Can nonlinear buckling analysis gives us an over estimate ?

I am working on thermal buckling of annular FGM plates using the DQ method in FORTRAN. The results show that for simply-simply edges, the nonlinear thermal buckling loads are greater than those of eigen buckling loads. But for clamped-clamped edges, as it may be expected, the nonlinear buckling loads are under estimate, i.e. they are lower than eigen buckling loads.Why?

Is it possible that the nonlinear buckling analysis gives us an over estimate load ?