INVARIANT PROPERTIES OF AN ORTHOTROPIC LAMINA

Tsai and Pagano [2-7] ingeniously recast the stiffness transformation equations to enable ready understanding of the consequences of rotating a lamina in a laminate. By use of various trigonometric identities between sin and cos to powers and sin and cos of multiples of the angle, the transformed reduced stiffnesses. Equation (2.85), can be written as 

The advantage of writing the tran forriTation eqi tions in the form of Equation (2.98) is that parts of Q. Q.,2, Q22. and Qgg are then obviously invariant under rotations about the z-axis (perpendicular to the lamina). This concept of invariance is useful when examining the prospect of orienting a lamina at various angles to achieve a certain stiffness profile. For example, 

Similar invariance concepts for anisotropic materials were also developed by Tsai and Pagano [2-7]. For anisotropy, the following definitions 

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