Auditable constraints and loads

A mesh does not define where the structure is supported or which external loads it must carry. In M05 we will turn the free-body diagram into constraints and loads, then check the values stored by MAPDL before solving.

Objectives

By completing M05 you will be able to demonstrate that:

• Translate a free-body diagram into regions, degrees of freedom, and force components.
• Apply constraints and loads exclusively on named components.
• Explain what each ALL means in D,ALL,ALL,0.
• Maintain a constant resultant force when the number of nodes changes.
• Distinguish selection, nodal system, visualization and results system.
• Read constraints and stored forces using *GET.
• Audit boundary conditions without using reactions or results.

Prerequisites and downloads

• Complete M02 to work with components and selections.
• Complete M04; we will use the first accepted mesh, with 40 elements.
• Remember that SOLID185 has the displacement DOFs UX, UY, and UZ.

How to use this lesson

Recommendation: run DLIST and FLIST before SOLVE. The intent of the script does not prove what conditions were actually stored.

Session map

Prediction — The error that grows as you refine

The base mesh has six nodes at the tip. What would be the total force if you executed F,ALL,FY,-1000 with those six nodes selected?

6 nodes × (−1000 N/node) = −6000 N

F takes a nodal load. MAPDL does not interpret -1000 as the resultant that you intend to distribute. That intent must be explicit in the script.

From a physical diagram to a test

Mental model — Boundary conditions are part of the model

An ideal fixed support is not simply “where the part touches a wall.” It is the mathematical assumption that specific degrees of freedom have prescribed values. A nodal force is not merely a decorative arrow either: it has a magnitude, sign, direction, point of application, and reference system.

Step 1 — Recover the mesh chosen in M04

We use mesh_h=0.05 m because it was the first mesh to meet the M04 displacement criterion. Its divisions are 20 × 2 × 1:

MSHAPE,0,3D
MSHKEY,1
! LESIZE on the three line families
VMESH,ALL

*GET,n_nodes,NODE,0,COUNT
*GET,n_elements,ELEM,0,COUNT

The M05 entry contract requires 126 nodes and 40 elements.

Step 2 — Build regions before applying anything

SELTOL,select_tol
CSYS,0

NSEL,S,LOC,X,0
CM,fixed_nodes,NODE
*GET,n_fixed,NODE,0,COUNT
ALLSEL,ALL

NSEL,S,LOC,X,beam_l
CM,tip_nodes,NODE
*GET,n_tip,NODE,0,COUNT
ALLSEL,ALL

SELTOL,

Selection and application are separate operations. We first show that each region exists; then we store its meaning in a component. The intersection test confirms that no node belongs simultaneously to both ends.

Step 3 — Enter /SOLU without solving

FINISH
/SOLU

M05 enters the solution processor because loads are part of the analysis definition. However, it contains neither ANTYPE nor SOLVE. At the end, we will have a prepared database, but no reactions, result sets, or stresses.

Step 4 — Apply the fixed support

CMSEL,S,fixed_nodes
D,ALL,ALL,0
ALLSEL,ALL

The line should be read with its two occurrences of ALL:

• the first ALL means all currently selected nodes;
• the second means all the active degrees of freedom of the element.

For SOLID185, those degrees of freedom are UX, UY, and UZ. No rotations appear because the solid element does not have them as degrees of nodal freedom.

Step 5 — Distribute a resultant

CMSEL,S,tip_nodes
*GET,n_tip,NODE,0,COUNT
force_per_node=tip_force/n_tip
F,ALL,FY,force_per_node
ALLSEL,ALL

For six nodes, force_per_node=-166.6667 N. The parameter expresses a fundamental distinction:

physical input:      tip_force
input to F:         force_per_node
final check:        sum of all stored FY forces

Safety pattern

CMSEL,S,nombre_region
*GET,n_region,NODE,0,COUNT
! abort or fail if n_region=0
comando_de_carga
ALLSEL,ALL

Select, check, apply, and restore form a single unit. Separating those steps with long blocks of code makes it easier for an incomplete selection to propagate.

Reference systems — Four different concepts

In the working example, all nodal systems remain global Cartesian. That is why FY unambiguously represents the global Y direction. Loads in systems rotated nodal systems require an explicit decision, not a cosmetic display change.

F vs. SF

! Conceptual example, not added to the running example
CMSEL,S,top_nodes
SF,ALL,PRES,pressure_value
SFLIST,ALL,PRES
ALLSEL,ALL

Pressure follows the face-normal convention; it does not automatically replace our transverse tip force. M05 retains a single load so that the audit remains unambiguous.

Step 6 — Listing is not yet automating

DLIST,ALL,ALL
FLIST,ALL,ALL

Listings allow you to read nodes, labels and values in the file .out. They are essential for debugging, but a human review is not enough to run many cases. We will convert the same questions into approval parameters and conditions.

Step 7 — Audit the three prescribed displacements

CMSEL,S,fixed_nodes
node_id=0

*DO,j,1,n_fixed
  node_id=NDNEXT(node_id)
  *GET,dof_ux,NODE,node_id,D,UX
  *GET,dof_uy,NODE,node_id,D,UY
  *GET,dof_uz,NODE,node_id,D,UZ
  ! check all three values
*ENDDO

NDNEXT returns the next selected node. This lets us traverse the actual IDs without assuming that they are consecutive. Each of the six nodes must store three zero values: n_constrained_dof=18.

Step 8 — Sum the forces stored in the model

ALLSEL,ALL
node_id=0
*DO,j,1,n_nodes
  node_id=NDNEXT(node_id)
  *GET,node_fx,NODE,node_id,F,FX
  *GET,node_fy,NODE,node_id,F,FY
  *GET,node_fz,NODE,node_id,F,FZ
  force_sum_x=force_sum_x+node_fx
  force_sum_y=force_sum_y+node_fy
  force_sum_z=force_sum_z+node_fz
*ENDDO

This sum runs through the entire model, not just tip_nodes. Therefore it can detect an accidental force outside the expected region or an unexpected component.

load_error=ABS(force_sum_y-tip_force)/ABS(tip_force)

The audit requires:

n_force_nodes = n_tip
force_sum_x   = 0
force_sum_y   = -1000
force_sum_z   = 0
load_error    < 0.001

CSV contract

05_loads_constraints.mac generates:

case,mesh_h,n_nodes,n_elements,n_fixed,n_tip,n_constrained_dof,n_force_nodes,force_per_node,force_sum_x,force_sum_y,force_sum_z,target_force,load_error,passes

The base row must contain 126 nodes, 40 elements, 18 constraints, 6 loaded nodes, and passes=1. In MAPDL 2025 R2 the validated sum is -1000 N with an error on the order of 10⁻¹⁶.

Bug hunting

Run 05_bug_hunt.mac. It does not contain a solver failure; it contains five logically incorrect implementations.

1. fixed_nodes is created after all nodes are restored.
2. The fixed support ends up applied to the entire model.
3. NSEL,R tries to find the tip within a selection that no longer contains it.
4. Full force is applied to each tip node.
5. CSYS, DSYS, and RSYS are used as if they rotated the nodal system.

Verifiable challenge — Same force, more nodes

Complete 05_challenge.mac with mesh_h=0.025 m. Do not copy case IDs from the previous case, and do not solve.

Before running, predict which columns should change and which should remain unchanged. Then explain why force_per_node is not a separate physical input.

Self-assessment

1. What are the two meanings of ALL in D,ALL,ALL,0?
2. Why does F,ALL,FY,tip_force not apply a total resultant?
3. What changes when you run DSYS,1?
4. Why does the force audit go through all nodes?
5. What evidence cannot yet exist before SOLVE?

Evidence of learning

• m05_bc_audit.csv with passes=1.
• The extracts from DLIST and FLIST.
• A screenshot of the constraint and load symbols.
• The CSV of the challenge with the same total force and 15 nodes loaded.
• The diagnosis of the five defects.

Exit checklist

• ☐ My components are created before applying conditions.
• ☐ I check that the regions are non-empty and disjoint.
• ☐ I distinguish total force and force per node.
• ☐ I restore the selection after each application.
• ☐ I do not confuse CSYS, nodal system, DSYS and RSYS.
• ☐ I read and sum the loads stored throughout the model.
• ☐ My script ends without ANTYPE, SOLVE, /POST1 or FSUM.

Technical traceability

The lesson uses Basic Analysis Guide for the definition of boundary conditions and Command Reference 2024 R1 for D, F, SF, DLIST, FLIST, NDNEXT, *GET, CSYS, DSYS and RSYS.