Coordinate system--x and y are in the middle plane and z axis is perpendicular to the middle plane. The system is a right hand system x 提 Fig. 12.1.1 第二版2002 弹性力学第十二章 6
第二版2002 弹性力学第十二章 6 • Coordinate system--x and y are in the middle plane and z axis is perpendicular to the middle plane . The system is a right hand system
oads 1. Longitudinal load in the middle plane--All the external forces are parallel to the faces of the plate and distributed uniformly over the thickness plane stress problem 2.Transverse load ----They are perpendicular to the middle plane---plate bending problem 第二版2002 弹性力学第十二章
第二版2002 弹性力学第十二章 7 Loads 1. Longitudinal load in the middle plane--All the external forces are parallel to the faces of the plate and distributed uniformly over the thickness.--------plane stress problem. 2.Transverse load ----They are perpendicular to the middle plane---plate bending problem
The surface force component z on the lower face of the plate and the body force component z are transmitted to the upper face of the plate along their lines of action that is q(x, y=Zt2+Z=+2+ [2t2 Zdz Z, Z and q are considered positive when they act in the positive direction of z q(x y) is total transverse load per unit area 第二版2002 弹性力学第十二章
第二版2002 弹性力学第十二章 8 • The surface force component Z on the lower face of the plate and the body force component Z are transmitted to the upper face of the plate along their lines of action, that is q(x,y)=Z)z=-t/2+Z)z=+t/2+ -t/2 t/2 Zdz Z, Z and q are considered positive when they act in the positive direction of z. q(x,y) is total transverse load per unit area
Deflection--the displacement of a point on the middle plane in the direction of z, w(x y, 0), is called the deflection of the point Small deflections--the deflection is much smaller than the thickness. W(, y,O<t/5 Only small deflections are considered here 第二版2002 弹性力学第十二章
第二版2002 弹性力学第十二章 9 • Deflection--the displacement of a point on the middle plane in the direction of z, w(x,y,0), is called the deflection of the point . • Small deflections--the deflection is much smaller than the thickness. W(x,y,0)<t/5 • Only small deflections are considered here
Basic assumptions Assumption stated in Sec. 1.3 1. The body is continuous, perfectly elastic homogeneous and isotropic 2.The displacements and strains are small -o--The deflection of the plate is small Thin plates 第二版2002 弹性力学第十二章
第二版2002 弹性力学第十二章 10 Basic Assumptions • Assumption stated in Sec.1.3 1. The body is continuous, perfectly elastic, homogeneous and isotropic. 2.The displacements and strains are small. ------The deflection of the plate is small. • Thin plates