Kinematics - Kernel Analysis
import ema as em
import matplotlib.pyplot as plt
import numpy as np
%config InlineBackend.figure_format = 'svg' # used to make plots look nicerbb
mdl = em.Model(2,3)
n = mdl.dnodes
e = mdl.delems
mdl.node('1', 0.0, 0.0)
mdl.node('2', 8.0, 0.0)
mdl.node('3', 8.0, 6.0)
mdl.node('4', 16.0, 6.0)
mdl.beam('a', n['1'], n['2'])
mdl.beam('b', n['2'], n['3'])
mdl.beam('c', n['3'], n['4'])
mdl.hinge(e['a'], n['1'])
mdl.hinge(e['b'], n['3'])
mdl.fix(n['1'], ['x', 'y', 'rz'])
mdl.fix(n['4'], ['y'])
mdl.numDOF()
[[9, 10, 11], [1, 2, 3], [4, 5, 6], [7, 12, 8]]
em.analysis.characterize(mdl)
m = 1
s = 0
fig, ax = plt.subplots(1,1)
em.plot_structure(mdl, ax)
svg
|
$1$ |
$2$ |
$3$ |
$4$ |
$5$ |
$6$ |
$7$ |
$8$ |
| $a_1$ |
1.000000 |
0.000 |
0.0 |
0.000000 |
0.000 |
0.0 |
0.0 |
0.0 |
| $a_2$ |
0.000000 |
-0.125 |
0.0 |
0.000000 |
0.000 |
0.0 |
0.0 |
0.0 |
| $a_3$ |
0.000000 |
-0.125 |
1.0 |
0.000000 |
0.000 |
0.0 |
0.0 |
0.0 |
| $b_1$ |
-0.000000 |
-1.000 |
0.0 |
0.000000 |
1.000 |
0.0 |
0.0 |
0.0 |
| $b_2$ |
-0.166667 |
0.000 |
1.0 |
0.166667 |
-0.000 |
0.0 |
0.0 |
0.0 |
| $b_3$ |
-0.166667 |
0.000 |
0.0 |
0.166667 |
-0.000 |
1.0 |
0.0 |
0.0 |
| $c_1$ |
0.000000 |
0.000 |
0.0 |
-1.000000 |
-0.000 |
0.0 |
1.0 |
0.0 |
| $c_2$ |
0.000000 |
0.000 |
0.0 |
-0.000000 |
0.125 |
1.0 |
0.0 |
0.0 |
| $c_3$ |
0.000000 |
0.000 |
0.0 |
-0.000000 |
0.125 |
0.0 |
0.0 |
1.0 |
A_cm = A.c.ker / -0.561490
A_cm
|
$1$ |
| $1$ |
-0.000 |
| $2$ |
1.000 |
| $3$ |
0.125 |
| $4$ |
-0.750 |
| $5$ |
1.000 |
| $6$ |
-0.125 |
| $7$ |
-0.750 |
| $8$ |
-0.125 |
em.plot_U(mdl, A_cm, ax, scale=1)
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4
5
6
7
8
svg
