For Example, 11.5, consider the case of only a normal boundary load (X = 0), and assume that the material is orthotropic with i

For Example, 11.5, consider the case of only a normal boundary load (X = 0), and assume that the material is orthotropic with μ_i = iβ_i (see Exercise 11.15). Show that the resulting stress field is given by:

Next compare the stress component σ_r with the corresponding isotropic value by plotting the stress contours σ_r /Y = constant for each case. Use orthotropic material values for the Carbon/ Epoxy composite given in Table 11.2 and compare with the corresponding isotropic case.

Data from example 11.5

Data from exercise 11.15

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

Justify the isotropic case where β_1,2 = 1. Finally, determine β_1,2 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

or YB1B2 (B1 +82) sin Tr(cos0+ sine) (cos20+ sin0) 3 de Tre=0