The linear buckling analysis consists of two steps. First a stationary problem is solved using a unit load of arbitrary size. The critical load is then obtained by solving an eigenvalue problem, where the eigenvalue λ is the multiplier to the original load that would cause buckling.

Here ε us the engineering strain, εGL is the Green-Lagrange strain and σ1 is the stress caused by the unit load. In terms of stiffness matrices, this corresponds to

where KL is the linear stiffness matrix, and KNL is the nonlinear contribution to the full stiffness matrix. The symbolic linearization point u0 is the displacement vector caused by the unit load.

Strictly speaking, this formulation assumes that geometric nonlinearity is not used in the eigenvalue step. The Green-Lagrange tensor is inserted explicitly in the second term of Equation 3-87, while the first term uses the linear (engineering) strain tensor.

If, however, geometric nonlinearity is selected in the linear buckling study step, Equation 3-87 is replaced by

By using the term (λ-1), the effect of using the Green-Lagrange strain tensor in the first term is to a large extent removed. Unless the unit load is significantly larger than the buckling load, the result will be the same as the intended, even if geometric nonlinearity was inadvertently selected in the eigenvalue study step.