370 Mechanics of Composite Materials,Second Edition First,special cases of laminates that are important in the design of laminated structures will be introduced.Then the failure criterion analysis will be shown for a laminate.Eventually,we will be designing laminates mainly on the basis of optimizing for cost,weight,strength,and stiffness. Other mechanical design issues are briefly introduced at the end of the chapter. 5.2 Special Cases of Laminates Based on angle,material,and thickness of plies,the symmetry or antisym- metry of a laminate may zero out some elements of the three stiffness matri- ces [A],[B],and [D].These are important to study because they may result in reducing or zeroing out the coupling of forces and bending moments, normal and shear forces,or bending and twisting moments.This not only simplifies the mechanical analysis of composites,but also gives desired mechanical performance.For example,as already shown in Chapter 4,the analysis of a symmetric laminate is simplified due to the zero coupling matrix [B].Mechanically,symmetric laminates result in no warpage in a flat panel due to temperature changes in processing. 5.2.1 Symmetric Laminates A laminate is called symmetric if the material,angle,and thickness of plies are the same above and below the midplane.An example of symmetric laminates is [0/30/60]: 0 30 60 30 0 For symmetric laminates from the definition of [B]matrix,it can be proved that [B]=0.Thus,Equation(4.29)can be decoupled to give N A12 A16 A12 A26 (5.1a) A16 A26 A6 2006 by Taylor Francis Group,LLC370 Mechanics of Composite Materials, Second Edition First, special cases of laminates that are important in the design of laminated structures will be introduced. Then the failure criterion analysis will be shown for a laminate. Eventually, we will be designing laminates mainly on the basis of optimizing for cost, weight, strength, and stiffness. Other mechanical design issues are briefly introduced at the end of the chapter. 5.2 Special Cases of Laminates Based on angle, material, and thickness of plies, the symmetry or antisym￾metry of a laminate may zero out some elements of the three stiffness matri￾ces [A], [B], and [D]. These are important to study because they may result in reducing or zeroing out the coupling of forces and bending moments, normal and shear forces, or bending and twisting moments. This not only simplifies the mechanical analysis of composites, but also gives desired mechanical performance. For example, as already shown in Chapter 4, the analysis of a symmetric laminate is simplified due to the zero coupling matrix [B]. Mechanically, symmetric laminates result in no warpage in a flat panel due to temperature changes in processing. 5.2.1 Symmetric Laminates A laminate is called symmetric if the material, angle, and thickness of plies are the same above and below the midplane. An example of symmetric laminates is : For symmetric laminates from the definition of [B] matrix, it can be proved that [B] = 0. Thus, Equation (4.29) can be decoupled to give (5.1a) 0 30 60 30 0 [ /0 30/60]s N N N A A A A A A A A x y xy ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ = 11 12 16 12 22 26 16 26 66 0 0 A 0 x y xy ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ε ε γ 1343_book.fm Page 370 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC