For the plane problem with an orthotropic material, show that the characteristic Eq. (11.5.7) reduces to the

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For the plane problem with an orthotropic material, show that the characteristic Eq. (11.5.7) reduces to the quadratic equation in μ2:

S114+ (2S12+S66)  + S22 = 0 Explicitly solve this equation for the roots ui, and show that they are purely

Justify the isotropic case where β1,2 = 1. Finally, determine β1,2 for each of the four composite materials given in Table 11.2. See MATLAB code C.10 for numerical methods to calculate b-parameters.

Table 11.2

Table 11.2 Typical Elastic Moduli for Some Planar Orthotopic Composite Materials Material E (GPa) E (GPa) "12

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