export geometric stiffness matrix in abaqus software
Let's discuss a little back ground on geometric nonlinear FEA. 
There are many different methods used for nonlinear geometric analysis of structure. The most well-known and established ones are [1]: 
Total Lagrangian (TL), Updated Lagrangian (UL). 
TL: Uses the full nonlinear definition of strains. 
UL: Uses the linear definition of strain but updates the reference configuration with previous deformation solutions. 
Abaqus's core solver uses a very specific type of geometric nonlinear algorithm called co-rotational in where the rotation and deformation with respect to reference configuration are treated separately. 
Abaqus's co-rotational formulation is propitiatory and I do not expect them to offer its output so easily. Even if you could see the output for nonlinear geometry matrices from Abaqus. These matrice(s) would be different than what you expect depending on the methods that you have used for nonlinear geometric modeling. 
[1] Reddy, Junuthula Narasimha. An Introduction to Nonlinear Finite Element Analysis: with applications to heat transfer, fluid mechanics, and solid mechanics. OUP Oxford, 2014.
I need export geometric(stress or diffrential) stiffness matrix in linear buckling problem at abaqus software for use in matlab program, i find method export  of usual stiffness matrix, but i cant find any data about export geometric stiffness matrix in abaqus script, 
Can some one help me about it?
for example when i export stiffness matrix in buckling problem,the result is same as stiffness matrix in linear static problem