Here the total stiffness matrix, K, has been split into a linear part,
KL, and a nonlinear contribution,
KNL.
In a first order approximation, KNL is proportional to the stress in the structure and thus to the external load. So if the linear problem is solved first for an arbitrary initial load level
f0,
COMSOL reports a critical load factor, which is the value of
λ at which the structure becomes unstable. The corresponding deformation is the shape of the structure in its buckled state.
The assumption for the buckling analysis is still that KNL is proportional to the external load, even though this may be disputable for a strongly nonlinear case.
KNL is based on the stresses, which must be computed in the same way for both cases, that is under the same assumption about geometric nonlinearity. The effect is that the stiffness matrix at the linearization point includes the nonlinear part from
Equation 2-15, and the eigenvalue problem is reformulated as