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As one can see from the table above the results do not change much as the mesh is refined. After 32 elements, the total deformation has converged up to the sixth decimal place. The exact solution for the deformation is cubic and for this setup ANSYS uses element BEAM 188 which in turn uses cubic interpolation. Thus, for the simple cantilever beam setup the numerical method converges very quickly.

Force Reactions Verification

From our statics knowledge, we know that the sum of all of the forces needs to be maintained at zero total net force on the structure, or there would be rigid body motion. We can thus add another check that the solution is reasonable by probing the force reactions and checking that in all directions the total forces add to zero:

Probing both of the reactions, we see

Image AddedImage Added

From our loading, we have two separate point loads of 4kN each. Then our X-axis balance yields, as we expect

-3988.8N - 4011.2N + 4kN + 4kN = 0

We also have two line pressures of -2kN/m, and with a length of 4m on the two horizontal beams we'd find a total of -16kN of force applied. Our Y-axis balance shows

-16kN + 13218N + 2781.6N = 15999.6N 

Thus we have a balance in all directions. 



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