Compute the coefficients in the plate stiffness equations

Question

Compute the stresses in laminate coordinates at top and bottom of each lamina in Example 1 when the laminate is subjected to ε⁰_x  = 765(10^-6 ) mm/mm, ε⁰_y = -280(10^-6 ) mm/mm, κ_xy = 34.2(10^-6)1/mm and all remaining strains and curvatures equal to zero.

Example 1

Compute the coefficients in the plate stiffness equations (given) for a twolamina laminate with θ₁ = 55°, θ₂ = -55°, t₁ = t₂ = 0.635 mm, with material properties given in Example 2.

Φ_{x =} δw_0/δx

Φ_{y =} δw_0/δy

Example 2

Compute the reduced stiffness matrix [Q] and the intralaminar shear coefficients using the following properties: E₁ = 19.981 GP a, ν₁₂ = 0.274, E₂ = 11.389 GP a, G₁₂ = G₁₃ = 3.789 GP a [172]. Lacking experimental data, assume the out-of-plane shear modulus G₂₃ ∼= G_m = 0.385 GP a.