Solve negative eigenvalue error

This answer is just a summary of the article:
Warning Messages Related to Negative Eigenvalues
If you need deeper insight, I suggest to read that article after visiting this page.

First of all, you must know that it is just a warning and not an error. If the error and warning concepts in Abaqus is not clear for you, take a look at
What is the difference of error and warning in Abaqus?

The negative eigenvalue in context of buckling basically just means that the load to cause the buckle is of the opposite sign to the applied load. So if I applied a reference load of 10 MPa and the first eigenvalue was -0.5, then the load required to trigger the buckling mode is -5 MPa.

In other analyses, this message is related to instabilities in the model. Negative eigenvalues may be produced because of the elements, which goes under distorting conditions. Some of the reasons are:

* Material properties have not defined properly.

** Geometrical properties of the meshes are not applicable or not enough for converging the solutions.

*** Boundary conditions have not restrained enough, so the model goes to act as a mechanism. You must check your boundary conditions. Improper BC’s may be the reason of the instability in the model. Due to this instability, you can have this issue related to negative eigenvalues.

Keep in mind:

1) Negative eigenvalues warnings that pop up during iterations that do not converge can generally be ignored.

2) If negative eigenvalues warnings appear during iterations that converge then the computed solution must be carefully evaluated.

For a detailed discussion, visit this article:
Warning messages related to negative eigenvalues