河海大学：《弹性力学及有限元》课程PPT教学课件（双语版）第十二章 薄板弯曲问题和经典解答（Bending of Thin Plates，Classical Solutions）

Chapter 12 Bending of Thin Plates Classical solutions 第十二章薄板弯曲问题。经典解答。 第二版2002 弹性力学第十二章

第二版2002 弹性力学第十二章 1 Chapter 12 Bending of Thin Plates. Classical Solutions 第十二章 薄板弯曲问题。经典解答

Section 12.1 Introduction and assumptions 引言和假定 a plate is a body bounded by two closely spaced parallel planes and one or more prismatical surfaces normal to the lanes Fig- 12.1.1 第二版2002 弹性力学第十二章

第二版2002 弹性力学第十二章 2 Section 12.1 Introduction and Assumptions 引言和假定 A plate is a body bounded by two closely spaced parallel planes and one or more prismatical surfaces normal to the planes

Plate faces--two closely spaced parallel planes Fg.2.1.I Plate edges--prismatical surfaces normal to the plate faces 第二版2002 弹性力学第十二章

第二版2002 弹性力学第十二章 3 • Plate faces--two closely spaced parallel planes • Plate edges--prismatical surfaces normal to the plate faces

Plate thickness--the distance between the two plate faces. It is denoted by t Thin plate-- t<<a t<<b t<min(a, b) 8 Thick plate 第二版2002 弹性力学第十二章

第二版2002 弹性力学第十二章 4 • Plate thickness--the distance between the two plate faces. It is denoted by t. • Thin plate-- t<<a t <<b t<min(a,b)/8 • Thick plate

Plate middle plane The plane parallel to the faces of the plate and bisecting the thickness t is called the middle plane of the plate 第二版2002 弹性力学第十二章

第二版2002 弹性力学第十二章 5 • Plate middle plane-- The plane parallel to the faces of the plate and bisecting the thickness t is called the middle plane of the plate

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