Singularity problem
As an effect of the mesh refinement the calculated results are converging to the theoretical solution. The problem is that at certain places we get infinite inner forces according to the theory, so the inner forces increase each time by refining the mesh. These places could be: point supports, end points of edge supports,vertices of surface supports, end points of beams and columns, end points of intersection lines of adjoining surfaces, point loads, end points of line loads, vertices of surface loads etc.
In practice, usually, the singularity problem occurs at supports because they heavily influence the inner forces (e.g. negative moments) in ratio.

The software â€śFEM-Designâ€ť can handle the the problem using â€śAuto Peak smoothingâ€ť.

For me those smoothing blackboix algorithms look quite dangerous to use. When smoothing the result not sure how it works with more complicated distribution of forces.
For column sofistik has some nice features like column macros or highend est constraints.
For reentrant corners in my opinion only enginering judgemnt is ok

The â€śbemess7_columnhead.datâ€ť shows how to do mesh refinement around the support.
How to achieve this around the inersection between 1D object and 2D object, e.g. around the inersection between column and slab?

Have you tried replacing the supports with columns?

+PROG SOFIMSHC urs:2
HEAD Example punching column heads
UNIT 5
SYST spac GDIV 10000 GDIR POSZ
CTRL MESH 1
CTRL HMIN 0.30 $ sonst entstehen bei den hohen Lasten Einzeldurchstanzpunkte
$ to avoid punching problems at high point loads.
SPT 1 X 2 2 BX 0.40 0.40 $ ohne StĂĽtzenmakro $ without macro
SPT 2 X 6 2 BX 0.40 - $ " rund $ " circular
SPT 3 X 10 2 BX 0.40 0.40 ; SPTP SUPP X 0.40 0.40 $ mit StĂĽtzenmakro $ with macro
SPT 4 X 2 6 BX 0.40 0.40 ; SPTP SUPP X 0.60 0.60 VAL 0.40 $ StĂĽtzenkopf klein $ column head small
SPT 5 X 6 6 BX 0.30 0.30 ; SPTP SUPP X 1.30 1.30 VAL 0.40 $ StĂĽtzenkopf groĂź $ " wide
SPT 6 X 10 6 BX 0.30 0.30 ; SPTP VOUT X 0.70 0.70 VAL 0.40 $ nur Voute $ only haunch
SPT 7 X 2 10 BX 0.30 0.30 ; SPTP SUPP X 1.20 1.20 VAL 0.40 $ Kopf und Voute $ head and haunch
SPTP VOUT X 1.40 1.40 VAL 0.40
SPT 8 X 6 10 BX 0.30 - ; SPTP SUPP X 0.60 - VAL 0.40 $ Kopf klein rund $ small circular
SPT 9 X 10 10 BX 0.30 - ; SPTP SUPP X 1.20 - VAL 0.40 $ Kopf und Voute rund $ head and haunch
SPTP VOUT X 1.40 - VAL 0.40 $ $ circular
SPT 41 X 2 2 4 fix f
SPT 42 X 6 2 4 fix f
SPT 43 X 10 2 4 fix f
SPT 44 X 2 6 4 fix f
SPT 45 X 6 6 4 fix f
SPT 46 X 10 6 4 fix f
SPT 47 X 2 10 4 fix f
SPT 48 X 6 10 4 fix f
SPT 49 X 10 10 4 fix f
sln npa (1 9 1) (41 1) sno 1
SAR 1 GRP 1 MNO 1 MRF 2 T 0.22[m] TITL "FlĂ¤che"
SARB OUT
SLNB X1 0.0 0.0 0.0 X2 12.0000 0.0 0.0
SARB OUT
SLNB X1 12.0000 0.0 0.0 X2 12.0000 12.0000 0.0
SARB OUT
SLNB X1 12.0000 12.0000 0.0 X2 0.0 12.0000 0.0
SARB OUT
SLNB X1 0.0 12.0000 0.0 X2 0.0 0.0 0.0
END