Figure 11.1 Orthotropic Axes and Arbitrary Direction in the Plane of a Ply Recall 1:The stress acting on a surface with a normal vector n is given by {o}=[ol{n} (11.2) column matrix of stress column matrix of stress components matrix direction cosines Recall 2:The coordinates of the same vector in axesy as well as e,t,such that (x.)=cose,are =v,t+vi=c+V动 with the relation: 份-{5 (11.3) In axes t the stress acting on the surface with a normal can be expressed as follows,using Equation 11.2 above: toae-io,tou-iol母 where fo is the stress vector and [ol is the stress matrix and in axes x,y, following Equation 11.3: aw周 2003 by CRC Press LLC
Recall 1: The stress acting on a surface with a normal vector is given by (11.2)
Recall 2: The coordinates of the same vector in axes x,y as well as
,t, such that = cosq, are with the relation: (11.3) In axes
,t the stress acting on the surface with a normal can be expressed as follows, using Equation 11.2 above: where {s/x} is the stress vector and [sij] is the stress matrix and in axes x,y, following Equation 11.3: Figure 11.1 Orthotropic Axes and Arbitrary Direction in the Plane of a Ply s n { } σ σij = [ ]{ } n column matrix of stress components σ stress matrix column matrix of direction cosines n V ( ) x .
V V

Vt = = + t Vx x + Vyy Vx ÓVy ˛ Ì ˝ Ï ¸ c s –s c Ó ˛ Ì ˝ Ï ¸ V
ÓVt ˛ Ì ˝ Ï ¸ c = cosq Ë ¯ c = sinq Ê ˆ = x { } s/x
,t sij [ ]
,t { }x
,t sij [ ]
,t c s Ó ˛ Ì ˝ Ï ¸ = = { } s/x x,y c s –s c sij [ ]
,t c s Ó ˛ Ì ˝ Ï ¸ = TX846_Frame_C11 Page 224 Monday, November 18, 2002 12:26 PM © 2003 by CRC Press LLC