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

D.￠-bxy,X=0,Yy=0 It satisfies the compatibility equation V4=0 find the stress components by x=020y2=0y=020x2=0Txy=02d0x0y=b for a rectangular plate with its edges parallel to the coordinate axes. find the surface force components by (ox+m tsx(mo +Itxvs=Y the stress function =bxy can solve the problem of a rectangular plate in pure shear P37 Fig.3.1.1(b) 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 11 D. =bxy , X=0, Y=0 • It satisfies the compatibility equation 4  =0 • find the stress components by x = 2/y 2=0 y =  2/x 2=0 xy =- 2/xy=-b • 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 =bxy can solve the problem of a rectangular plate in pure shear. P37 Fig.3.1.1(b)

bX X=0。Y=0 满足相容方程V4φ=0 由下式求出应力分量 =0240y2=0=0200x2=0Ty=02Ox0=-b 对和坐标轴平行的矩形板求出面力分量知 φ=bxy能解决矩形板受纯剪作用。P37 Fig.3.1.1(b) 徐汉忠第一版20007 弹性力学第三章 12

徐汉忠第一版2000/7 弹性力学第三章 12 D. =bxy , 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=0 xy =- 2/xy=-b • 对和坐标轴平行的矩形板求出面力分量知 = bxy 能解决矩形板受纯剪作用。P37 Fig.3.1.1(b)

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 13

徐汉忠第一版2000/7 弹性力学第三章 13

E.φay3,X=0,Y=0 It satisfies the compatibility equation 满足相容方程V4φ=0 Find the stress components by 由下式求出应力分量3=02d/0y2=6ay =02d/0x2=0 Txv=-02p/0x0y=0 For a rectangular plate shown in fig. l, find the surface force components shown in fig.对矩形 板求出面力分量,如图1所示。 Solve the problem of pure bending of a rectangular beam.矩形板纯弯曲问题 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 14 E. =ay3 , X=0, Y=0 • It satisfies the compatibility equation 满足相容方程 4  =0 • Find the stress components by 由下式求出应力分量 x = 2/y 2=6ay y =  2/x 2=0 xy =- 2/xy=0 • For a rectangular plate shown in fig.1, find the surface force components shown in fig.1对矩形 板求出面力分量，如图1所示。 • Solve the problem of pure bending of a rectangular beam. 矩形板纯弯曲问题

g312 徐汉忠第一版20007 弹性力学第三章 15

徐汉忠第一版2000/7 弹性力学第三章 15