河海大学：《弹性力学及有限元》课程PPT教学课件（双语版）第三章 平面问题直角坐标解答 solution of plane problems in rectangular coordinates

B.￠ax2,X=0,Y=0 满足相容方程V4φ=0 由下式求出应力分量 o=020y2=0G=020x2=2atxy=020x0y=0 ·对和坐标轴平行的矩形板求出面力分量知 ￠ax2能解决矩形板y向受均匀拉力(a>0)或均 匀压力(a<0)的问题。P37Fg31.1(a) 徐汉忠第一版20007 弹性力学第三章 6

徐汉忠第一版2000/7 弹性力学第三章 6 B. =ax2 , X=0, Y=0 • 满足相容方程 4  =0 • 由下式求出应力分量 x = 2/y 2=0 y =  2/x 2=2a xy =- 2/xy=0 • 对和坐标轴平行的矩形板求出面力分量知 =ax2 能解决矩形板y向受均匀拉力(a>0)或 均 匀压力(a<0)的问题。P37 Fig.3.1.1(a)

x 2C 2C 2a↑t (a) (C Fig 3.1.1 徐汉忠第一版20007 弹性力学第三章

徐汉忠第一版2000/7 弹性力学第三章 7

C.φ=cy2,x=0,Y=0 It satisfies the compatibility equation V49=0 find the stress components by x=0240y2=2cay=020/0x2=0tx=020xoy=0 for a rectangular plate with its edges parallel to the coordinate axes find the surface force components by (ox+m tsX (mσ+lxy)s=Y the stress function =cy can solve the problem of uniform tension(c>0)or uniform compression (c<0)of a rectangular plate in x direction. P37 Fig3.1.1(c) 徐汉忠第一版20007 弹性力学第三章 8

徐汉忠第一版2000/7 弹性力学第三章 8 C. =cy2 , X=0, Y=0 • It satisfies the compatibility equation 4  =0 • find the stress components by x = 2/y 2=2c y =  2/x 2=0 xy =- 2/xy=0 for a rectangular plate with its edges parallel to the coordinate axes, find the surface force components by (lx+m yx)s=X (my+lxy)s =Y • the stress function =cy2 can solve the problem of uniform tension (c>0) or uniform compression (c<0) of a rectangular plate in x direction. P37 Fig.3.1.1(c)

C.φ=cy2,X=0,Y=0 满足相容方程V4φ=0 由下式求出应力分量 o=020y2=2coy=0200x2=0y=02Oxy=0 ·对和坐标轴平行的矩形板求出面力分量知 cy2能解决矩形板x向受均匀拉力(c>0)或均 匀压力(c<0)的问题。P37Fig311(c) 徐汉忠第一版20007 弹性力学第三章

徐汉忠第一版2000/7 弹性力学第三章 9 C. =cy2 , X=0, Y=0 • 满足相容方程 4  =0 • 由下式求出应力分量 x = 2/y 2= 2c y =  2/x 2=0 xy =- 2/xy=0 • 对和坐标轴平行的矩形板求出面力分量知 =cy2 能解决矩形板x向受均匀拉力(c>0)或 均 匀压力(c<0)的问题。P37 Fig.3.1.1(c)

x 2C 2C 2a↑t (a) (C Fig 3.1.1 徐汉忠第一版20007 弹性力学第三章

徐汉忠第一版2000/7 弹性力学第三章 10