Kinematics
import ema as em
import matplotlib.pyplot as plt
import numpy as np
import sympy as sp
%config InlineBackend.figure_format = 'svg'
import scipy.linalg as la
mdl = em.Model(2,3)
n = mdl.dnodes
e = mdl.delems
mdl.node('1', 0.0, 0.0)
mdl.node('2', 0.0, 5.0)
mdl.node('3', 4.0, 5.0)
mdl.node('4', 8.0, 5.0)
mdl.node('5', 8.0, 0.0)
mdl.node('6', 8.0, 10.)
mdl.beam('a', n['1'], n['2'])
mdl.beam('b', n['2'], n['3'])
mdl.beam('c', n['3'], n['4'])
mdl.truss('d', n['4'], n['5'])
mdl.beam('e', n['4'], n['6'])
mdl.hinge(e['a'], n['1'])
mdl.hinge(e['c'], n['3'])
mdl.hinge(e['e'], n['6'])
mdl.fix(n['1'], ['x','y','rz'])
mdl.fix(n['5'], ['x','y','rz'])
mdl.fix(n['6'], ['x','y','rz'])
mdl.numDOF()
em.analysis.characterize(mdl)
m = 1
s = 2
fig, ax = plt.subplots()
em.plot_structure(mdl, ax)
svg
|
$1$ |
$2$ |
$3$ |
$4$ |
$5$ |
$6$ |
$7$ |
$8$ |
$9$ |
| $a_1$ |
0.0 |
1.00 |
0.0 |
0.0 |
0.00 |
0.0 |
0.0 |
0.00 |
0.0 |
| $a_2$ |
0.2 |
-0.00 |
0.0 |
0.0 |
0.00 |
0.0 |
0.0 |
0.00 |
0.0 |
| $a_3$ |
0.2 |
-0.00 |
1.0 |
0.0 |
0.00 |
0.0 |
0.0 |
0.00 |
0.0 |
| $b_1$ |
-1.0 |
-0.00 |
0.0 |
1.0 |
0.00 |
0.0 |
0.0 |
0.00 |
0.0 |
| $b_2$ |
-0.0 |
0.25 |
1.0 |
0.0 |
-0.25 |
0.0 |
0.0 |
0.00 |
0.0 |
| $b_3$ |
-0.0 |
0.25 |
0.0 |
0.0 |
-0.25 |
1.0 |
0.0 |
0.00 |
0.0 |
| $c_1$ |
0.0 |
0.00 |
0.0 |
-1.0 |
-0.00 |
0.0 |
1.0 |
0.00 |
0.0 |
| $c_2$ |
0.0 |
0.00 |
0.0 |
-0.0 |
0.25 |
1.0 |
0.0 |
-0.25 |
0.0 |
| $c_3$ |
0.0 |
0.00 |
0.0 |
-0.0 |
0.25 |
0.0 |
0.0 |
-0.25 |
1.0 |
| $d_1$ |
0.0 |
0.00 |
0.0 |
0.0 |
0.00 |
0.0 |
-0.0 |
1.00 |
0.0 |
| $e_1$ |
0.0 |
0.00 |
0.0 |
0.0 |
0.00 |
0.0 |
-0.0 |
-1.00 |
0.0 |
| $e_2$ |
0.0 |
0.00 |
0.0 |
0.0 |
0.00 |
0.0 |
-0.2 |
0.00 |
1.0 |
| $e_3$ |
0.0 |
0.00 |
0.0 |
0.0 |
0.00 |
0.0 |
-0.2 |
0.00 |
0.0 |
ker = A.c.ker
ker = ker.round(6)/ker[0]
ker
|
$1$ |
| $1$ |
1.000001 |
| $2$ |
-0.000000 |
| $3$ |
-0.200000 |
| $4$ |
1.000001 |
| $5$ |
-0.799999 |
| $6$ |
-0.200000 |
| $7$ |
1.000001 |
| $8$ |
0.000000 |
| $9$ |
0.200000 |
em.plot_U(mdl, ker, ax, scale=1)
svg
