Here is a hint: what beam theory does MAPDL use and is it the same as what you are comparing to....?
MAPDL beams are based on Timoshenko beam theory. Whereas the stiffness matrix shown is based on Euler-Bernoulli beam theory. Timoshenko accounts for shear deformation and rotary inertia effect (that E-B does not), but the resulting beam stiffness is slightly lower than E-B theory.
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