Obsah
Triangles, BEAM4S1
Problem
Mesh
| element | type | nodes |
|---|---|---|
| 1 | 4 | 1 3 2 12 13 11 |
| 2 | 4 | 3 4 2 15 14 13 |
| 3 | 4 | 3 5 4 16 17 15 |
| 4 | 4 | 5 6 4 19 18 17 |
| 5 | 4 | 5 7 6 20 21 19 |
| 6 | 4 | 7 8 6 23 22 21 |
| 7 | 4 | 7 9 8 24 25 23 |
| 8 | 4 | 9 10 8 27 26 25 |
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 $$q_n|_\text{S2}=\frac{l_y}{0.01}=-0.01\times10^6\text{ Pa},$$ where the normal surface traction $q_n$ acts on the top areas $0.25\times0.01\text{ m}^2$ (face S2) of elements 2, 4, 6 and 8.
The computation is executed with the following commands:
- beam4s1.bat
rmd2 beam4s1.i1 rpd2 beam4s1.i2 srh2 beam4s1.i3 fefs beam4s1.i4 str2 beam4s1.i5
Input
- beam4s1.i1
; NELEM NNOD ITED ... KSS IP 8 27 4 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 1:8 N =P 1 3 2 =P =Q 12 13 11 =Q =R 3 4 2 =R =S 15 14 13 =S =2P =4Q =2R =4S =4P =8Q =4R =8S =6P =12Q =6R =12S EN EN
- beam4s1.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 8 S1 /S 2 E 2 4 6 8 S2 EN EN
- beam4s1.i3
; KREST IP 1 EN EN
- beam4s1.i4
; KREST IP 1 EN EN
- beam4s1.i5
; KLC 0 KOUT ILC ... KPROB KGRAF IP 1 0 1 0 6*0 0 2 EN EN
Output
- beam4s1.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 -0.2992859E-05 3 0.2047806E-04 -0.1311764E-02 4 0.2295466E-03 -0.1314745E-02 5 0.8479629E-04 -0.4687553E-02 6 0.4152325E-03 -0.4690540E-02 7 0.1819172E-03 -0.9169225E-02 8 0.5681155E-03 -0.9172217E-02 9 0.3000179E-03 -0.1408448E-01 10 0.7000149E-03 -0.1408748E-01 11 0.0000000E+00 -0.8698878E-06 12 0.1004158E-04 -0.3292840E-03 13 0.6250914E-04 -0.3301623E-03 14 0.1149862E-03 -0.3322954E-03 15 0.1250124E-03 -0.1312759E-02 16 0.5247234E-04 -0.2810052E-02 17 0.1875117E-03 -0.2811192E-02 18 0.3225487E-03 -0.2813061E-02 19 0.2500144E-03 -0.4688781E-02 20 0.1332408E-03 -0.6841294E-02 21 0.3125136E-03 -0.6842630E-02 22 0.4917839E-03 -0.6844301E-02 23 0.3750164E-03 -0.9170617E-02 24 0.2409022E-03 -0.1160532E-01 25 0.4375164E-03 -0.1160678E-01 26 0.6341261E-03 -0.1160833E-01 27 0.5000166E-03 -0.1408594E-01 REACTIONS NODE RX RY [N] [N] 1 0.1652952E+03 0.1200000E+03 2 -0.6834705E+04 0.0000000E+00 11 -0.1333059E+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 0.50000E-01 0.40000E-02 49.6 -0.1 -1.0 0.0 2 0.15000E+00 0.40000E-02 50.1 -0.1 0.3 0.0 3 0.50000E-01 0.12000E-01 116.7 0.0 -1.0 0.0 4 0.83333E-01 0.66667E-02 72.1 -0.1 -0.6 0.0 2 1 0.20000E+00 0.80000E-02 82.6 -2.2 -1.0 0.0 2 0.20000E+00 0.16000E-01 150.6 2.3 -0.9 0.0 3 0.10000E+00 0.16000E-01 150.4 -0.1 0.3 0.0 4 0.16667E+00 0.13333E-01 127.9 -0.0 -0.5 0.0 3 1 0.30000E+00 0.40000E-02 71.4 2.3 -0.8 0.0 2 0.40000E+00 0.40000E-02 71.1 -0.1 0.3 0.0 3 0.30000E+00 0.12000E-01 109.0 -2.2 -0.8 0.0 4 0.33333E+00 0.66667E-02 83.8 0.0 -0.4 0.0 4 1 0.45000E+00 0.80000E-02 89.8 -1.7 -0.7 0.0 2 0.45000E+00 0.16000E-01 129.4 1.7 -0.7 0.0 3 0.35000E+00 0.16000E-01 129.3 -0.1 0.2 0.0 4 0.41667E+00 0.13333E-01 116.2 -0.0 -0.4 0.0 5 1 0.55000E+00 0.40000E-02 87.0 1.7 -0.5 0.0 2 0.65000E+00 0.40000E-02 86.7 -0.1 0.2 0.0 3 0.55000E+00 0.12000E-01 104.0 -1.7 -0.6 0.0 4 0.58333E+00 0.66667E-02 92.6 0.0 -0.3 0.0 6 1 0.70000E+00 0.80000E-02 95.2 -1.1 -0.5 0.0 2 0.70000E+00 0.16000E-01 113.6 1.1 -0.5 0.0 3 0.60000E+00 0.16000E-01 113.5 -0.1 0.2 0.0 4 0.66667E+00 0.13333E-01 107.4 -0.0 -0.3 0.0 7 1 0.80000E+00 0.40000E-02 96.9 1.1 -0.3 0.0 2 0.90000E+00 0.40000E-02 96.8 -0.0 0.1 0.0 3 0.80000E+00 0.12000E-01 100.8 -1.1 -0.3 0.0 4 0.83333E+00 0.66667E-02 98.2 0.0 -0.2 0.0 8 1 0.95000E+00 0.80000E-02 98.9 0.0 -0.3 0.0 2 0.95000E+00 0.16000E-01 103.2 0.0 -0.3 0.0 3 0.85000E+00 0.16000E-01 103.4 -0.0 0.1 0.0 4 0.91667E+00 0.13333E-01 101.8 -0.0 -0.1 0.0 * END OF STR3 * TOTAL CPU: 00:00:00