Invariant stiffness concepts

Invariant stiffness concepts as developed by Tsai and Pagano [7-16 and 7-17] can be used as an aid to understanding the stiffnesses of laminates of arbitrary orientation and how those stiffnesses can be varied. The concepts and their use are discussed in Sections 7.7.3.1 through 7.7.3.3. 

The invariant stiffness concepts for a iamina will now be extended to a laminate. All results in this and succeeding subsections on invariant laminate stiffnesses were obtained by Tsai and Pagano [7-16 and 7-17]. The laminate is composed of orthotropic laminae with arbitrary orientations and thicknesses. The stiffnesses of the laminate in the x-y plane can be written in the usual manner as... 

The analytical tools to accomplish laminate design are at least twofold. First, the invariant laminate stiffness concepts developed by Tsai and Pagano [7-16 and 7-17] used to vary laminate stiffnesses. Second, structural optimization techniques as described by Schmit [7-12] can be used to provide a decision-making process for variation of iami-nate design parameters. This duo of techniques is particularly well suited to composite structures design because the simultaneous possibility and necessity to tailor the material to meet structural requirements exists to a degree not seen in isotropic materials. 

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,... 

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