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The stiffness matrix [C] for a specially orthotropic material associated with the principal material axes (1, 2, 3) is given in Equation 2

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The stiffness matrix [C] for a specially orthotropic material associated with the principal material axes (1, 2, 3) is given in Equation 2.16. Prove that, when the material is specially orthotropic and transversely isotropic in the 2–3 planes (i.e., the properties are invariant to rotations about the 1 axis) the stiffness matrix [C] is given by Equation 2.17. Hint: to prove that C44 = (C22 − C23)/2, consider the stresses and strains acting on an element under pure shear stress σ23 and the corresponding stresses and strains acting on the same element, which has been rotated by a convenient angle in the 2–3 planes.

An orthotropic, transversely isotropic material is subjected to a 2D stress condition along the principal material axes 1, 2, 3 as shown in Figure 2.11 and the engineering constants for the material are as follows: E G 1 E 6 12 6 2 6 = × 20 10 psi p , , = ×1 10 1 si = × . , 5 10 0 psi ν ν 12 = = . , 3 0 23 .2 Determine all strains associated with the 1, 2, 3 axes.