withs 2 -2sc [T]= 2sc SC -SC (c2-s3 In a similar manner,the strain components can be transformed as: 2 s2 2cs s2 -2cs Exy -CS CS (c2-s3) or: s2 CS -CS E -2cs 2cs (c2-523) then: with: [T']= -CS -2cs 2cs (c2-s3 The stress-strain Equation 11.1 can then be expressed in the axes x,y since we have written: -Vie 0 月，：月 0()e ()t [TH(Gbs 0 0 5This matrix is readily established if one knows the relation that allows one to express the components of a tensor in one system in terms of the components of the same tensor in another system.Here this relation is:oy=cos"cos"with cos"=cos(m,1);see Section 13.1. 2003 by CRC Press LLCwith5 In a similar manner, the strain components can be transformed as: or: The stress–strain Equation 11.1 can then be expressed in the axes x,y since we have written: 5 This [T ] matrix is readily established if one knows the relation that allows one to express the components of a tensor in one system in terms of the components of the same tensor in another system. Here this relation is: sIJ = cos smn with = cos( ); see Section 13.1. I m cosJ m cosI m m,I [ ] T c 2 s 2 2– sc s 2 c 2 2sc sc sc c2 s 2 – ( ) – = ex e y Óexy ˛ Ô Ô Ì ˝ Ô Ô Ï ¸ c 2 s 2 2cs s 2 c 2 –2cs –cs cs c 2 s 2 ( ) – e
et Óe
t˛ Ô Ô Ì ˝ Ô Ô Ï ¸ = then: with: ex e y Óg xy ˛ Ô Ô Ì ˝ Ô Ô Ï ¸ c 2 s 2 cs s 2 c 2 –cs –2cs 2cs c 2 s 2 ( ) – e
et Óg
t˛ Ô Ô Ì ˝ Ô Ô Ï ¸ = e gÓ ˛ Ì ˝ Ï ¸ x,y [ ] T ¢ e gÓ ˛ Ì ˝ Ï ¸
,t = [ ] T ¢ c 2 s 2 cs s 2 c 2 –cs –2cs 2cs c2 s 2 ( ) – = e gÓ ˛ Ì ˝ Ï ¸ x,y [ ] T ¢ e gÓ ˛ Ì ˝ Ï ¸
,t ; e gÓ ˛ Ì ˝ Ï ¸
,t 1 E
----- nt
– Et --------- 0 n
t – E
--------- 1 Et ---- 0 0 0 1 G
t ------- { } s
,t == = ; { } s
,t [ ] T { } s x,y TX846_Frame_C11 Page 226 Monday, November 18, 2002 12:26 PM © 2003 by CRC Press LLC