Reactions and summation with FSUM

Reactions — Read the support response

Reactions are queried at constrained nodes. We do not need fixed IDs because the physical region is stored in the fixed_nodes component.

CMSEL,S,fixed_nodes
node_id=0

*DO,j,1,n_fixed
  node_id=NDNEXT(node_id)
  *GET,rfx_node,NODE,node_id,RF,FX
  *GET,rfy_node,NODE,node_id,RF,FY
  *GET,rfz_node,NODE,node_id,RF,FZ

  rfx=rfx+rfx_node
  rfy=rfy+rfy_node
  rfz=rfz+rfz_node
*ENDDO

RF returns reactions in the nodal coordinate system. In the working example, all nodal systems remain aligned with the global Cartesian system.

The hidden moment in translational forces

SOLID185 has UX, UY and UZ, but not ROTX, ROTY nor ROTZ. This does not prevent transmitting moment. The reactions distributed over the support face form a force couple.

Each nodal reaction contributes:

{M} = {r} × {RF}

Mx = ry·RFz − rz·RFy
My = rz·RFx − rx·RFz
Mz = rx·RFy − ry·RFx

Adding these contributions gives the reaction moment at the fixed support without introducing a rotational degree of freedom that the element does not possess.

Choose the sum point

We will use the center of the fixed-support face:

x_ref=0
y_ref=beam_h/2
z_ref=beam_b/2

A moment is always referred to a point. Changing that point can change its components, although the force system remains physically equivalent. Choosing the support center eliminates artificial eccentricities associated with the block's geometric origin.

FSUM and SPOINT — An independent check

SPOINT,0,x_ref,y_ref,z_ref
CMSEL,S,fixed_nodes
FSUM
*GET,fsum_fy,FSUM,0,ITEM,FY
*GET,fsum_mz,FSUM,0,ITEM,MZ

FSUM sums the nodal contributions of elements connected to the selected set. SPOINT defines the global point about which moments are calculated. Do not assume that these internal contributions use the same sign convention as RF.