatibility requirement for the structure.

以相似的方法，如果要确定结构上某一点切线的转动位移或转角，可在该点上施加一个虚的单位力偶矩M’。因此，力偶矩在物体的某一单元中形成一个虚力。假定实际的力使单元的变形值为dL，则转角 可从虚功方程1 = u dL中得到。运用虚功原理的方法通常称为虚力法，因为施加虚力能计算出实际的位移。在这种情况下虚功方程代表着对结构的协调要求。

Although not important here, realize（意识）that we can also apply the principle of virtual work as a method of virtual displacements（虚位移）. In this case virtual displacements are imposed on（强加于）the structure, while the structure is subjected to real loadings. This method can be used to determine a force on or in a structure, so that the equation of virtual work is then expressed as an equilibrium requirement.

了解到我们也能运用虚功原理形成虚位移法，尽管在这儿不太重要。这种情况下，虚位移强加于结构，而结构承受实际的荷载。该法能用以确定结构上或结构中的力，因此虚功方程表示为平衡要求。

In 1879 Alberto Castigliano, an Italian railroad engineer, published a book in which he outline（概述）a method for determining the deflection or slope at a point in a structure, be it a truss, beam, or frame. This method, which is referred to as Castigliano’s second theorem（卡氏第二定理）, or the method of least work（最小功法）, applies only to structures that have constant temperature（恒温）, unyielding（不易弯曲）supports, and linear elastic material response.

1879年Alberto Castigliano，一个意大利的铁路工程师，出版了一本书，书中他概述了确定结构（无论是桁架、梁或框架）中某一点的挠度或转角的方法。这种称为卡氏第二定理或最小功法的方法仅应用于具有恒温、支座不易弯曲和材料线弹性响应的结构中。

If the displacement of a point is to be determined, the theorem states（表明）that it is equal to the first partial derivative（一阶偏导数）of the strain energy in the structure with respect to （关于）a force acting at a point and in the direction of displacement. In a similar manner, the slope at a point in a structure is equal to the first partial derivative of the strain energy in the structure with respect to a couple moment acting at the point and in the direction of rotation. 如果要确定某一点的位移，该定理表明位移等于结构中的应变能对于作用在该点并沿该位移方向的力的一阶偏导数。以相似的方式，结构上某一点的转角等于结构中的应变能对于作用在该点并沿该转角方向的力偶的一阶偏导数。

The derivation（推导）of the theorem requires that only conservative forces（保守力）be considered for the analysis. These forces do work that is independent of（与..无关）the path and therefore create no energy loss（能量损失）. Since forces causing a linear elastic response are conservative, the theorem is restricted to linear elastic behavior of the material. This is unlike the method of virtual force, which applies to both elastic and inelastic behavior.

定理的推导要求分析时只考虑保守力。这些力作功与路径无关，因此不造成能量的损失。由于引起线弹性响应的力是保守的，因此该定理（在运用时）被限制在材料的线弹性状态。它不象虚力法可以运用于弹性和非弹性状态。

When analyzing any indeterminate structure, it is necessary to satisfy equilibrium, compatibility, and force-displacement requirements for the structure. Equilibrium is satisfied when the reactive forces hold the structure at rest（保持结构静止）, and compatibility is satisfied when the various segments（部分）of the structure fit together（配合在一起）without intentional（故意的）breaks or overlaps（断裂或重叠）. The force displacement requirements depend upon the way the material responds, which in this chapter we have assumed linear-elastic response. In general there are two different ways to satisfy these requirements when analyzing a statically indeterminate structure: the force or flexibility method（柔度法）, and the stiffness or displacement method.

当分析任何不确定的结构时，有必要满足结构的平衡 …… 此处隐藏：5088字，全部文档内容请下载后查看。喜欢就下载吧 ……