Axisymmetric solution, TUBE7TS1
Problem
Mesh
| element | type | nodes |
|---|---|---|
| 1 | 7 | 1 3 7 5 2 6 8 4 |
| 2 | 7 | 5 7 12 10 8 11 13 9 |
| 3 | 7 | 10 12 17 15 13 16 18 14 |
| 4 | 7 | 15 17 22 20 18 21 23 19 |
| 5 | 7 | 20 22 27 25 23 26 28 24 |
| 6 | 7 | 25 27 32 30 28 31 33 29 |
| 7 | 7 | 30 32 37 35 33 36 38 34 |
| 8 | 7 | 35 37 42 40 38 41 43 39 |
| 9 | 7 | 40 42 47 45 43 46 48 44 |
| 10 | 7 | 45 47 52 50 48 51 53 49 |
Boundary conditions
The plane strain condition is enforced by setting $v=0$ for all the nodes 1 to 53, where $v$ is the displacement component parallel to the axis of revolution.
Computation
The steady-state temperature field is calculated first, following the procedures described in Steady-state analysis of a slab. The internal temperature $T_1$ is assigned to nodes 1, 2, 3 and the external temperature $T_2$ to nodes 50, 52, 53. Subsequently, the internal pressure is added by introducing the surface traction $$q_n|_\text{S1}=-p=-287.47075\times10^6\text{ Pa}$$ that acts on face S1 of element 1.
The computation is executed with the following commands:
- tube7ts1.bat
xrm2 tube7ts1.i1 xrpd tube7ts1.iB xt2s tube7ts1 rmd2 tube7ts1.i1 rpd2 tube7ts1.i2 srh2 tube7ts1.i3 fefs tube7ts1.i4 str2 tube7ts1.i5
Input
- tube7ts1.i1
; NELEM NNOD ITED ... KSS IP 10 53 7 6*0 2 ; CRIT SCALE THDEF RP 1.01 1 0.01 XY N 1 3 5 7 10 12 15 17 20 22 25 27 30 32 35 37 40 42 45 47 50 52 X 2*1.0 2*1.1 2*1.2 2*1.3 2*1.4 2*1.5 2*1.6 2*1.7 2*1.8 2*1.9 2*2.0 Y 11*(0 -0.1) EL E 1:10 N 1 3 7 5 2 6 8 4 5 7 12 10 8 11 13 9 10 12 17 15 13 16 18 14 15 17 22 20 18 21 23 19 20 22 27 25 23 26 28 24 25 27 32 30 28 31 33 29 30 32 37 35 33 36 38 34 35 37 42 40 38 41 43 39 40 42 47 45 43 46 48 44 45 47 52 50 48 51 53 49 EN EN
- tube7ts1.iB
; KREST 0 KOUT INT3 NSAX NSTEPX KSU IP 1 0 2 0 0 0 1 MP 1 T 1 V 20 0 NV 1 T 1 V 100 ; inside temperature = 100 °C NV 2 T 1 V 0 ; outside temperature = 0 °C AS 1 /M 1 /N 1 N 1 2 3 /N 2 N 50 52 53 EN EN
- tube7ts1.i2
; KREST IP 1 ; E α ν ρ MP 1 T 1 V 2e11 1e-5 0.3 0 SV 1 T 6 V -287.47075e6 ; p = 287 MPa GV 1 T 6 D 4 1 ; temperature field AS 1 /M 1 /B 0 C 2 N 1:53 /S 1 E 1 S1 /R 0 0 99 ; current temp. is arbitrary but different to initial temp. /G 1 EN EN
- tube7ts1.i3
; KREST IP 1 EN EN
- tube7ts1.i4
; KREST IP 1 EN EN
- tube7ts1.i5
; KLC 0 KOUT ILC ... KPROB KGRAF IP 1 0 1 0 6*0 0 2 EN EN
Output
- tube7ts1.STR
# 1 0.10000E+01 0 $TEMPERATURE 1 0.1000E+03 0.0000E+00 0.0000E+00 2 0.1000E+03 0.0000E+00 0.0000E+00 3 0.1000E+03 0.0000E+00 0.0000E+00 4 0.9296E+02 0.0000E+00 0.0000E+00 5 0.8625E+02 0.0000E+00 0.0000E+00 6 0.9296E+02 0.0000E+00 0.0000E+00 7 0.8625E+02 0.0000E+00 0.0000E+00 8 0.8625E+02 0.0000E+00 0.0000E+00 9 0.7984E+02 0.0000E+00 0.0000E+00 10 0.7370E+02 0.0000E+00 0.0000E+00 11 0.7984E+02 0.0000E+00 0.0000E+00 12 0.7370E+02 0.0000E+00 0.0000E+00 13 0.7370E+02 0.0000E+00 0.0000E+00 14 0.6781E+02 0.0000E+00 0.0000E+00 15 0.6215E+02 0.0000E+00 0.0000E+00 16 0.6781E+02 0.0000E+00 0.0000E+00 17 0.6215E+02 0.0000E+00 0.0000E+00 18 0.6215E+02 0.0000E+00 0.0000E+00 19 0.5671E+02 0.0000E+00 0.0000E+00 20 0.5146E+02 0.0000E+00 0.0000E+00 21 0.5671E+02 0.0000E+00 0.0000E+00 22 0.5146E+02 0.0000E+00 0.0000E+00 23 0.5146E+02 0.0000E+00 0.0000E+00 24 0.4640E+02 0.0000E+00 0.0000E+00 25 0.4150E+02 0.0000E+00 0.0000E+00 26 0.4640E+02 0.0000E+00 0.0000E+00 27 0.4150E+02 0.0000E+00 0.0000E+00 28 0.4150E+02 0.0000E+00 0.0000E+00 29 0.3677E+02 0.0000E+00 0.0000E+00 30 0.3219E+02 0.0000E+00 0.0000E+00 31 0.3677E+02 0.0000E+00 0.0000E+00 32 0.3219E+02 0.0000E+00 0.0000E+00 33 0.3219E+02 0.0000E+00 0.0000E+00 34 0.2775E+02 0.0000E+00 0.0000E+00 35 0.2345E+02 0.0000E+00 0.0000E+00 36 0.2775E+02 0.0000E+00 0.0000E+00 37 0.2345E+02 0.0000E+00 0.0000E+00 38 0.2345E+02 0.0000E+00 0.0000E+00 39 0.1927E+02 0.0000E+00 0.0000E+00 40 0.1520E+02 0.0000E+00 0.0000E+00 41 0.1927E+02 0.0000E+00 0.0000E+00 42 0.1520E+02 0.0000E+00 0.0000E+00 43 0.1520E+02 0.0000E+00 0.0000E+00 44 0.1125E+02 0.0000E+00 0.0000E+00 45 0.7400E+01 0.0000E+00 0.0000E+00 46 0.1125E+02 0.0000E+00 0.0000E+00 47 0.7400E+01 0.0000E+00 0.0000E+00 48 0.7400E+01 0.0000E+00 0.0000E+00 49 0.3653E+01 0.0000E+00 0.0000E+00 50 0.3022E-04 0.0000E+00 0.0000E+00 51 0.3653E+01 0.0000E+00 0.0000E+00 52 0.3022E-04 0.0000E+00 0.0000E+00 53 0.1209E-03 0.0000E+00 0.0000E+00
- tube7ts1.o5
; KLC 0 KOUT ILC ... KPROB KGRAF IP 1 0 1 0 6*0 0 2 EN EN AXISYMMETRIC PROBLEM 1TH LOAD CASE DISPLACEMENTS NODE U V [m] [m] 1 0.3244984E-02 0.0000000E+00 2 0.3244984E-02 0.0000000E+00 3 0.3244984E-02 0.0000000E+00 4 0.3216259E-02 0.0000000E+00 5 0.3189765E-02 0.0000000E+00 6 0.3216259E-02 0.0000000E+00 7 0.3189765E-02 0.0000000E+00 8 0.3189766E-02 0.0000000E+00 9 0.3164947E-02 0.0000000E+00 10 0.3141340E-02 0.0000000E+00 11 0.3164947E-02 0.0000000E+00 12 0.3141340E-02 0.0000000E+00 13 0.3141340E-02 0.0000000E+00 14 0.3118577E-02 0.0000000E+00 15 0.3096345E-02 0.0000000E+00 16 0.3118577E-02 0.0000000E+00 17 0.3096345E-02 0.0000000E+00 18 0.3096345E-02 0.0000000E+00 19 0.3074394E-02 0.0000000E+00 20 0.3052511E-02 0.0000000E+00 21 0.3074394E-02 0.0000000E+00 22 0.3052511E-02 0.0000000E+00 23 0.3052511E-02 0.0000000E+00 24 0.3030523E-02 0.0000000E+00 25 0.3008282E-02 0.0000000E+00 26 0.3030523E-02 0.0000000E+00 27 0.3008282E-02 0.0000000E+00 28 0.3008282E-02 0.0000000E+00 29 0.2985667E-02 0.0000000E+00 30 0.2962575E-02 0.0000000E+00 31 0.2985667E-02 0.0000000E+00 32 0.2962575E-02 0.0000000E+00 33 0.2962575E-02 0.0000000E+00 34 0.2938921E-02 0.0000000E+00 35 0.2914633E-02 0.0000000E+00 36 0.2938921E-02 0.0000000E+00 37 0.2914633E-02 0.0000000E+00 38 0.2914633E-02 0.0000000E+00 39 0.2889652E-02 0.0000000E+00 40 0.2863926E-02 0.0000000E+00 41 0.2889652E-02 0.0000000E+00 42 0.2863926E-02 0.0000000E+00 43 0.2863926E-02 0.0000000E+00 44 0.2837415E-02 0.0000000E+00 45 0.2810083E-02 0.0000000E+00 46 0.2837415E-02 0.0000000E+00 47 0.2810083E-02 0.0000000E+00 48 0.2810083E-02 0.0000000E+00 49 0.2781904E-02 0.0000000E+00 50 0.2752851E-02 0.0000000E+00 51 0.2781904E-02 0.0000000E+00 52 0.2752851E-02 0.0000000E+00 53 0.2752851E-02 0.0000000E+00 REACTIONS NODE RX RY [N] [N] 1 0.0000000E+00 -0.2041699E+08 2 0.0000000E+00 0.5772454E-06 3 0.0000000E+00 0.2041699E+08 4 0.0000000E+00 -0.7690668E+08 5 0.0000000E+00 -0.3586915E+08 6 0.0000000E+00 0.7690668E+08 7 0.0000000E+00 0.3586915E+08 8 0.0000000E+00 -0.1518987E-05 9 0.0000000E+00 -0.6615927E+08 10 0.0000000E+00 -0.3012196E+08 11 0.0000000E+00 0.6615927E+08 12 0.0000000E+00 0.3012196E+08 13 0.0000000E+00 0.3242167E-06 14 0.0000000E+00 -0.5391135E+08 15 0.0000000E+00 -0.2365206E+08 16 0.0000000E+00 0.5391135E+08 17 0.0000000E+00 0.2365206E+08 18 0.0000000E+00 -0.3269641E-05 19 0.0000000E+00 -0.4028255E+08 20 0.0000000E+00 -0.1651589E+08 21 0.0000000E+00 0.4028255E+08 22 0.0000000E+00 0.1651589E+08 23 0.0000000E+00 -0.8841744E-06 24 0.0000000E+00 -0.2537477E+08 25 0.0000000E+00 -0.8761528E+07 26 0.0000000E+00 0.2537477E+08 27 0.0000000E+00 0.8761528E+07 28 0.0000000E+00 0.1341803E-05 29 0.0000000E+00 -0.9276046E+07 30 0.0000000E+00 -0.4305257E+06 31 0.0000000E+00 0.9276046E+07 32 0.0000000E+00 0.4305257E+06 33 0.0000000E+00 0.4086178E-07 34 0.0000000E+00 0.7936894E+07 35 0.0000000E+00 0.8440853E+07 36 0.0000000E+00 -0.7936894E+07 37 0.0000000E+00 -0.8440853E+07 38 0.0000000E+00 0.6982591E-06 39 0.0000000E+00 0.2619657E+08 40 0.0000000E+00 0.1782067E+08 41 0.0000000E+00 -0.2619657E+08 42 0.0000000E+00 -0.1782067E+08 43 0.0000000E+00 0.1405133E-05 44 0.0000000E+00 0.4544320E+08 45 0.0000000E+00 0.2768056E+08 46 0.0000000E+00 -0.4544320E+08 47 0.0000000E+00 -0.2768056E+08 48 0.0000000E+00 -0.1513193E-06 49 0.0000000E+00 0.6562346E+08 50 0.0000000E+00 0.1899779E+08 51 0.0000000E+00 -0.6562346E+08 52 0.0000000E+00 -0.1899779E+08 53 0.0000000E+00 -0.1485241E-05 EQUILIBRIUM OF FORCES AND REACTIONS SUM OF FORCES [N] SUM OF REACTIONS [N] DIR. X: 319703546.24 0.00 DIR. Y: 0.00 0.00 STRESSES AT GAUSS POINTS IE IGP RG AG SIG-R SIG-A SIG-RA SIG-T [m] [m] [MPa] [MPa] [MPa] [MPa] 1 1 0.10211E+01 -0.21132E-01 -275.3 -186.4 0.0 300.7 2 0.10211E+01 -0.78868E-01 -275.3 -186.4 -0.0 300.7 3 0.10789E+01 -0.21132E-01 -244.7 -163.7 -0.0 292.7 4 0.10789E+01 -0.78868E-01 -244.7 -163.7 0.0 292.7 2 1 0.11211E+01 -0.21132E-01 -224.5 -147.8 -0.0 288.4 2 0.11211E+01 -0.78868E-01 -224.5 -147.8 0.0 288.4 3 0.11789E+01 -0.21132E-01 -199.5 -127.1 0.0 284.1 4 0.11789E+01 -0.78868E-01 -199.5 -127.1 -0.0 284.1 3 1 0.12211E+01 -0.21132E-01 -182.8 -112.6 0.0 281.9 2 0.12211E+01 -0.78868E-01 -182.8 -112.6 -0.0 281.9 3 0.12789E+01 -0.21132E-01 -161.8 -93.6 0.0 280.0 4 0.12789E+01 -0.78868E-01 -161.8 -93.6 -0.0 280.0 4 1 0.13211E+01 -0.21132E-01 -147.7 -80.2 -0.0 279.3 2 0.13211E+01 -0.78868E-01 -147.7 -80.2 0.0 279.3 3 0.13789E+01 -0.21132E-01 -129.9 -62.5 -0.0 279.1 4 0.13789E+01 -0.78868E-01 -129.9 -62.5 0.0 279.1 5 1 0.14211E+01 -0.21132E-01 -117.7 -50.1 0.0 279.4 2 0.14211E+01 -0.78868E-01 -117.7 -50.1 -0.0 279.4 3 0.14789E+01 -0.21132E-01 -102.2 -33.7 0.0 280.3 4 0.14789E+01 -0.78868E-01 -102.2 -33.7 -0.0 280.3 6 1 0.15211E+01 -0.21132E-01 -91.5 -22.1 -0.0 281.2 2 0.15211E+01 -0.78868E-01 -91.5 -22.1 0.0 281.2 3 0.15789E+01 -0.21132E-01 -77.9 -6.7 -0.0 282.9 4 0.15789E+01 -0.78868E-01 -77.9 -6.7 0.0 282.9 7 1 0.16211E+01 -0.21132E-01 -68.5 4.2 0.0 284.4 2 0.16211E+01 -0.78868E-01 -68.5 4.2 -0.0 284.4 3 0.16789E+01 -0.21132E-01 -56.3 18.6 0.0 286.6 4 0.16789E+01 -0.78868E-01 -56.3 18.6 -0.0 286.6 8 1 0.17211E+01 -0.21132E-01 -47.8 28.9 -0.0 288.4 2 0.17211E+01 -0.78868E-01 -47.8 28.9 0.0 288.4 3 0.17789E+01 -0.21132E-01 -36.9 42.5 -0.0 291.1 4 0.17789E+01 -0.78868E-01 -36.9 42.5 0.0 291.1 9 1 0.18211E+01 -0.21132E-01 -29.2 52.1 -0.0 293.1 2 0.18211E+01 -0.78868E-01 -29.2 52.1 0.0 293.1 3 0.18789E+01 -0.21132E-01 -19.3 65.0 0.0 296.1 4 0.18789E+01 -0.78868E-01 -19.3 65.0 -0.0 296.1 10 1 0.19211E+01 -0.21132E-01 -12.3 74.2 0.0 298.3 2 0.19211E+01 -0.78868E-01 -12.3 74.2 -0.0 298.3 3 0.19789E+01 -0.21132E-01 -3.2 86.4 -0.0 301.4 4 0.19789E+01 -0.78868E-01 -3.2 86.4 0.0 301.4 * END OF STR3 * TOTAL CPU: 00:00:00