Quadrilaterals, BEAM6S1
Problem
Mesh
| element | type | nodes |
|---|---|---|
| 1 | 6 | 1 3 4 2 12 14 13 11 |
| 2 | 6 | 3 5 6 4 15 17 16 14 |
| 3 | 6 | 5 7 8 6 18 20 19 17 |
| 4 | 6 | 7 9 10 8 21 23 22 20 |
Boundary conditions
$u=0$ at nodes 2, 11
$u=v=0$ at node 1
Computation
The end force is replaced with the equivalent surface traction $$\begin{align} q_x&=\frac{20000}{0.01\times0.02}=100\times10^6\text{ Pa}, \\ q_y&=-0.1\times10^6\text{ Pa}. \end{align}$$ Similarly, the distributed loading is replaced with $$q_n|_\text{S3}=\frac{l_y}{0.01}=-0.01\times10^6\text{ Pa},$$ where the normal surface traction $q_n$ acts on the top areas $0.25\times0.01\text{ m}^2$ (face S3) of elements.
The computation is executed with the following commands:
- beam6s1.bat
rmd2 beam6s1.i1 rpd2 beam6s1.i2 srh2 beam6s1.i3 fefs beam6s1.i4 str2 beam6s1.i5
Input
- beam6s1.i1
; NELEM NNOD ITED ... KSS IP 4 23 6 6*0 -1 ; 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) EL E 1:4 N =A 1 3 4 2 =A =B 12 14 13 11 =B =2A =3B =4A =6B =6A =9B EN EN
- beam6s1.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 SV 2 T 6 V -0.01e6 ; ly = -100 N/m AS 1 /M 1 /B 0 N 1 /B 0 C 1 N 2 11 /S 1 E 4 S2 /S 2 E 1:4 S3 EN EN
- beam6s1.i3
; KREST IP 1 EN EN
- beam6s1.i4
; KREST IP 1 EN EN
- beam6s1.i5
; KLC 0 KOUT ILC ... KPROB KGRAF IP 1 0 1 0 6*0 0 2 EN EN
Output
- beam6s1.o5
; KLC 0 KOUT ILC ... KPROB KGRAF IP 1 0 1 0 6*0 0 2 EN EN PLANE STRESS 1TH LOAD CASE DISPLACEMENTS NODE U V [m] [m] 1 0.0000000E+00 0.0000000E+00 2 0.0000000E+00 -0.3019974E-05 3 0.2038337E-04 -0.1317942E-02 4 0.2296356E-03 -0.1320945E-02 5 0.8460987E-04 -0.4701293E-02 6 0.4154152E-03 -0.4704294E-02 7 0.1818417E-03 -0.9189014E-02 8 0.5681875E-03 -0.9192015E-02 9 0.3000180E-03 -0.1410675E-01 10 0.7000150E-03 -0.1410975E-01 11 0.0000000E+00 -0.8181496E-06 12 0.9690531E-05 -0.3320718E-03 13 0.1153345E-03 -0.3350697E-03 14 0.1250095E-03 -0.1318934E-02 15 0.5208838E-04 -0.2819743E-02 16 0.3229360E-03 -0.2822743E-02 17 0.2500126E-03 -0.4702546E-02 18 0.1329441E-03 -0.6858423E-02 19 0.4920834E-03 -0.6861423E-02 20 0.3750146E-03 -0.9190425E-02 21 0.2407731E-03 -0.1162660E-01 22 0.6342581E-03 -0.1162960E-01 23 0.5000165E-03 -0.1410823E-01 REACTIONS NODE RX RY [N] [N] 1 0.1710232E+03 0.1200000E+03 2 -0.6828977E+04 0.0000000E+00 11 -0.1334205E+05 0.0000000E+00 EQUILIBRIUM OF FORCES AND REACTIONS SUM OF FORCES [N] SUM OF REACTIONS [N] DIR. X: 20000.00 -20000.00 DIR. Y: -120.00 120.00 STRESSES AT GAUSS POINTS IE IGP XG YG SIG-X SIG-Y SIG-XY SIG-Z [m] [m] [MPa] [MPa] [MPa] [MPa] 1 1 0.52831E-01 0.42265E-02 51.3 0.4 -0.6 0.0 2 0.19717E+00 0.42265E-02 51.7 -1.8 -0.5 0.0 3 0.52831E-01 0.15774E-01 148.7 -0.5 -0.6 0.0 4 0.19717E+00 0.15774E-01 148.3 1.9 -0.5 0.0 2 1 0.30283E+00 0.42265E-02 72.1 2.1 -0.4 0.0 2 0.44717E+00 0.42265E-02 71.9 -1.4 -0.4 0.0 3 0.30283E+00 0.15774E-01 127.9 -2.1 -0.4 0.0 4 0.44717E+00 0.15774E-01 128.1 1.4 -0.4 0.0 3 1 0.55283E+00 0.42265E-02 87.2 1.1 -0.3 0.0 2 0.69717E+00 0.42265E-02 87.2 -1.0 -0.3 0.0 3 0.55283E+00 0.15774E-01 112.8 -1.1 -0.3 0.0 4 0.69717E+00 0.15774E-01 112.8 1.0 -0.3 0.0 4 1 0.80283E+00 0.42265E-02 96.9 0.8 -0.2 0.0 2 0.94717E+00 0.42265E-02 97.0 -0.2 -0.1 0.0 3 0.80283E+00 0.15774E-01 103.1 -0.8 -0.2 0.0 4 0.94717E+00 0.15774E-01 103.0 0.2 -0.1 0.0 * END OF STR3 * TOTAL CPU: 00:00:00