Equilibrium audit

Force audit

force_error=ABS(rfy+tip_force)/ABS(tip_force)
force_parasitic=(ABS(rfx)+ABS(rfz))/ABS(tip_force)

The “plus” sign is not arbitrary: the load and its reaction must be opposite. The second indicator detects unintended resultants in X or Z that would remain hidden if we examined only RFY.

Moment audit

external_mz=(beam_l-x_ref)*tip_force
target_mz=-external_mz
moment_error=ABS(rmz+external_mz)/ABS(external_mz)
moment_parasitic=(ABS(rmx)+ABS(rmy))/ABS(external_mz)

Checking force without checking moment leaves the free-body diagram incomplete. A load applied at the wrong position can retain exactly the same resultant and produce a different moment.

Acceptance contract

The base case is only approved when it simultaneously meets:

• 126 nodes, 40 elements, 6 fixed nodes and 6 loaded nodes.
• Exactly one set of results available.
• Force error less than 0.5 %.
• Moment error less than 0.5 %.
• Parasitic resultant force and moment less than 0.5 %.
• passes=1.

The threshold is much larger than the expected residual in this linear problem. Its pedagogical purpose is to clearly separate a passing case from a modeling error.

CSV — Reproducible evidence

The macro generates m06_equilibrium_audit.csv:

case,n_nodes,n_elements,n_fixed,n_tip,n_sets,result_time,target_fy,
rfx,rfy,rfz,rmx,rmy,rmz,target_mz,force_error,moment_error,
fsum_fy,fsum_mz,passes

The file preserves inputs, topology, active state, results, and decision. A screenshot of the deformed shape does not provide that traceability.

Guided practice

1. Write the predictions RFY and RMZ without running MAPDL.
2. Run 06_start.mac in blocks and review the selection before SOLVE.
3. Check the .out file to confirm that the solution completed.
4. Activate the last set and list the reactions of the fixed component.
5. Reconstruct the moment about the center of the support.
6. Compare your CSV with 06_expected_results.csv.
7. Run the entire solution only after justifying each sign.