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Flexural response equations

Flexural response equations. Flexure is just a fancy term for bending. For laminate under transverse loading. Importance of D16 and D26 terms. Nemeth has paper (see refs for Chapter 8) that investigated when you can neglect D16 and D26 terms.

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Flexural response equations

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  1. Flexural response equations • Flexure is just a fancy term for bending. • For laminate under transverse loading

  2. Importance of D16 and D26 terms • Nemeth has paper (see refs for Chapter 8) that investigated when you can neglect D16 and D26 terms. • The in-plane coefficients A16 and A26 can be made to vanish by using a balanced laminate. • Why can’t we do that for D16 and D26.

  3. Some results for balanced laminates • Angle-ply Graphite-epoxy laminates ()

  4. Can improve with thicker laminates • Can we do better with 8-ply laminates?

  5. Comparing two laminates • Compare to • Contribution to D’s goes like • For first laminate 45s have and -45s have • In second laminate 45s have , and -45s have • By how much do we reduce D16?

  6. Quasi-isotropic laminates • Much better situation on D16, but not on isotropy

  7. Simply supported plate with sinusoidal loading • Simplified equation • Sinusoidal load • Solution is • Checks? • For more general loading can use Fourier series

  8. Natural frequencies • For natural vibration we replace loading with inertial load • For simply supported boundary conditions, the natural modes are of the form • Then we can check that a nontrivial solution exists only for the following frequencies • What does it tell us about the effect of aspect ratio on the mode shape of the lowest frequency? • Fundamental frequency is for m=n=1.

  9. Buckling • Simply supported plate under bi-axial loading, (no shear load). • The buckling load multiplier such that will cause buckling is given as • For isotropic plate, it tends to buckle into squares (m/a is close to n/b). • Unlike vibration the lowest value is not necessarily m=n=1.

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