I'll ask first why you would want to do this. I can't think of a scenario where I'd want to tell the owner "I'm taking credit for flange flexibility to get piping / equipment to pass code."

But maybe you have another reason, so I'll offer some more.

I don't think there's a "great" way to input this into CAESAR using element stiffness.

Let's consider replacing the anchor with Cartesian components, instead.

Consider the compression case - you wouldn't expect the flange face to significantly compress, so that 1e12 is as good as any.

Consider the tension case, delta = tension * length / area * modulus... so k = tension / delta = area * modulus / length, where area is number of bolts * individual bolt smallest cross sectional area.

So you have a non-linearity in the axial component (let's call this x)

You could do similar for shear, but only for Y and Z axes specifically, once input into CAESAR, would mean that the stiffness in arbitrary radial directions (+Y+Z, -Y+Z, etc) aren't going to be equal to the stiffness in either Y or Z, but up to 41% higher than reality.

You could estimate radial sheer stiffness (RX) decently.

But you'd be in another tough position for bending (RY, RZ).

This could be estimated by assuming half the bolts are put into tension, and you're leveraging them about the flange OD. But again, if your bending action is working outside the Y and Z axes, your stiffness could be as high as 41% higher than reality.

So I suppose you could create a CNODE +X, Y, Z, RX, RY, RZ on one with stiffnesses and a CNODE -X on the next without stiffness, and that's pretty accurate.

Granted, 41% over is still a lot closer than 1e12, and maybe you're fine with a cnode anchor with stiffness handling all these situations as it's still better than cnode anchor with 1e12.

Some additional considerations:

Bolt pre-stress would be a consideration, and the friction between faces would impact real world effective stiffness in the shear force and shear moment directions.

Flange deformation would also be a consideration, which would reduce the stiffness.

Alternatively, I suppose you could model each bolt as a piping / rigid element that approximates the stiffness of a bolt...