Table of Contents
Semi-loofs, BEAM61S1
Problem
Mesh
| element | type | nodes |
|---|---|---|
| 1 | 61 | 1 2 4 3 11 13 14 12 |
| 2 | 61 | 3 4 6 5 14 16 17 15 |
| 3 | 61 | 5 6 8 7 17 19 20 18 |
| 4 | 61 | 7 8 10 9 20 22 23 21 |
Boundary conditions
$u=v=w=0$ at node 1
$u=w=0$ at node 2
$u=w=\alpha=\beta=0$ at node 11
Computation
The end force is replaced with the equivalent edge traction $$\begin{align} l_x&=\frac{20000}{0.02}=1000\times10^3\text{ N/m}, \\ l_y&=-10^3\text{ N/m}, \\ l_z&=0.5\times10^3\text{ N/m}. \end{align}$$ The distributed loading in $y$ direction is transformed to the local coordinate systems of the elements' edges L2 that coincide with the line $y=0.02,$ $z=0.$ Thus we have $$l_{xh}|_\text{L2}=l_y=-100\text{ N/m}$$ for elements 1 to 4.
The distributed loading in $z$ direction is replaced with the normal surface traction $$q_n|_\text{S1}=-\frac{l_z}{0.02}=-0.01\times10^6\text{ Pa}$$ acting on the semi-loof’s face S1 only.
The computation is executed with the following commands:
- beam61s1.bat
rmd3 beam61s1.i1 rpd3 beam61s1.i2 srh3 beam61s1.i3 fefs beam61s1.i4 str3 beam61s1.i5
Input
- beam61s1.i1
; NELEM NNOD ITED IP 4 23 61 ; CRIT SCALE THDEF RP 1.01 1 0.01 XY N 1:10 X 2*0 2*0.25 2*0.5 2*0.75 2*1 Y 5*(0 0.02) Z 10*0 EL E 1:4 N =A 1 2 4 3 =A =B 11 13 14 12 =B =2A =3B =4A =6B =6A =9B EN EN
- beam61s1.i2
; KREST IP 1 ; E α ν ρ MP 1 T 1 V 2e11 0 0.3 0 LV 1 T 9 V 1000e3 -1e3 0 ; Fx = 20000 N, Fy = -20 N, Fz = 0 N LV 2 T 9 V 0 0 0.5e3 ; Fx = 0 N, Fy = 0 N, Fz = 10 N LV 3 T 6 V -100 ; ly = -100 N/m SV 1 T 6 V -0.01e6 ; lz = 200 N/m AS 1 /M 1 /B 0 N 1 /B 0 C 1 3 N 2 /B 0 C 1 2 4 5 N 11 ; in-plane loading ly, Fx, Fy /L 1 E 4 L3 /L 3 E 1:4 L2 AS 2 ; three-dimensional loading ly, lz, Fx, Fy, Fz /L 1 E 4 L3 /L 2 E 4 L3 /L 3 E 1:4 L2 /S 1 E 1:4 S1 EN EN
- beam61s1.i3
; KREST IP 1 EN EN
- beam61s1.i4
; KREST IP 1 EN EN
- beam61s1.i5
; KLC 0 KOUT ILC ... KPROB KGRAF IP 1 0 1 0 6*0 0 2 EN EN
Output
- beam61s1.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 -0.1767590E-05 0.0000000E+00 3 0.1880983E-04 -0.1331416E-02 0.0000000E+00 4 0.2302284E-03 -0.1334231E-02 0.0000000E+00 5 0.8322892E-04 -0.4738301E-02 0.0000000E+00 6 0.4156647E-03 -0.4741274E-02 0.0000000E+00 7 0.1803843E-03 -0.9247236E-02 0.0000000E+00 8 0.5684913E-03 -0.9250232E-02 0.0000000E+00 9 0.2985709E-03 -0.1418682E-01 0.0000000E+00 10 0.7003044E-03 -0.1418982E-01 0.0000000E+00 11 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00 12 0.8367713E-05 -0.3349822E-03 0.0000000E+00 0.0000000E+00 0.0000000E+00 13 0.1151700E-03 -0.3381439E-03 0.0000000E+00 0.0000000E+00 0.0000000E+00 14 0.1245174E-03 -0.1332362E-02 0.0000000E+00 0.0000000E+00 0.0000000E+00 15 0.5054521E-04 -0.2845755E-02 0.0000000E+00 0.0000000E+00 0.0000000E+00 16 0.3232725E-03 -0.2848779E-02 0.0000000E+00 0.0000000E+00 0.0000000E+00 17 0.2494470E-03 -0.4739527E-02 0.0000000E+00 0.0000000E+00 0.0000000E+00 18 0.1315113E-03 -0.6905823E-02 0.0000000E+00 0.0000000E+00 0.0000000E+00 19 0.4923510E-03 -0.6908827E-02 0.0000000E+00 0.0000000E+00 0.0000000E+00 20 0.3744377E-03 -0.9248648E-02 0.0000000E+00 0.0000000E+00 0.0000000E+00 21 0.2393201E-03 -0.1169579E-01 0.0000000E+00 0.0000000E+00 0.0000000E+00 22 0.6345525E-03 -0.1169879E-01 0.0000000E+00 0.0000000E+00 0.0000000E+00 23 0.4994377E-03 -0.1418830E-01 0.0000000E+00 0.0000000E+00 0.0000000E+00 REACTIONS NODE RX RY RZ RALPHA RBETA RGAMMA [N] [N] [N] [Nm] [Nm] [Nm] 1 -0.1091564E+03 -0.7597486E+04 0.0000000E+00 2 -0.7109156E+04 0.0000000E+00 0.0000000E+00 11 -0.1278169E+05 0.7717486E+04 0.0000000E+00 0.0000000E+00 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 IP XG YG ZG ERROR X1 X2 X3 SIGX SIGY TAUZ SIGRED [m] [m] [m] [%] [MPa] [MPa] [MPa] [MPa] 1 0.0 1 0.5283E-01 0.4226E-02 -0.5000E-02 -0.00 1.00 0.00 8.18 51.75 -0.31 48.19 0.5283E-01 0.4226E-02 0.5000E-02 -0.00 1.00 0.00 8.18 51.75 -0.31 48.19 2 0.5283E-01 0.1577E-01 -0.5000E-02 0.00 1.00 0.00 0.43 148.25 -0.84 148.04 0.5283E-01 0.1577E-01 0.5000E-02 0.00 1.00 0.00 0.43 148.25 -0.84 148.04 3 0.1972E+00 0.4226E-02 -0.5000E-02 -0.00 1.00 0.00 -3.67 51.18 -0.60 53.12 0.1972E+00 0.4226E-02 0.5000E-02 -0.00 1.00 0.00 -3.67 51.18 -0.60 53.12 4 0.1972E+00 0.1577E-01 -0.5000E-02 -0.00 1.00 0.00 0.19 148.82 -0.40 148.73 0.1972E+00 0.1577E-01 0.5000E-02 -0.00 1.00 0.00 0.19 148.82 -0.40 148.73 2 0.0 1 0.3028E+00 0.4226E-02 -0.5000E-02 -0.00 1.00 0.00 1.92 72.01 -0.42 71.07 0.3028E+00 0.4226E-02 0.5000E-02 -0.00 1.00 0.00 1.92 72.01 -0.42 71.07 2 0.3028E+00 0.1577E-01 -0.5000E-02 0.00 1.00 0.00 -0.63 127.99 -0.48 128.31 0.3028E+00 0.1577E-01 0.5000E-02 0.00 1.00 0.00 -0.63 127.99 -0.48 128.31 3 0.4472E+00 0.4226E-02 -0.5000E-02 -0.00 1.00 0.00 -1.66 72.06 -0.39 72.91 0.4472E+00 0.4226E-02 0.5000E-02 -0.00 1.00 0.00 -1.66 72.06 -0.39 72.91 4 0.4472E+00 0.1577E-01 -0.5000E-02 -0.00 1.00 0.00 1.12 127.94 -0.36 127.38 0.4472E+00 0.1577E-01 0.5000E-02 -0.00 1.00 0.00 1.12 127.94 -0.36 127.38 3 0.0 1 0.5528E+00 0.4226E-02 -0.5000E-02 -0.00 1.00 0.00 1.42 87.24 -0.32 86.54 0.5528E+00 0.4226E-02 0.5000E-02 -0.00 1.00 0.00 1.42 87.24 -0.32 86.54 2 0.5528E+00 0.1577E-01 -0.5000E-02 0.00 1.00 0.00 -1.24 112.76 -0.33 113.39 0.5528E+00 0.1577E-01 0.5000E-02 0.00 1.00 0.00 -1.24 112.76 -0.33 113.39 3 0.6972E+00 0.4226E-02 -0.5000E-02 -0.00 1.00 0.00 -1.06 87.14 -0.25 87.68 0.6972E+00 0.4226E-02 0.5000E-02 -0.00 1.00 0.00 -1.06 87.14 -0.25 87.68 4 0.6972E+00 0.1577E-01 -0.5000E-02 -0.00 1.00 0.00 0.97 112.86 -0.25 112.38 0.6972E+00 0.1577E-01 0.5000E-02 -0.00 1.00 0.00 0.97 112.86 -0.25 112.38 4 0.0 1 0.8028E+00 0.4226E-02 -0.5000E-02 -0.00 1.00 0.00 0.73 96.90 -0.20 96.54 0.8028E+00 0.4226E-02 0.5000E-02 -0.00 1.00 0.00 0.73 96.90 -0.20 96.54 2 0.8028E+00 0.1577E-01 -0.5000E-02 0.00 1.00 0.00 -0.71 103.10 -0.20 103.46 0.8028E+00 0.1577E-01 0.5000E-02 0.00 1.00 0.00 -0.71 103.10 -0.20 103.46 3 0.9472E+00 0.4226E-02 -0.5000E-02 -0.00 1.00 0.00 -0.20 96.96 -0.13 97.06 0.9472E+00 0.4226E-02 0.5000E-02 -0.00 1.00 0.00 -0.20 96.96 -0.13 97.06 4 0.9472E+00 0.1577E-01 -0.5000E-02 -0.00 1.00 0.00 0.18 103.04 -0.13 102.95 0.9472E+00 0.1577E-01 0.5000E-02 -0.00 1.00 0.00 0.18 103.04 -0.13 102.95 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 -0.1767590E-05 0.0000000E+00 3 0.1880983E-04 -0.1331416E-02 0.8771865E-02 4 0.2302284E-03 -0.1334231E-02 0.8771865E-02 5 0.8322892E-04 -0.4738301E-02 0.2969195E-01 6 0.4156647E-03 -0.4741274E-02 0.2969195E-01 7 0.1803843E-03 -0.9247236E-02 0.5643215E-01 8 0.5684913E-03 -0.9250232E-02 0.5643215E-01 9 0.2985709E-03 -0.1418682E-01 0.8500809E-01 10 0.7003044E-03 -0.1418982E-01 0.8500809E-01 11 0.0000000E+00 0.0000000E+00 0.4925822E-05 0.0000000E+00 0.0000000E+00 12 0.8367713E-05 -0.3349822E-03 0.2374474E-02 0.8936692E-03 0.6525084E-03 13 0.1151700E-03 -0.3381439E-03 0.2374474E-02 -0.8936692E-03 -0.6525084E-03 14 0.1245174E-03 -0.1332362E-02 0.8774679E-02 -0.6437942E-01 -0.6437942E-01 15 0.5054521E-04 -0.2845755E-02 0.1815809E-01 0.5001449E-03 0.3249778E-03 16 0.3232725E-03 -0.2848779E-02 0.1815809E-01 -0.5001449E-03 -0.3249778E-03 17 0.2494470E-03 -0.4739527E-02 0.2969325E-01 -0.9875488E-01 -0.9875488E-01 18 0.1315113E-03 -0.6905823E-02 0.4263275E-01 0.2202495E-03 0.1099227E-03 19 0.4923510E-03 -0.6908827E-02 0.4263275E-01 -0.2202495E-03 -0.1099227E-03 20 0.3744377E-03 -0.9248648E-02 0.5643249E-01 -0.1125055E+00 -0.1125055E+00 21 0.2393201E-03 -0.1169579E-01 0.7064238E-01 0.5279840E-04 0.7409074E-05 22 0.6345525E-03 -0.1169879E-01 0.7064238E-01 -0.5279840E-04 -0.7409069E-05 23 0.4994377E-03 -0.1418830E-01 0.8500804E-01 -0.1150063E+00 -0.1150063E+00 REACTIONS NODE RX RY RZ RALPHA RBETA RGAMMA [N] [N] [N] [Nm] [Nm] [Nm] 1 -0.1091564E+03 -0.7597486E+04 -0.1050000E+03 2 -0.7109156E+04 0.0000000E+00 -0.1050000E+03 11 -0.1278169E+05 0.7717486E+04 0.0000000E+00 0.5500000E+02 0.5500000E+02 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 IP XG YG ZG ERROR X1 X2 X3 SIGX SIGY TAUZ SIGRED [m] [m] [m] [%] [MPa] [MPa] [MPa] [MPa] 1 0.0 1 0.5283E-01 0.4226E-02 -0.5000E-02 -0.00 1.00 0.00 8.08 349.32 -1.30 345.35 0.5283E-01 0.4226E-02 0.5000E-02 -0.00 1.00 0.00 8.28 -245.81 0.69 250.05 2 0.5283E-01 0.1577E-01 -0.5000E-02 0.00 1.00 0.00 0.33 445.81 0.16 445.64 0.5283E-01 0.1577E-01 0.5000E-02 0.00 1.00 0.00 0.53 -149.32 -1.84 149.62 3 0.1972E+00 0.4226E-02 -0.5000E-02 -0.00 1.00 0.00 -3.69 268.62 -1.10 270.49 0.1972E+00 0.4226E-02 0.5000E-02 -0.00 1.00 0.00 -3.65 -166.26 -0.10 164.47 4 0.1972E+00 0.1577E-01 -0.5000E-02 -0.00 1.00 0.00 0.18 366.26 0.10 366.17 0.1972E+00 0.1577E-01 0.5000E-02 -0.00 1.00 0.00 0.21 -68.62 -0.91 68.74 2 0.0 1 0.3028E+00 0.4226E-02 -0.5000E-02 -0.00 1.00 0.00 1.92 238.74 -1.21 237.79 0.3028E+00 0.4226E-02 0.5000E-02 -0.00 1.00 0.00 1.92 -94.72 0.37 95.70 2 0.3028E+00 0.1577E-01 -0.5000E-02 0.00 1.00 0.00 -0.62 294.72 0.31 295.03 0.3028E+00 0.1577E-01 0.5000E-02 0.00 1.00 0.00 -0.63 -38.74 -1.26 38.49 3 0.4472E+00 0.4226E-02 -0.5000E-02 -0.00 1.00 0.00 -1.67 180.33 -0.68 181.18 0.4472E+00 0.4226E-02 0.5000E-02 -0.00 1.00 0.00 -1.64 -36.21 -0.10 35.42 4 0.4472E+00 0.1577E-01 -0.5000E-02 -0.00 1.00 0.00 1.11 236.21 -0.07 235.66 0.4472E+00 0.1577E-01 0.5000E-02 -0.00 1.00 0.00 1.14 19.67 -0.65 19.16 3 0.0 1 0.5528E+00 0.4226E-02 -0.5000E-02 -0.00 1.00 0.00 1.42 160.64 -0.90 159.95 0.5528E+00 0.4226E-02 0.5000E-02 -0.00 1.00 0.00 1.43 13.84 0.27 13.19 2 0.5528E+00 0.1577E-01 -0.5000E-02 0.00 1.00 0.00 -1.24 186.16 0.26 186.79 0.5528E+00 0.1577E-01 0.5000E-02 0.00 1.00 0.00 -1.23 39.36 -0.92 40.02 3 0.6972E+00 0.4226E-02 -0.5000E-02 -0.00 1.00 0.00 -1.08 123.74 -0.35 124.28 0.6972E+00 0.4226E-02 0.5000E-02 -0.00 1.00 0.00 -1.05 50.54 -0.16 51.08 4 0.6972E+00 0.1577E-01 -0.5000E-02 -0.00 1.00 0.00 0.96 149.46 -0.16 148.98 0.6972E+00 0.1577E-01 0.5000E-02 -0.00 1.00 0.00 0.99 76.26 -0.34 75.78 4 0.0 1 0.8028E+00 0.4226E-02 -0.5000E-02 -0.00 1.00 0.00 0.72 114.48 -0.59 114.13 0.8028E+00 0.4226E-02 0.5000E-02 -0.00 1.00 0.00 0.74 79.33 0.19 78.96 2 0.8028E+00 0.1577E-01 -0.5000E-02 0.00 1.00 0.00 -0.72 120.67 0.19 121.04 0.8028E+00 0.1577E-01 0.5000E-02 0.00 1.00 0.00 -0.71 85.52 -0.59 85.88 3 0.9472E+00 0.4226E-02 -0.5000E-02 -0.00 1.00 0.00 -0.21 99.39 -0.02 99.49 0.9472E+00 0.4226E-02 0.5000E-02 -0.00 1.00 0.00 -0.18 94.54 -0.23 94.63 4 0.9472E+00 0.1577E-01 -0.5000E-02 -0.00 1.00 0.00 0.17 105.46 -0.23 105.38 0.9472E+00 0.1577E-01 0.5000E-02 -0.00 1.00 0.00 0.19 100.61 -0.02 100.52 * END OF STR3 * TOTAL CPU: 00:00:00