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530.418 Aerospace Structures and Materials Lecture 22: Laminate Design

530.418 Aerospace Structures and Materials Lecture 22: Laminate Design. Composite lay up:. Lamina orthotropic properties Laminate Isotropic/anisotropic properties determined by composite design Fiber orientation used to specify composite lay up, e.g. [ 0/90/+45/-45/0/-45/+45/90/0]. n.

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530.418 Aerospace Structures and Materials Lecture 22: Laminate Design

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  1. 530.418 Aerospace Structures and MaterialsLecture 22: Laminate Design

  2. Composite lay up: • Lamina • orthotropic properties • Laminate • Isotropic/anisotropic properties determined bycomposite design • Fiber orientation used to specify composite lay up,e.g. [0/90/+45/-45/0/-45/+45/90/0] n

  3. Laminate Ply Orientation Code • Each ply accounted for • Start at top • Angles between -90 and +90 • Repeat plies by subscript • [02 90 02] = [0 0 90 0 0] • Repeat sub groups also possible • [0 (45 -45)3 0] = [0 45 -45 45 -45 45 -45 0] • Entire laminate may be repeated • [0 90 0]3 = [0 90 0 0 90 0 0 90 0] • A strike through last ply means it is center but not repeated • S = symmetric • [0 45 -45 90]S = [0 45 -45 90 90 -45 45 0] • Can subscript # and S • [0 45 -45 90]2S = [0 45 -45 90 0 45 -45 90 90 -45 45 0 90 -45 45 0] 90 -45 45 0

  4. Influence of individual laminates [0 45 -45 90 90 -45 45 0]

  5. Lay up effect on strength and stiffness

  6. Elastic behavior and constants

  7. Anisotropic laminate behavior

  8. Key point … Loading composites can lead to ply coupling and funny shapes !!!

  9. Deflection of laminates

  10. Effect of symmetry Reduces out-of-plan coupling and distortions associated with Poisson ration mismatch.

  11. Tailoring ply orientations

  12. Laminate stress distributions

  13. Voight Model  Iso-strain A = B =  Av.  = VA A + VBB Av. E = Av. /  = VAA /  + VBB /  Ecomposite = VA EA + VB EB A B

  14. Reuss Model  Iso-stress A = B =  Av.  = VA A + VBB Av.  = VA A + VB B 1 / Ecomposite = VA / EA + VB / EB A B

  15. Terminology • Micro mechanics • Interaction between constituents (fiber and matrix) and ply • Too detailed for failure • OK for elasticity -> rule of mixtures • Macro mechanics • Relation between plies and laminate • Continuum mechanics, each level homogeneous + orthotropic • Lamination theory principle mathematical tool for relationship • Ply properties measured • Laminate theory assumptions • Thin plate or shell (2D stresses) • Plies orthotropic elasticity (4 ind. Const.) • Must transform elastic constants (ply) to laminate axes using law of Cosines

  16. Extrenal loading and deflections • External loading • N1 = Nx = in-plane axial load • N2 = Ny = in-plane transverse load • N3 = Nz = N4 = Nxz = N5 = Nyz = 0 • N6 = Nxy = in-plane shear load • M1 = axial bending load • M2 = transverse bending load • M6 = twisting load • External deflections • e1 = ex = in-plane axial strain • e2 = ey = in-plane transverse strain • e3 = ez = e4 = exz = e5 = eyz = 0 • e6 = exy = in-plane shear strain • k1 = axial curvature • k2 = transverse curvature • k6 = twist

  17. Hooke’s law si = Cijej sxx C11 C12 C13 C14 C15 C16exx syy C21 C22 C23 C24 C25 C26 eyy szz = C31 C32 C33 C34 C35 C36 ezz syz C41 C42 C43 C44 C45 C46 eyz sxz C51 C52 C53 C54 C55 C56 exz sxy C61 C62 C63 C64 C65 C66 exy

  18. Hooke’s law si = Cijej sxx C11 C12 C13 C14 C15 C16exx syy C21 C22 C23 C24 C25 C26 eyy 0 = C31 C32 C33 C34 C35 C36 0 0 C41 C42 C43 C44 C45 C46 0 0 C51 C52 C53 C54 C55 C56 0 sxy C61 C62 C63 C64 C65 C66 exy

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