Thank you for the Archive. I noticed is there is only one element through the thickness. The elements used are linear PLANE183 elements, so with only one element, the stress profile through the thickness can only be a straight line. In this particular model, that is the exact solution, so you got away with one element, but in general, you almost always want a minimum of two elements through the thickness to detect curvature in the result.
I checked all the inputs to the ANSYS model, and all is correct except you selected Plane Stress and you said you wanted Plane Strain. ANSYS won't let you change to that for the SS Thermal. To accomplish that for the Static Structural, you need to connect just the SS Thermal to the Setup cell of the Static Structural, then you can select Plane Strain. In this particular case, the radial normal stress (x-direction) component is the same for both assumptions, but the axial normal stress (z-direction) is zero in the Plane Stress assumption but it is 466 MPa for the Plane Strain assumption. However, Mathematica is not calculating this component of stress.
I assume the graphs above are from Mathematica. If so, then they agree with the ANSYS results.
You are ready to advance to the next phase of testing the agreement. Build a 3-layer ANSYS model with 3 different constant material properties and see if Mathematica and ANSYS still give the same result.
Please reply at your convenience with the Mathematica code and the 3-layer ANSYS archive.