Failure,Analysis,and Design of Laminates 373 5.2.5 Balanced Laminate A laminate is balanced if layers at angles other than 0 and 90 occur only as plus and minus pairs of +0 and-0.The plus and minus pairs do not need to be adjacent to each other,but the thickness and material of the plus and minus pairs need to be the same.Here,the terms A16=A26=0.An example of a balanced laminate is [30/40/-30/30/-30/-40]: 30 40 -30 30 -30 -40 From Equation(4.28a), Nx An A12 0 B B12 B16 e Ny An An 0 B12 B22 B26 Na 0 0 A26 B16 B26 B66 M (5.4) Bu B12 B16 D Dv2 D16 Kx B1 B22 B26 D2 D2 D Ky May B16 B26 Bes Di6 D26 D66 5.2.6 Quasi-Isotropic Laminates For a plate of isotropic material with Young's modulus,E,Poisson's ratio, v,and thickness,h,the three stiffness matrices are E VE 1-v2 1-v2 [A]= vE E 1-v 1-v2 0 h, (5.5) E 0 0 2(1+v) [B= 0 0 (5.6) 0 0 0 2006 by Taylor Francis Group,LLCFailure, Analysis, and Design of Laminates 373 5.2.5 Balanced Laminate A laminate is balanced if layers at angles other than 0 and 90° occur only as plus and minus pairs of +θ and –θ. The plus and minus pairs do not need to be adjacent to each other, but the thickness and material of the plus and minus pairs need to be the same. Here, the terms A16 = A26 = 0. An example of a balanced laminate is [30/40/–30/30/–30/–40]: From Equation (4.28a), . (5.4) 5.2.6 Quasi-Isotropic Laminates For a plate of isotropic material with Young’s modulus, E, Poisson’s ratio, ν, and thickness, h, the three stiffness matrices are , (5.5) , (5.6) 30 40 –30 30 –30 –40 N N N M M M x A A B y xy x y xy ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ = 11 12 0 11 12 16 12 22 12 22 26 26 16 26 66 11 0 0 0 B B A A B B B A B B B B B12 16 11 12 16 12 22 26 12 22 26 16 26 66 B D D D B B B D D D B B B D16 26 66 0 0 0 D D x y xy x y ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ε ε γ κ κ κxy ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ [ ] ( ) A E E E E E = − − − − + ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ 1 1 0 1 1 0 0 0 2 1 2 2 2 2 ν ν ν ν ν ν ν ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ h [ ] B = ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ 000 000 000 1343_book.fm Page 373 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC