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Laminates of Orthotropic plies

Laminates of Orthotropic plies. Section 2.4.3 for in-plane loading only Hooke’s law for k- th ply Stress resultants. A Matrix. Basic equation is the same as in isotropic case, , but 16 and 26 terms We now use the Tsai-Pagano “invariants” Leading to lamination parameters.

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Laminates of Orthotropic plies

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  1. Laminates of Orthotropic plies • Section 2.4.3 for in-plane loading only • Hooke’s law for k-th ply • Stress resultants

  2. A Matrix • Basic equation is the same as in isotropic case, , but 16 and 26 terms • We now use the Tsai-Pagano “invariants” • Leading to lamination parameters

  3. Effective properties • From Q’s to A’s using lamination parameters • Effective properties

  4. Hooke’s law with effective properties • Average stresses • Hooke’s law

  5. Typical stiffness optimization problem • No stresses in individual plies, so no credible failure constraint. • When 0-deg, 90-deg and 45-deg plies are present this is reasonable even for strength.

  6. Example 4.1.1 • Graphite/epoxy • Two load conditions • Allowable strains: Normal strains 0.4%, shear strain 0.006 • Try

  7. Sanity checks for first two laminates • For all-zero laminate • We find that to satisfy normal strain we need at least 0.135 in, while to satisfy the shear constraint we need 0.538 in. Are these numbers reasonable? • For laminate we find • We need 0.787 in for normal strain constraint, and 0.102 in for shear constraint. Are these reasonable?

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