# Periodic boundary conditions **URL:** \ **Category:** Model setup\ **Created:** [July 27, 2025, 8:28pm UTC](https://calculix.discourse.group/t/periodic-boundary-conditions/2828 "2025-07-27T20:28:51Z")\ **Posts on this page:** 3\ **Page:** 1
**Author:** ![Basem](https://avatars.discourse-cdn.com/v4/letter/b/6bbea6/32.png) [@Basem](https://calculix.discourse.group/u/Basem)\ **Post date:** [July 27, 2025, 8:28pm UTC](https://calculix.discourse.group/t/periodic-boundary-conditions/2828/1 "2025-07-27T20:28:51Z")
Hey everyone, I’m looking for a more efficient way to set up periodic boundary conditions for an RVE. Manually writing the `*EQUATION` command for every node pair is very tedious with fine meshes. Is there a better method to apply these constraints? I was looking through the documentation, but I didn’t find anything useful. Thanks in advance! The following is a working example of 1 element with periodic bc on all sides using \*equation: \*NODE,NSET=NODES\_ALL 1 ,0,0,0 2 ,0.5,0,0 3 ,1,0,0 4 ,0,0.5,0 5 ,0.5,0.5,0 6 ,1,0.5,0 7 ,0,1,0 8 ,0.5,1,0 9 ,1,1,0 10 ,0,0,0.5 11 ,0.5,0,0.5 12 ,1,0,0.5 13 ,0,0.5,0.5 14 ,0.5,0.5,0.5 15 ,1,0.5,0.5 16 ,0,1,0.5 17 ,0.5,1,0.5 18 ,1,1,0.5 19 ,0,0,1 20 ,0.5,0,1 21 ,1,0,1 22 ,0,0.5,1 23 ,0.5,0.5,1 24 ,1,0.5,1 25 ,0,1,1 26 ,0.5,1,1 27 ,1,1,1 \*NODE, NSET=STRAIN\_NODE1 28, -1.0, 0.0, 0.0 \*NODE, NSET=STRAIN\_NODE2 29, 0.0, -1.0, 0.0 \*NODE, NSET=STRAIN\_NODE3 30, 0.0, 0.0, -1.0 \*NSET, NSET=STRAIN\_NODES 28,29,30 \*NSET, NSET=CORNER\_NODE 1 \*NSET, NSET=FACE\_X\_MIN 1,4,7,10,13,16,19,22,25 \*NSET, NSET=FACE\_X\_MAX 3,6,9,12,15,18,21,24,27 \*NSET, NSET=FACE\_Y\_MIN 1,2,3,10,11,12,19,20,21 \*NSET, NSET=FACE\_Y\_MAX 7,8,9,16,17,18,25,26,27 \*NSET, NSET=FACE\_Z\_MIN 1,2,3,4,5,6,7,8,9 \*NSET, NSET=FACE\_Z\_MAX 19,20,21,22,23,24,25,26,27 \*ELEMENT, TYPE=C3D20R, ELSET=ELEMENTS\_ALL 1 ,1,3,9,7,19,21,27,25,2,6, 8,4,20,24,26,22,10,12,18,16 \*ELSET, ELSET=ELEM\_FACE\_X\_MIN 1 \*Surface, Name=ELEM\_FACE\_X\_MIN\_S6, Type=Element ELEM\_FACE\_X\_MIN, S6 \*ELSET, ELSET=ELEM\_FACE\_X\_MAX 1 \*Surface, Name=ELEM\_FACE\_X\_MAX\_S4, Type=Element ELEM\_FACE\_X\_MAX, S4 \*ELSET, ELSET=ELEM\_FACE\_Y\_MIN 1 \*Surface, Name=ELEM\_FACE\_Y\_MIN\_S3, Type=Element ELEM\_FACE\_Y\_MIN, S3 \*ELSET, ELSET=ELEM\_FACE\_Y\_MAX 1 \*Surface, Name=ELEM\_FACE\_Y\_MAX\_S5, Type=Element ELEM\_FACE\_Y\_MAX, S5 \*ELSET, ELSET=ELEM\_FACE\_Z\_MIN 1 \*Surface, Name=ELEM\_FACE\_Z\_MIN\_S5, Type=Element ELEM\_FACE\_Z\_MIN, S1 \*ELSET, ELSET=ELEM\_FACE\_Z\_MAX 1 \*Surface, Name=ELEM\_FACE\_Z\_MAX\_S5, Type=Element ELEM\_FACE\_Z\_MAX, S2 \*\* PERIODIC BOUNDARY CONDITIONS \*\* EQUATIONS FOR X-FACES \*EQUATION 3 3,1,1, 1,1,-1, 28,1,-1 \*EQUATION 3 3,2,1, 1,2,-1, 28,2,-1 \*EQUATION 3 3,3,1, 1,3,-1, 28,3,-1 \*EQUATION 3 6,1,1, 4,1,-1, 28,1,-1 \*EQUATION 3 6,2,1, 4,2,-1, 28,2,-1 \*EQUATION 3 6,3,1, 4,3,-1, 28,3,-1 \*EQUATION 3 9,1,1, 7,1,-1, 28,1,-1 \*EQUATION 3 9,2,1, 7,2,-1, 28,2,-1 \*EQUATION 3 9,3,1, 7,3,-1, 28,3,-1 \*EQUATION 3 12,1,1, 10,1,-1, 28,1,-1 \*EQUATION 3 12,2,1, 10,2,-1, 28,2,-1 \*EQUATION 3 12,3,1, 10,3,-1, 28,3,-1 \*EQUATION 3 15,1,1, 13,1,-1, 28,1,-1 \*EQUATION 3 15,2,1, 13,2,-1, 28,2,-1 \*EQUATION 3 15,3,1, 13,3,-1, 28,3,-1 \*EQUATION 3 18,1,1, 16,1,-1, 28,1,-1 \*EQUATION 3 18,2,1, 16,2,-1, 28,2,-1 \*EQUATION 3 18,3,1, 16,3,-1, 28,3,-1 \*EQUATION 3 21,1,1, 19,1,-1, 28,1,-1 \*EQUATION 3 21,2,1, 19,2,-1, 28,2,-1 \*EQUATION 3 21,3,1, 19,3,-1, 28,3,-1 \*EQUATION 3 24,1,1, 22,1,-1, 28,1,-1 \*EQUATION 3 24,2,1, 22,2,-1, 28,2,-1 \*EQUATION 3 24,3,1, 22,3,-1, 28,3,-1 \*EQUATION 3 27,1,1, 25,1,-1, 28,1,-1 \*EQUATION 3 27,2,1, 25,2,-1, 28,2,-1 \*EQUATION 3 27,3,1, 25,3,-1, 28,3,-1 \*\* EQUATIONS FOR Y-FACES \*EQUATION 3 7,1,1, 1,1,-1, 29,1,-1 \*EQUATION 3 7,2,1, 1,2,-1, 29,2,-1 \*EQUATION 3 7,3,1, 1,3,-1, 29,3,-1 \*EQUATION 3 8,1,1, 2,1,-1, 29,1,-1 \*EQUATION 3 8,2,1, 2,2,-1, 29,2,-1 \*EQUATION 3 8,3,1, 2,3,-1, 29,3,-1 \*EQUATION 3 16,1,1, 10,1,-1, 29,1,-1 \*EQUATION 3 16,2,1, 10,2,-1, 29,2,-1 \*EQUATION 3 16,3,1, 10,3,-1, 29,3,-1 \*EQUATION 3 17,1,1, 11,1,-1, 29,1,-1 \*EQUATION 3 17,2,1, 11,2,-1, 29,2,-1 \*EQUATION 3 17,3,1, 11,3,-1, 29,3,-1 \*EQUATION 3 25,1,1, 19,1,-1, 29,1,-1 \*EQUATION 3 25,2,1, 19,2,-1, 29,2,-1 \*EQUATION 3 25,3,1, 19,3,-1, 29,3,-1 \*EQUATION 3 26,1,1, 20,1,-1, 29,1,-1 \*EQUATION 3 26,2,1, 20,2,-1, 29,2,-1 \*EQUATION 3 26,3,1, 20,3,-1, 29,3,-1 \*\* EQUATIONS FOR Z-FACES \*EQUATION 3 19,1,1, 1,1,-1, 30,1,-1 \*EQUATION 3 19,2,1, 1,2,-1, 30,2,-1 \*EQUATION 3 19,3,1, 1,3,-1, 30,3,-1 \*EQUATION 3 20,1,1, 2,1,-1, 30,1,-1 \*EQUATION 3 20,2,1, 2,2,-1, 30,2,-1 \*EQUATION 3 20,3,1, 2,3,-1, 30,3,-1 \*EQUATION 3 22,1,1, 4,1,-1, 30,1,-1 \*EQUATION 3 22,2,1, 4,2,-1, 30,2,-1 \*EQUATION 3 22,3,1, 4,3,-1, 30,3,-1 \*EQUATION 3 23,1,1, 5,1,-1, 30,1,-1 \*EQUATION 3 23,2,1, 5,2,-1, 30,2,-1 \*EQUATION 3 23,3,1, 5,3,-1, 30,3,-1 \*Material, Name=MAT1 \*Elastic 100, 0.3 \*Solid section, Elset=ELEMENTS\_ALL, Material=MAT1 \*Step, Nlgeom \*Static 1, 1, 1e-5, 1 \*SOLVER,PARDISO \*Output, Frequency=1 \*Boundary, op=New \*Boundary \*\* 1. Prevent rigid body motion by fixing one corner node CORNER\_NODE, 1, 3, 0.0 \*\* 2. Apply a prescribed strain by moving a master node \*\* Master node 1 STRAIN\_NODE1, 1, 1, 0.01 \*\* Master node 2 STRAIN\_NODE2, 1, 1, 0.00 STRAIN\_NODE2, 2, 2, 0.00 STRAIN\_NODE2, 3, 3, 0.00 \*\* Master node 3 STRAIN\_NODE3, 1, 1, 0.00 STRAIN\_NODE3, 2, 2, 0.00 STRAIN\_NODE3, 3, 3, 0.00 \*Node print, Nset=FACE\_X\_MAX,Totals=Only, Global=Yes RF \*Node file RF U \*El file, Output=3D S E \*End step ---
**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:** [July 28, 2025, 6:46am UTC](https://calculix.discourse.group/t/periodic-boundary-conditions/2828/2 "2025-07-28T06:46:02Z")
Check this script for brick RVE by Martin Kraska: [CalculiX-Examples/Scripts/periodic.py at master · calculix/CalculiX-Examples · GitHub](https://github.com/calculix/CalculiX-Examples/blob/master/Scripts/periodic.py) ---
**Author:** ![Basem](https://avatars.discourse-cdn.com/v4/letter/b/6bbea6/32.png) [@Basem](https://calculix.discourse.group/u/Basem)\ **Post date:** [July 28, 2025, 8:58am UTC](https://calculix.discourse.group/t/periodic-boundary-conditions/2828/3 "2025-07-28T08:58:17Z")
Thank you, that is helpful. So I guess there is no consice way to do this and I do have to generate an \*equation commnd for every node pair.