# Explicit dynamics: B32/B32R beams with SECTION=CIRC get an unstable increment (element height taken as √2·d), and the run ends in NaN with "Job finished" **URL:** \ **Category:** Analysis issues\ **Created:** [October 19, 2026, 7:27am UTC](https://calculix.discourse.group/t/explicit-dynamics-b32-b32r-beams-with-section-circ-get-an-unstable-increment-element-height-taken-as-2-d-and-the-run-ends-in-nan-with-job-finished/4189 "2026-10-19T07:27:50Z")\ **Posts on this page:** 3\ **Page:** 1
**Author:** ![Sandervdb](https://avatars.discourse-cdn.com/v4/letter/s/49beb7/32.png) [@Sandervdb](https://calculix.discourse.group/u/Sandervdb)\ **Post date:** [October 19, 2026, 7:27am UTC](https://calculix.discourse.group/t/explicit-dynamics-b32-b32r-beams-with-section-circ-get-an-unstable-increment-element-height-taken-as-2-d-and-the-run-ends-in-nan-with-job-finished/4189/1 "2026-10-19T07:27:50Z")
Forum topic: ## Summary In a `*DYNAMIC, EXPLICIT` step, ccx sizes the increment of a quadratic beam with a circular section as if the section were √2 times thicker than it is. The increment it selects is therefore unstable: - The displacements exceed 1e66 by increment 200 and are NaN from increment 800 on. - The job still prints “Job finished” and exits with code 0. A RECT section of the same width gets a √2 smaller increment and runs fine. ## Version ccx 2.23 (conda-forge build pl5321h484372f\_2, macOS arm64). On master, calcstabletimeincvol.f has changed since 2.23 only for C3D8R, and gen3dfrom1d.f has not changed. The problem should therefore still be there. ## Already reported or fixed? Not reported: there is no matching GitHub issue (open or closed) or open pull request in Dhondtguido/CalculiX, and no calculix.discourse.group topic (searched 17 Oct 2026). Not fixed: the routine involved is unchanged on master, and conda-forge’s latest 2.23 build (pl5321hd17ca8b\_8, which carries about 40 extra patches) gives the same output. ## Minimal input `circ_explicit.inp`: ```auto ** One B32R cantilever, length 40, CIRC section of diameter 20, steel (N, mm, s). ** Tip load 1000 in y applied at t = 0 and held, explicit dynamics, 2e-3 s. *NODE, NSET=NALL 1, 0.0, 0.0, 0.0 2, 20.0, 0.0, 0.0 3, 40.0, 0.0, 0.0 *ELEMENT, TYPE=B32R, ELSET=EALL 1, 1, 2, 3 *MATERIAL, NAME=STEEL *ELASTIC 210000.0, 0.3 *DENSITY 7.85e-9 *BEAM SECTION, ELSET=EALL, MATERIAL=STEEL, SECTION=CIRC 20.0, 20.0 0.0, 0.0, -1.0 *BOUNDARY 1, 1, 6 *STEP, INC=100000 *DYNAMIC, EXPLICIT , 2.e-3 *CLOAD 3, 2, 1000.0 *NODE PRINT, NSET=NALL, FREQUENCY=200 U *END STEP ``` ## How to run ```auto ccx circ_explicit ``` Then cap the increment below ccx’s own by changing the `*DYNAMIC` data line to `, 2.e-3, , 6.e-7`, and run again. ## Expected The increment ccx selects should be stable, so the tip displacement stays bounded. For a load applied suddenly and then held, it oscillates between 0 and about twice the static deflection. Euler-Bernoulli gives PL³/(3EI) = 1000·40³/(3·210000·7854) = 0.0129. With the increment capped at 6e-7 the run does exactly that. Over 3334 increments the tip u\_y runs from 3.8e-6 to 0.0264, with a mean of 0.0131, and there is no NaN. The manual (6.9.7) bases the estimate on ω\_max ≈ 2c/h\_min, “where … h\_min is the minimum height of the element”. The expanded section here is 20 wide, so with h = 20 the formula gives 5.90e-7. That is the increment ccx itself selects for `SECTION=RECT`, `20.0, 20.0`, and that run is stable. ## Actual stdout: ```auto Explicit time integration: Volumetric COURANT initial stable time increment:8.341279e-07 SELECTED time increment (not considering penalty contact):8.341279e-07 ... Job finished ``` The exit code is 0. `.dat`: ```auto INCREMENT 200 displacements (vx,vy,vz) for set NALL and time 0.1668256E-03 1 0.000000E+00 0.000000E+00 0.000000E+00 2 1.513252E+66 4.967292E+65 6.496154E+66 3 -7.070765E+66 -3.819730E+67 -4.990000E+68 ... INCREMENT 800 displacements (vx,vy,vz) for set NALL and time 0.6673024E-03 1 NaN NaN NaN 2 NaN NaN NaN 3 NaN NaN NaN ``` Every later output, up to increment 2398 at t = 2e-3, is NaN. B32 behaves the same way. I bisected the stable limit by capping the increment over a step of 1e-2 s: - This one-element deck is stable at 7.5e-7 for 13,333 increments and turns NaN at 7.6e-7. - A cantilever of four such elements (4 x 40) is stable at 6.3e-7 and turns NaN at 6.4e-7. In both cases ccx selects 8.34e-7, which is 1.11 and 1.32 times the limit. ## Where it goes wrong calcstabletimeincvol.f takes h as the smallest volume/face-area ratio. Both are evaluated with a one-point rule, at the element centre and at the face centres: ```fortran volume=weight*xsj ... area=weight*dsqrt(xsj2(1)*xsj2(1)+xsj2(2)*xsj2(2)+ & xsj2(3)*xsj2(3)) hmin=min(hmin,(volume*volfac/area)) ... smscale(nelem)=critom*hmin*elemfac/(2.d0*wavspd) ``` For SECTION=CIRC, gen3dfrom1d.f places the C3D20(R) corner nodes at ±d/(2√2) (`sc=.5d0/dsqrt(2.d0)`), at 45 degrees on the circle, and the midside nodes at ±d/2. The two one-point quantities then come out as: - The Jacobian at the centre is that of the box around the circle, so volume = l·d² (16000 here). The true volume of the expanded element is 12418. - Each side face is measured by the chord between its corner nodes, so area = l·d/√2. Together they give h = min(l, √2·d) = 28.3 instead of about d = 20. Then dt = 1.9172·28.28·0.3/(2·6.001e6)·0.8/1.3 = 8.34e-7, the value printed above. With the volume and the face areas integrated properly, h = 12418/625.0 = 19.9 and dt = 5.86e-7, which is stable in both models above. Taking h from the section size for CIRC beams would also work. Separately, the explicit run carries on past NaN and reports success, so a diverged run looks like a successful one. ## Workaround Either of these avoids the NaN: - Cap the increment with the fourth field of the `*DYNAMIC` data line, at half of ccx’s own value for CIRC beams (4.17e-7 here, the estimate for a square of side d/√2). - Model the solid circle as `SECTION=PIPE`, `10.0, 10.0` (wall thickness equal to the radius). PIPE is expanded as the square around the section, so ccx selects 5.90e-7. That run is stable, with a mean tip deflection of 0.0136 against 0.0131 for CIRC. ---
**Author:** ![Calc\_em](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Calc\_em](https://calculix.discourse.group/u/Calc_em)\ **Post date:** [October 19, 2026, 8:39am UTC](https://calculix.discourse.group/t/explicit-dynamics-b32-b32r-beams-with-section-circ-get-an-unstable-increment-element-height-taken-as-2-d-and-the-run-ends-in-nan-with-job-finished/4189/2 "2026-10-19T08:39:07Z")
Confirmed (using official build of ccx 2.23 on Windows), needs a GitHub ticket. Explicit dynamics procedure in CalculiX is particularly important for bug fixes. ```auto Calculating Material Wave Speeds... Wave Speed for mat. 1 6000979.8318020739 Explicit time integration: Volumetric COURANT initial stable time increment:8.341279e-07 SELECTED time increment (not considering penalty contact):8.341279e-07 the increment size exceeds the remainder of the step and is decreased to 8,341279e-07 the increment size exceeds the remainder of the step and is decreased to 5,953067e-07 Job finished ________________________________________ Total CalculiX Time: 43.856345 ________________________________________ ``` ```auto INCREMENT 600 displacements (vx,vy,vz) for set NALL and time 0.5004768E-03 1 0.000000E+00 0.000000E+00 0.000000E+00 2 8.037718+217 2.638404+217 3.450467+218 3 -3.755675+218 -2.028870+219 -2.650465+220 INCREMENT 800 displacements (vx,vy,vz) for set NALL and time 0.6673024E-03 1 NaN NaN NaN 2 NaN NaN NaN 3 NaN NaN NaN INCREMENT 1000 displacements (vx,vy,vz) for set NALL and time 0.8341279E-03 1 NaN NaN NaN 2 NaN NaN NaN 3 NaN NaN NaN ``` ---
**Author:** ![Sandervdb](https://avatars.discourse-cdn.com/v4/letter/s/49beb7/32.png) [@Sandervdb](https://calculix.discourse.group/u/Sandervdb)\ **Post date:** [October 19, 2026, 8:40am UTC](https://calculix.discourse.group/t/explicit-dynamics-b32-b32r-beams-with-section-circ-get-an-unstable-increment-element-height-taken-as-2-d-and-the-run-ends-in-nan-with-job-finished/4189/3 "2026-10-19T08:40:18Z")
Posted: [Explicit dynamics: B32/B32R beams with SECTION=CIRC get an unstable increment (element height taken as √2·d), and the run ends in NaN with "Job finished" · Issue #217 · Dhondtguido/CalculiX · GitHub](https://github.com/Dhondtguido/CalculiX/issues/217)