文档介绍：Elasticity
Chapter plex-variable
Methods for Plane Elasticity
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第五章平面问题的复变函数法
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§5-4 The single-valued condition of stress and
displacement in multiply connected region
§5-plex-variable representation of boundary
condition
§5-plex-variable representation of stress and
displacement
§5-plex-variable representation of stress function
§5-6 Problem of infinite plane including hole
§5-5 Situation of infinite multiply connected body
Chapter plex-variable
Methods for Plane Elasticity
Complex-variable Methods for Plane Elasticity
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§5-4 多连通域内应力与位移的单值条件
§5-3 边界条件的复变函数表示
§5-2 应力和位移的复变函数表示
§5-1 应力函数的复变函数表示
§5-6 含孔口的无限大板问题
§5-5 无限大多连体的情形
平面问题的复变函数法
第五章平面问题的复变函数法
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Complex-variable Methods for Plane Elasticity
Chapter plex-variable
Methods for Plane Elasticity
When solving plane problems by Cartesian coordinates or polar coordinates, the boundary of object is straight line or circular arc .To other boundary, for example ellipse, hyperbola, non-concentric circles and so on, we need use different curvilinear coordinates. plex-variable can predigest these problems.
In this chapter, we just introduce the simple application plex-variable in elasticity.
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平面问题的复变函数法
第五章平面问题的复变函数法
直角坐标及极坐标求解平面问题,所涉及的物体边界是直线或圆弧形。对于其他一些边界,例如椭圆形、双曲形、非同心圆等就要用不同的曲线坐标。应用复变函数可使该类问题得以简化。本章只限于介绍复变函数方法在弹性力学中的简单应用。
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§5-plex-variable representation of stress function
In chapter 2,we have proved, in plane problems, there is a stress function φ that is biharmonic function of position coordinates, if body force is constant, .
Complex-variable Methods for Plane Elasticity
Now plex variable z= x+iy and z=x-iy to replace real variable x and y. Noticing,
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§5-1 应力函数的复变函数表示
在第二章中已经证明,在平面问题里,如果体力是常量,就一定存在一个应力函数φ,它是位置坐标的重调和函数,即
现在,引入复变数z= x+iy和 z=x-iy以代替实变数x 和y。注意
平面问题的复变函数法
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We find the transformation are
furthermore,
Complex-variable Methods for Plane Elasticity
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可以得到变换式
进而
平面问题的复变函数法
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