Flow for the API Methods to be used for Linear Buckling Analysis:

1st: call the Stiffness Matrix method for K_L

2nd: solve the system of equations for the displacements

3rd: call the Stresses method to get the stresses at the Gauss points

4th: call the Geometric Stiffness Matrix method for K_G

5th: solve the eigenvalue problem K_L.u = s.K_G.u

where s are the eigenvalues (buckling loads) and u are the eigenvectors (buckling modes)