N is the number of laminae and aknbsp bknbsp qknbsp and

Question

Given the following stresses
σ_x = A^kz sin(αx) sin(βy)
σ_y = B^kz sin(αx) sin(βy)
σ_xy = 0
σ_yz = Q^k sin(αx) cos(βy)
σxz = R^k cos(αx) sin(βy)

where k = 1 . . . N, N is the number of laminae, and A^k , B^k , Q^k , and R^k are constants, derive the seven stress resultants integrating over the thickness of a laminated plate with N = 3, t₁ = t₂ = t₃.