英汉双语弹性力学5.ppt

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1、ElasticityChapter5Complex-variableMethodsforPlaneElasticity1第五章平面问题的复变函数法2§5-4Thesingle-valuedconditionofstressanddisplacementinmultiplyconnectedregion§5-3Complex-variablerepresentationofboundarycondition§5-2Complex-variablerepresentationofstressanddisplacement§5-1Complex-variabler

2、epresentationofstressfunction§5-6Problemofinfiniteplaneincludinghole§5-5SituationofinfinitemultiplyconnectedbodyChapter5Complex-variableMethodsforPlaneElasticityComplex-variableMethodsforPlaneElasticity3§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

3、§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4Complex-variableMethodsforPlaneElasticityChapter5Complex-variableMethodsforPlaneElasticityWhensolvingplaneproblemsbyCartesiancoordinatesorpolarcoordinates,theboundaryofobjectisstraightlineorcirculararc.Tootherboundary,forexampleellipse,hyperbola

4、,non-concentriccirclesandsoon,weneedusedifferentcurvilinearcoordinates.Applyingcomplex-variablecanpredigesttheseproblems.Inthischapter,wejustintroducethesimpleapplicationofcomplex-variableinelasticity.5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

5、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。6§5-1Complex-variablerepresentationofstressfunctionInchapter2,wehaveproved,inplaneproblems,thereisastressfunctionφthatisbiharmonicfunctionofpositioncoordinates,ifbodyforceisconstant,i.e.Complex-variableMethodsforPlaneElasticityNowi

6、ntroducecomplexvariablez=x＋iyandz＝x－iytoreplacerealvariablexandy.Noticing,7§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8Wefindthetransformationarefurthermore,Complex-variableMethodsforPlaneElasticity9可以得到变换式进而平面问题的复变

7、函数法10LetSowecantransformthefunctionasForComplex-variableMethodsforPlaneElasticity11令于是可将方程式变换成为由平面问题的复变函数法12ItisobviousknownPisharmonicfunctionwhichcanbeobtainedbyrealpartofanalyticalfunction.Supposef(z)asanalyticalfunctionandletForLetyieldsthusComplex-variableMethodsforPlaneElasti

8、city13可知，P是调和函数可由解析函数的实部得到