Kinematics 3
import ema as em
import numpy as np
import sympy as sp
import matplotlib.pyplot as plt
%config InlineBackend.figure_format = 'svg'
#Remove
mdl = em.Model(2,3)
n = mdl.dnodes
e = mdl.delems
mdl.node('1', 0.0, 0.0)
mdl.node('2', 6.0, 0.0)
mdl.node('3', 10., 0.0)
mdl.node('4', 6.0, 6.0)
mdl.node('5', 10., 6.0)
mdl.node('6', 6.0, 10.)
mdl.beam('a', n['1'], n['2'])
mdl.beam('b', n['2'], n['3'])
mdl.beam('c', n['2'], n['4'])
mdl.beam('d', n['4'], n['5'])
mdl.beam('e', n['4'], n['6'])
mdl.hinge(e['a'], n['1'])
mdl.hinge(e['b'], n['2'])
mdl.hinge(e['b'], n['3'])
mdl.hinge(e['c'], n['4'])
mdl.fix(n['1'], ['x', 'y', 'rz'])
mdl.fix(n['3'], ['x','y','rz'])
mdl.fix(n['5'], ['y'])
mdl.fix(n['6'], ['x'])
mdl.numDOF()
em.analysis.characterize(mdl)
mdl.DOF
m = 1
s = 2
[[11, 12, 13], [1, 2, 3], [14, 15, 16], [4, 5, 6], [7, 17, 8], [18, 9, 10]]
#Remove
fig, ax = plt.subplots(1,1)
em.plot_structure(mdl, ax)
svg
# Matrices
B = em.B_matrix(mdl)
A = em.A_matrix(mdl)
# Vectors
Q = em.column_vector(B)
V = em.V_vector(A)
3 Find \(A_{cm}\)
ker = A.c.ker
A_cm = ker/ ker[5]
A_cm
|
$1$ |
| $1$ |
0.000000 |
| $2$ |
-4.000000 |
| $3$ |
-0.666667 |
| $4$ |
4.000000 |
| $5$ |
-4.000000 |
| $6$ |
1.000000 |
| $7$ |
4.000000 |
| $8$ |
1.000000 |
| $9$ |
-4.000000 |
| $10$ |
1.000000 |
em.plot_U(mdl, ker, ax, scale=1)
svg
Part 4
|
$1$ |
| $a_1$ |
0.000000e+00 |
| $a_2$ |
6.666667e-01 |
| $a_3$ |
0.000000e+00 |
| $b_1$ |
0.000000e+00 |
| $b_2$ |
-1.666667e+00 |
| $b_3$ |
-1.000000e+00 |
| $c_1$ |
0.000000e+00 |
| $c_2$ |
0.000000e+00 |
| $c_3$ |
1.666667e+00 |
| $d_1$ |
1.000000e-14 |
| $d_2$ |
-1.000000e-14 |
| $d_3$ |
0.000000e+00 |
| $e_1$ |
0.000000e+00 |
| $e_2$ |
-1.000000e-14 |
| $e_3$ |
0.000000e+00 |
