12 MECHANICAL BEHAVIOR OF THIN LAMINATED PLATES The definition of a laminate was given in Chapter 5.In the same chapter the practical calculation methods for the laminate was also described.We propose here to justify these methods,meaning to study the behavior of the laminate when it is subjected to a combination of loadings.This study is necessary if one wants to have correct design with strains or stresses within their admissible values. 12.1 LAMINATE WITH MIDPLANE SYMMETRY 12.1.1 Membrane Behavior We consider in the following a laminate with midplane symmetry.The total thickness of the laminate is denoted as b.It consists of n plies.Ply number k has a thickness denoted as es(see Figure 12.1).Plane x,y is the plane of symmetry 12.1.1.1 Loadings The laminate is subjected to loadings in its plane.The stress resultants are denoted as NN T=T These are the membrane stress resultants.They are defined as: N:Stress resultant in the x direction over a unit width along the y direction. n中p Nx= c.dc=∑(o×es b/2 (12.1) k=1p时 M:Stress resultant along the y direction over a unit width along thex direction. =马，k=∑(o×e (12.2) =1"ply TSee Section 5.2. 2 The problem of buckling of the laminates is not the scope of this chapter.See Appendix 2. 3 See Section 5.2.3. 2003 by CRC Press LLC12 MECHANICAL BEHAVIOR OF THIN LAMINATED PLATES The definition of a laminate was given in Chapter 5.1 In the same chapter the practical calculation methods for the laminate was also described. We propose here to justify these methods, meaning to study the behavior of the laminate when it is subjected to a combination of loadings. This study is necessary if one wants to have correct design with strains or stresses within their admissible values.2 12.1 LAMINATE WITH MIDPLANE SYMMETRY 12.1.1 Membrane Behavior We consider in the following a laminate with midplane symmetry. 3 The total thickness of the laminate is denoted as h. It consists of n plies. Ply number k has a thickness denoted as ek (see Figure 12.1). Plane x,y is the plane of symmetry. 12.1.1.1 Loadings The laminate is subjected to loadings in its plane. The stress resultants are denoted as Nx, Ny, Txy = Tyx. These are the membrane stress resultants.They are defined as:
Nx: Stress resultant in the x direction over a unit width along the y direction. (12.1)
Ny: Stress resultant along the y direction over a unit width along the x direction. (12.2) 1 See Section 5.2. 2 The problem of buckling of the laminates is not the scope of this chapter. See Appendix 2. 3 See Section 5.2.3. Nx sxdz –h/2 h/2 Ú sx ( )k ¥ ek k=1 stply nthply = = Â Ny sy dz –h/2 h/2 Ú sy ( )k ¥ ek k=1 stply nthply = = Â TX846_Frame_C12 Page 235 Monday, November 18, 2002 12:27 PM © 2003 by CRC Press LLC