Obsah
Hexahedra, BEAM56S1
Problem
Mesh
| element | type | nodes |
|---|---|---|
| 1 | 56 | 1 2 3 4 5 6 7 8 21 22 23 24 25 26 27 28 29 30 31 32 |
| 2 | 56 | 5 6 7 8 9 10 11 12 29 30 31 32 33 34 35 36 37 38 39 40 |
| 3 | 56 | 9 10 11 12 13 14 15 16 37 38 39 40 41 42 43 44 45 46 47 48 |
| 4 | 56 | 13 45 15 16 17 18 19 20 45 46 47 48 49 50 51 52 53 54 55 56 |
Boundary conditions
$u=0$ at nodes 3, 22, 23
$u=v=0$ at nodes 4, 24
$u=v=w=0$ at node 1
$u=w=0$ at nodes 2, 21
Computation
The end force is replaced with the equivalent surface traction $$\begin{align} q_x&=\frac{20000}{0.01\times0.02}=100\times10^6\text{ Pa}, \\ q_y&=-0.1\times10^6\text{ Pa}, \\ q_z&=0.05\times10^6\text{ Pa}. \end{align}$$ Similarly, the distributed loading is replaced with $$\begin{align} q_n|_\text{S3}&=\frac{l_y}{0.01}=-0.01\times10^6\text{ Pa}, \\ q_n|_\text{S2}&=-\frac{lz}{0.02}=-0.01\times10^6\text{ Pa}, \end{align}$$ where the normal surface tractions $q_n$ are now defined in the local coordinate systems of the elements' faces S3, S2 forming the $y=0.02$ and $z=0$ planes, respectively.
The computation is executed with the following commands:
- beam56s1.bat
rmd3 beam56s1.i1 rpd3 beam56s1.i2 srh3 beam56s1.i3 fefs beam56s1.i4 str3 beam56s1.i5
Input
- beam56s1.i1
; NELEM NNOD ITED IP 4 56 56 ; CRIT SCALE RP 1.01 1 XY N 1:20 X 4*0 4*0.25 4*0.5 4*0.75 4*1 Y 5*(0 0.02 0.02 0) Z 5*(0 0 0.01 0.01) EL E 1:4 N =A 1:8 =A =B 21:32 =B =4A =8B =8A =16B =12A =24B EN EN
- beam56s1.i2
; KREST IP 1 ; E α ν ρ MP 1 T 1 V 2e11 0 0.3 0 SV 1 T 9 V 100e6 -0.1e6 0 ; Fx = 20000 N, Fy = -20 N, Fz = 0 N SV 2 T 9 V 0 0 0.05e6 ; Fx = 0 N, Fy = 0 N, Fz = 10 N SV 3 T 6 V -0.01e6 ; ly = -100 N/m SV 4 T 6 V -0.01e6 ; lz = 200 N/m AS 1 /M 1 /B 0 N 1 /B 0 C 1 3 N 2 21 /B 0 C 1 2 N 4 24 /B 0 C 1 N 3 22 23 ; in-plane loading ly, Fx, Fy /S 1 E 4 S6 /S 3 E 1:4 S3 AS 2 ; three-dimensional loading ly, lz, Fx, Fy, Fz /S 1 E 4 S6 /S 2 E 4 S6 /S 3 E 1:4 S3 /S 4 E 1:4 S2 EN EN
- beam56s1.i3
; KREST IP 1 EN EN
- beam56s1.i4
; KREST IP 1 EN EN
- beam56s1.i5
; KLC 0 KOUT ILC ... KPROB KGRAF IP 1 0 1 0 6*0 0 2 EN EN
Output
- beam56s1.o5
; KLC 0 KOUT ILC ... KPROB KGRAF IP 1 0 1 0 6*0 0 2 EN EN 1TH LOAD CASE DISPLACEMENTS NODE U V W ALPHA BETA GAMMA [m] [m] [m] [rad] [rad] [rad] 1 0.0000000E+00 0.0000000E+00 0.0000000E+00 2 0.0000000E+00 -0.3172796E-05 0.0000000E+00 3 0.0000000E+00 -0.2524599E-05 -0.2633415E-05 4 0.0000000E+00 0.0000000E+00 -0.5750364E-06 5 0.2135549E-04 -0.1308906E-02 0.5098606E-05 6 0.2290595E-03 -0.1311969E-02 0.5046863E-05 7 0.2286679E-03 -0.1311478E-02 0.2654847E-05 8 0.2095755E-04 -0.1308442E-02 0.4550025E-05 9 0.8552110E-04 -0.4675211E-02 0.1567512E-04 10 0.4149398E-03 -0.4678213E-02 0.1527528E-04 11 0.4145046E-03 -0.4677726E-02 0.1320523E-04 12 0.8508458E-04 -0.4674751E-02 0.1473010E-04 13 0.1825536E-03 -0.9149111E-02 0.2689128E-04 14 0.5679250E-03 -0.9152115E-02 0.2619798E-04 15 0.5674759E-03 -0.9151633E-02 0.2442893E-04 16 0.1821041E-03 -0.9148628E-02 0.2566497E-04 17 0.3003738E-03 -0.1405948E-01 0.3819719E-04 18 0.7001098E-03 -0.1406248E-01 0.3739258E-04 19 0.6996592E-03 -0.1406200E-01 0.3573164E-04 20 0.2999230E-03 -0.1405900E-01 0.3685608E-04 21 0.0000000E+00 -0.9295842E-06 0.0000000E+00 22 0.0000000E+00 -0.3105548E-05 -0.1310102E-05 23 0.0000000E+00 -0.5231508E-06 -0.1442628E-05 24 0.0000000E+00 0.0000000E+00 -0.2753973E-06 25 0.1014940E-04 -0.3300792E-03 0.1117917E-05 26 0.1150808E-03 -0.3330235E-03 0.1489614E-05 27 0.1148741E-03 -0.3325392E-03 -0.1371497E-05 28 0.9945803E-05 -0.3296130E-03 0.8990238E-06 29 0.1252071E-03 -0.1309923E-02 0.5074821E-05 30 0.2288668E-03 -0.1311827E-02 0.3848594E-05 31 0.1248122E-03 -0.1309467E-02 0.3561234E-05 32 0.2115365E-04 -0.1308847E-02 0.4820576E-05 33 0.5295969E-04 -0.2801962E-02 0.1027104E-04 34 0.3224810E-03 -0.2804964E-02 0.1002086E-04 35 0.3220635E-03 -0.2804485E-02 0.7811136E-05 36 0.5254432E-04 -0.2801453E-02 0.9501764E-05 37 0.2502308E-03 -0.4676464E-02 0.1547487E-04 38 0.4147235E-03 -0.4678038E-02 0.1424080E-04 39 0.2497948E-03 -0.4675985E-02 0.1397897E-04 40 0.8530142E-04 -0.4675031E-02 0.1520355E-04 41 0.1337028E-03 -0.6824790E-02 0.2129414E-04 42 0.4917674E-03 -0.6827787E-02 0.2064247E-04 43 0.4913245E-03 -0.6827304E-02 0.1882728E-04 44 0.1332600E-03 -0.6824310E-02 0.2010388E-04 45 0.3752392E-03 -0.9150522E-02 0.2654480E-04 46 0.5677023E-03 -0.9151894E-02 0.2531328E-04 47 0.3747899E-03 -0.9150041E-02 0.2504380E-04 48 0.1823271E-03 -0.9148896E-02 0.2627784E-04 49 0.2412864E-03 -0.1158191E-01 0.3262502E-04 50 0.6341948E-03 -0.1158491E-01 0.3170536E-04 51 0.6337447E-03 -0.1158443E-01 0.3016110E-04 52 0.2408365E-03 -0.1158143E-01 0.3117053E-04 53 0.5002419E-03 -0.1406096E-01 0.3779481E-04 54 0.6998827E-03 -0.1406225E-01 0.3656220E-04 DISPLACEMENTS NODE U V W ALPHA BETA GAMMA [m] [m] [m] [rad] [rad] [rad] 55 0.4997912E-03 -0.1406048E-01 0.3629545E-04 56 0.3001502E-03 -0.1405924E-01 0.3752678E-04 REACTIONS NODE RX RY RZ RALPHA RBETA RGAMMA [N] [N] [N] [Nm] [Nm] [Nm] 1 0.2295530E+04 -0.4459869E+03 0.4362402E+03 2 0.1057637E+04 0.0000000E+00 -0.1884624E+03 3 0.1065811E+04 0.0000000E+00 0.0000000E+00 4 0.2256586E+04 -0.1695392E+04 0.0000000E+00 21 -0.6694678E+04 0.0000000E+00 -0.2477778E+03 22 -0.8944154E+04 0.0000000E+00 0.0000000E+00 23 -0.6663909E+04 0.0000000E+00 0.0000000E+00 24 -0.4372822E+04 0.2261379E+04 0.0000000E+00 EQUILIBRIUM OF FORCES AND REACTIONS SUM OF FORCES [N] SUM OF REACTIONS [N] DIRECTION X: 20000.00 -20000.00 DIRECTION Y: -120.00 120.00 DIRECTION Z: -0.00 0.00 STRESSES AT GAUSSPOINTS IE IGP XG YG ZG ERROR SIG-X SIG-Y SIG-Z TAU-XY TAU-YZ TAU-ZX SIG-HMH [m] [m] [m] [%] [MPa] [MPa] [MPa] [MPa] [MPa] [MPa] [MPa] 1 0.00000 1 0.5283E-01 0.4226E-02 0.2113E-02 51.25 -0.87 -0.22 -0.63 0.59 -0.05 51.82 2 0.5283E-01 0.1577E-01 0.2113E-02 148.36 -1.17 0.15 -0.55 -0.44 0.05 148.87 3 0.1972E+00 0.4226E-02 0.2113E-02 51.49 -2.30 -1.70 -0.49 0.48 0.03 53.50 4 0.1972E+00 0.1577E-01 0.2113E-02 148.91 2.85 1.94 -0.50 0.20 -0.02 146.52 5 0.5283E-01 0.4226E-02 0.7887E-02 52.05 2.04 0.17 -0.52 -1.59 0.03 51.05 6 0.5283E-01 0.1577E-01 0.7887E-02 148.35 -0.30 -0.10 -0.58 0.02 -0.03 148.55 7 0.1972E+00 0.4226E-02 0.7887E-02 51.09 -2.81 -1.94 -0.51 0.10 -0.02 53.47 8 0.1972E+00 0.1577E-01 0.7887E-02 148.52 2.35 1.70 -0.50 -0.18 0.02 146.50 2 0.00000 1 0.3028E+00 0.4226E-02 0.2113E-02 73.04 3.14 2.34 -0.46 -0.66 -0.01 70.32 2 0.3028E+00 0.1577E-01 0.2113E-02 126.91 -3.19 -2.56 -0.45 -0.09 0.01 129.79 3 0.4472E+00 0.4226E-02 0.2113E-02 71.08 -2.27 -2.16 -0.37 0.09 -0.00 73.30 4 0.4472E+00 0.1577E-01 0.2113E-02 128.97 2.36 2.19 -0.38 0.04 -0.00 126.70 5 0.3028E+00 0.4226E-02 0.7887E-02 72.99 2.89 2.48 -0.44 0.33 0.00 70.31 6 0.3028E+00 0.1577E-01 0.7887E-02 127.07 -2.89 -2.25 -0.44 0.18 -0.00 129.64 7 0.4472E+00 0.4226E-02 0.7887E-02 71.03 -2.36 -2.19 -0.38 0.01 0.00 73.31 8 0.4472E+00 0.1577E-01 0.7887E-02 128.92 2.27 2.15 -0.38 -0.03 -0.00 126.71 3 0.00000 1 0.5528E+00 0.4226E-02 0.2113E-02 87.86 1.86 1.93 -0.32 0.08 0.01 85.97 2 0.5528E+00 0.1577E-01 0.2113E-02 112.12 -1.96 -1.91 -0.33 -0.02 -0.01 114.06 3 0.6972E+00 0.4226E-02 0.2113E-02 86.50 -1.63 -1.50 -0.25 0.04 -0.01 88.07 4 0.6972E+00 0.1577E-01 0.2113E-02 113.51 1.63 1.50 -0.25 0.03 0.01 111.94 5 0.5528E+00 0.4226E-02 0.7887E-02 87.91 2.02 1.93 -0.32 -0.09 -0.01 85.93 6 0.5528E+00 0.1577E-01 0.7887E-02 112.11 -1.95 -1.95 -0.32 -0.00 0.01 114.06 7 0.6972E+00 0.4226E-02 0.7887E-02 86.49 -1.65 -1.51 -0.25 -0.02 0.01 88.06 8 0.6972E+00 0.1577E-01 0.7887E-02 113.50 1.62 1.50 -0.25 -0.03 -0.02 111.94 4 0.00000 1 0.8028E+00 0.4226E-02 0.2113E-02 97.18 1.21 1.06 -0.20 -0.07 0.02 96.04 2 0.8028E+00 0.1577E-01 0.2113E-02 102.82 -1.21 -1.07 -0.20 -0.03 -0.02 103.96 3 0.9472E+00 0.4226E-02 0.2113E-02 96.69 -0.33 -0.28 -0.13 0.02 -0.00 97.00 4 0.9472E+00 0.1577E-01 0.2113E-02 103.31 0.32 0.29 -0.13 0.01 0.00 103.01 5 0.8028E+00 0.4226E-02 0.7887E-02 97.17 1.18 1.06 -0.20 0.05 -0.02 96.05 6 0.8028E+00 0.1577E-01 0.7887E-02 102.83 -1.20 -1.05 -0.20 0.04 0.02 103.96 7 0.9472E+00 0.4226E-02 0.7887E-02 96.69 -0.32 -0.28 -0.13 -0.01 0.00 97.00 8 0.9472E+00 0.1577E-01 0.7887E-02 103.31 0.31 0.28 -0.13 -0.01 -0.00 103.01 2TH LOAD CASE DISPLACEMENTS NODE U V W ALPHA BETA GAMMA [m] [m] [m] [rad] [rad] [rad] 1 0.0000000E+00 0.0000000E+00 0.0000000E+00 2 0.0000000E+00 -0.4761029E-05 0.0000000E+00 3 0.0000000E+00 -0.6066909E-06 -0.4301044E-05 4 0.0000000E+00 0.0000000E+00 -0.1137286E-05 5 0.3319901E-03 -0.1313775E-02 0.7800357E-02 6 0.5408308E-03 -0.1323331E-02 0.7799365E-02 7 -0.8199485E-04 -0.1315829E-02 0.7797231E-02 8 -0.2907933E-03 -0.1319193E-02 0.7800155E-02 9 0.5707184E-03 -0.4697536E-02 0.2775690E-01 10 0.9014916E-03 -0.4703148E-02 0.2775545E-01 11 -0.7070918E-04 -0.4699444E-02 0.2775327E-01 12 -0.4014738E-03 -0.4699102E-02 0.2775589E-01 13 0.7372490E-03 -0.9189211E-02 0.5381030E-01 14 0.1124003E-02 -0.9193409E-02 0.5380855E-01 15 0.1277627E-04 -0.9191213E-02 0.5380681E-01 16 -0.3739756E-03 -0.9189395E-02 0.5380910E-01 17 0.8692327E-03 -0.1411730E-01 0.8194961E-01 18 0.1270360E-02 -0.1412072E-01 0.8194775E-01 19 0.1307978E-03 -0.1411928E-01 0.8194608E-01 20 -0.2703279E-03 -0.1411670E-01 0.8194826E-01 21 0.0000000E+00 -0.1462343E-05 0.0000000E+00 22 0.0000000E+00 -0.3196639E-05 -0.3393406E-05 23 0.0000000E+00 0.5890163E-07 -0.8727441E-06 24 0.0000000E+00 0.0000000E+00 -0.1848768E-05 25 0.1658622E-03 -0.3293434E-03 0.1954133E-02 26 0.2714340E-03 -0.3386125E-03 0.1953322E-02 27 -0.4084202E-04 -0.3311587E-03 0.1950060E-02 28 -0.1464344E-03 -0.3346849E-03 0.1953490E-02 29 0.4364153E-03 -0.1318105E-02 0.7803971E-02 30 0.2294217E-03 -0.1319616E-02 0.7797603E-02 31 -0.1864108E-03 -0.1316915E-02 0.7802308E-02 32 0.2059509E-04 -0.1316657E-02 0.7799571E-02 33 0.4513158E-03 -0.2815063E-02 0.1668696E-01 34 0.7220783E-03 -0.2822728E-02 0.1668568E-01 35 -0.7629361E-04 -0.2817165E-02 0.1668360E-01 36 -0.3470702E-03 -0.2818763E-02 0.1668628E-01 37 0.7361062E-03 -0.4700076E-02 0.2775722E-01 38 0.4153923E-03 -0.4701383E-02 0.2775401E-01 39 -0.2360863E-03 -0.4699047E-02 0.2775576E-01 40 0.8462100E-04 -0.4698369E-02 0.2775604E-01 41 0.6539145E-03 -0.6856134E-02 0.4034926E-01 42 0.1013347E-02 -0.6860645E-02 0.4034755E-01 43 -0.2889430E-04 -0.6858110E-02 0.4034571E-01 44 -0.3883274E-03 -0.6856638E-02 0.4034804E-01 45 0.9306296E-03 -0.9191224E-02 0.5380991E-01 46 0.5683915E-03 -0.9192326E-02 0.5380758E-01 47 -0.1806060E-03 -0.9190206E-02 0.5380840E-01 48 0.1816349E-03 -0.9189329E-02 0.5380960E-01 49 0.8031729E-03 -0.1163111E-01 0.6779165E-01 50 0.1197467E-02 -0.1163441E-01 0.6778967E-01 51 0.7185633E-04 -0.1163310E-01 0.6778813E-01 52 -0.3224387E-03 -0.1163040E-01 0.6779020E-01 53 0.1069789E-02 -0.1411899E-01 0.8194869E-01 54 0.7005770E-03 -0.1412001E-01 0.8194690E-01 DISPLACEMENTS NODE U V W ALPHA BETA GAMMA [m] [m] [m] [rad] [rad] [rad] 55 -0.6975657E-04 -0.1411798E-01 0.8194720E-01 56 0.2994542E-03 -0.1411700E-01 0.8194892E-01 REACTIONS NODE RX RY RZ RALPHA RBETA RGAMMA [N] [N] [N] [Nm] [Nm] [Nm] 1 0.2991665E+03 -0.2615965E+04 0.5247045E+04 2 -0.6860303E+03 0.0000000E+00 0.9465038E+04 3 0.2956882E+04 0.0000000E+00 0.0000000E+00 4 0.4260213E+04 0.5820022E+04 0.0000000E+00 21 -0.1396504E+05 0.0000000E+00 -0.1492208E+05 22 -0.9003832E+04 0.0000000E+00 0.0000000E+00 23 0.4310006E+03 0.0000000E+00 0.0000000E+00 24 -0.4292360E+04 -0.3084056E+04 0.0000000E+00 EQUILIBRIUM OF FORCES AND REACTIONS SUM OF FORCES [N] SUM OF REACTIONS [N] DIRECTION X: 20000.00 -20000.00 DIRECTION Y: -120.00 120.00 DIRECTION Z: 210.00 -210.00 STRESSES AT GAUSSPOINTS IE IGP XG YG ZG ERROR SIG-X SIG-Y SIG-Z TAU-XY TAU-YZ TAU-ZX SIG-HMH [m] [m] [m] [%] [MPa] [MPa] [MPa] [MPa] [MPa] [MPa] [MPa] 1 0.00000 1 0.5283E-01 0.4226E-02 0.2113E-02 202.75 22.62 1.66 0.03 -5.77 1.09 191.74 2 0.5283E-01 0.1577E-01 0.2113E-02 295.50 14.19 -6.38 -0.91 9.16 0.91 292.58 3 0.1972E+00 0.4226E-02 0.2113E-02 198.87 4.08 6.30 -0.57 -3.05 0.84 193.77 4 0.1972E+00 0.1577E-01 0.2113E-02 297.55 10.07 11.85 -0.53 1.14 0.87 286.61 5 0.5283E-01 0.4226E-02 0.7887E-02 -98.22 -21.23 4.33 -1.21 -1.27 1.04 92.53 6 0.5283E-01 0.1577E-01 0.7887E-02 -0.03 -15.88 0.60 -0.20 7.50 0.95 20.82 7 0.1972E+00 0.4226E-02 0.7887E-02 -97.53 -10.02 -11.90 -0.51 -3.16 0.82 86.77 8 0.1972E+00 0.1577E-01 0.7887E-02 1.11 -4.04 -6.37 -0.40 1.03 0.88 7.07 2 0.00000 1 0.3028E+00 0.4226E-02 0.2113E-02 146.51 -11.54 -8.35 -0.59 4.75 0.77 156.71 2 0.3028E+00 0.1577E-01 0.2113E-02 200.96 -16.57 -13.01 -0.22 -3.67 0.73 215.87 3 0.4472E+00 0.4226E-02 0.2113E-02 155.97 5.40 5.92 -0.60 -0.65 0.58 150.32 4 0.4472E+00 0.1577E-01 0.2113E-02 214.10 10.18 10.61 -0.21 0.33 0.62 203.71 5 0.3028E+00 0.4226E-02 0.7887E-02 -0.25 18.37 13.58 -0.38 3.67 0.77 17.98 6 0.3028E+00 0.1577E-01 0.7887E-02 52.78 9.67 7.80 -0.60 -3.10 0.72 44.43 7 0.4472E+00 0.4226E-02 0.7887E-02 -14.09 -10.18 -10.62 -0.13 -0.67 0.60 4.03 8 0.4472E+00 0.1577E-01 0.7887E-02 44.02 -5.40 -5.94 -0.56 0.30 0.61 49.72 3 0.00000 1 0.5528E+00 0.4226E-02 0.2113E-02 116.78 -3.17 -4.61 -0.42 -0.59 0.52 120.68 2 0.5528E+00 0.1577E-01 0.2113E-02 140.77 -7.50 -8.87 -0.21 0.62 0.47 148.97 3 0.6972E+00 0.4226E-02 0.2113E-02 121.21 3.12 3.38 -0.27 -0.10 0.34 117.96 4 0.6972E+00 0.1577E-01 0.2113E-02 148.26 6.42 6.44 -0.24 0.11 0.37 141.83 5 0.5528E+00 0.4226E-02 0.7887E-02 59.03 6.99 8.71 -0.19 -0.26 0.49 51.21 6 0.5528E+00 0.1577E-01 0.7887E-02 83.42 3.65 4.76 -0.48 0.51 0.51 79.24 7 0.6972E+00 0.4226E-02 0.7887E-02 51.75 -6.42 -6.45 -0.24 -0.17 0.37 58.19 8 0.6972E+00 0.1577E-01 0.7887E-02 78.79 -3.14 -3.39 -0.26 0.05 0.34 82.06 4 0.00000 1 0.8028E+00 0.4226E-02 0.2113E-02 101.72 -2.46 -2.33 -0.29 0.28 0.26 104.11 2 0.8028E+00 0.1577E-01 0.2113E-02 107.41 -4.77 -4.40 -0.10 -0.29 0.23 112.00 3 0.9472E+00 0.4226E-02 0.2113E-02 103.68 0.65 0.61 -0.13 -0.07 0.10 103.05 4 0.9472E+00 0.1577E-01 0.2113E-02 110.29 1.26 1.17 -0.12 0.08 0.11 109.07 5 0.8028E+00 0.4226E-02 0.7887E-02 92.64 4.89 4.43 -0.12 0.26 0.23 87.98 6 0.8028E+00 0.1577E-01 0.7887E-02 98.23 2.31 2.28 -0.28 -0.20 0.26 95.94 7 0.9472E+00 0.4226E-02 0.7887E-02 89.70 -1.31 -1.19 -0.12 -0.07 0.11 90.95 8 0.9472E+00 0.1577E-01 0.7887E-02 96.34 -0.63 -0.61 -0.13 0.05 0.10 96.96 * END OF STR3 * TOTAL CPU: 00:00:00