The forces which purely depends of position are always conservative. Following forces are always non-conservative and can never be conservative:

- force depend on infinitesimally small displacement (hysteretic damping),

- velocity dependent forces (fluid/viscous damping)

- force depends explicitly on time (time dependent excitation force)

One can add any other category of forces in the above list.

It doesn't make any difference regarding the symmetry of stiffness matrix !

If I understand the question correctly, I would say any force that deals with energy dissipation is non-conservative. From high school physics, friction, and from mechanical vibrations, viscous damping, are two examples of non-conservative forces, because they dissipate energy over time and cause the moving object to come to rest. On the other hand, forces that deal with potential and kinetic energies only are conservative. That is because the summation of these energies remain constant (total energy is conserved) over time. I hope I understood the question correctly and that the answer helps!

Following the answers

Follow

Generally buckling comes under conservative and non-conservative loads.Buckling problem of a cantilever under a quite general sets of loads which can be either conservative or non-conservatives.For a discrete model, elastic linkage which show the static stability is related to a chaotic map which is conservative both in case of conservative and non-conservatives.

One another example I put conservative load transfer on the curved fluids on curvatures. That means any force that deals with an energy dissipation is non-conservative. They are not always depends upon the position of the loads are non-conservatives. Here, force depends upon the infinitesimally small displacements(like damping).