Assumption 1.--E, Ix and r are neglected, since they are small The three physical equations are not valid again and have to be abandoned E-10,- Hox-HoVVE ET/G ZX G ZY 第二版2002 弹性力学第十二章
第二版2002 弹性力学第十二章 11 Assumption 1.--z rzx and rzy are neglected, since they are small. • The three physical equations are not valid again and have to be abandoned. z=[z - x - y ]/E rzx =zx/G rzy =zy/G
E=Ow/0z≈0 w=W(x,y) This equation shows that all the points aligned on a normal to the middle plane will have the same displacement in the transverse direction and that this displacement is just the deflection of the plate 第二版2002 弹性力学第十二章 12
第二版2002 弹性力学第十二章 12 z =w/z ≈ 0-------w=w(x,y) • This equation shows that all the points aligned on a normal to the middle plane will have the same displacement in the transverse direction and that this displacement is just the deflection of the plate
ZX Initially straight lines which are normal to the middle plane remain straight and normal to the deformed middle plane 第二版2002 弹性力学第十二章 13
第二版2002 弹性力学第十二章 13 rzx= rzy ≈ 0 • Initially straight lines which are normal to the middle plane remain straight and normal to the deformed middle plane
Assumption 2.--The strains due to o, are Z neglected. since o is small The three physical equations will be the same as those in the plane stress problems Ex=[ox- Hoy- AvE E、=oyp0xE /G The other physical equations are abandoned 第二版2002 弹性力学第十二章
第二版2002 弹性力学第十二章 14 Assumption 2.--The strains due to z are neglected, since z is small. • The three physical equations will be the same as those in the plane stress problems: x=[x - y - z ]/E y=[y - x - z ]/E rxy =xy/G • The other physical equations are abandoned
Assumption 3. --0ro and v-o are neglected. The longitudinal displacements of all the points in the middle plane may be neglected 8=8.=r xy=0≈ 0 The middle plane of the plate remains unstrained, although the plane becomes curved alter bending 第二版2002 弹性力学第十二章 15
第二版2002 弹性力学第十二章 15 Assumption 3.--u)z=0 and v)z=0 are neglected. The longitudinal displacements of all the points in the middle plane may be neglected • ( x= y= rxy)z=0 ≈ 0 The middle plane of the plate remains unstrained, although the plane becomes curved after bending