In the alternative method we eliminate the strain-components and the displacements. This method leads to a system of partial differential equations to be satisfied by the stress-components. In this system there are three equations of the type

∂Xx + ∂Xy+ ∂Xz+ ρX = 0,
∂x ∂y∂z

(1 bis)

three of the type

∂²Xx+ ∂²Xx+ ∂²Xx+ 1 ∂²(Xx + Yy + Zz) =
∂x² ∂y²∂z² 1 + σ∂x²
− σρ ( ∂X+ ∂Y+ ∂Z) − 2ρ ∂X,
1 − σ ∂x∂y ∂z∂x

(5)

and three of the type

∂²Yz+ ∂²Yz+ ∂²Yz+ 1 ∂²(Xx + Yy + Zz) = − ρ ( ∂Z+ ∂Y),
∂x² ∂y²∂z² 1 + σ∂y∂z ∂y∂z

(6)