Event to Event Analysis
(220_HW12_P2r)
import ema as em
import numpy as np
# import sympy as sp
import matplotlib.pyplot as plt
%config InlineBackend.figure_format = 'svg'
mdl = em.rModel(2,3) # reduced model in 2 dimensions with 3 dofs / node
n = mdl.dnodes
e = mdl.delems
# pre-define element properties for convenience; these can alse be assigned indiviudally.
mdl.material('default', E=1000)
mdl.xsection('default', 1e6, 50)
xt = mdl.xsection('truss', 10, 1)
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., 6.0)
mdl.node('5', 16., -4.)
# elements
mdl.beam('a', n['1'], n['2'], Qpl=[1e6, 120, 120])
mdl.beam('b', n['2'], n['3'], Qpl=[1e6, 120, 120])
mdl.beam('c', n['3'], n['4'], Qpl=[1e6, 120, 120])
mdl.beam('d', n['4'], n['5'], Qpl=[1e6, 180, 180])
mdl.truss('e', n['2'], n['4'], xsec=xt, Qpl=[ 30])
# Fixities
mdl.fix(n['1'], ['x', 'y', 'rz'])
mdl.fix(n['5'], ['x', 'y', 'rz'])
# Loading
n['3'].p['y'] = -30
n['3'].p['x'] = 50
mdl.DOF = mdl.numdofs()
fig, ax = plt.subplots(1,1)
em.plot_structure(mdl, ax)
svg
ee = em.Event2Event(mdl)
ee.run()
ee.lamda
array([0. , 1.26346229, 1.42471482, 1.53116075, 1.70774411,
1.75555556])
ee.Q[-1] # forces at last event
|
$Q_{{}}$ |
| $a_1$ |
0.000000 |
| $a_2$ |
120.000000 |
| $a_3$ |
-82.666667 |
| $b_1$ |
0.000000 |
| $b_2$ |
82.666667 |
| $b_3$ |
120.000000 |
| $c_1$ |
0.000000 |
| $c_2$ |
-120.000000 |
| $c_3$ |
-120.000000 |
| $d_1$ |
0.000000 |
| $d_2$ |
120.000000 |
| $d_3$ |
180.000000 |
| $e_1$ |
30.000000 |
ee.U # displacement vectors at each event
|
0 |
1 |
2 |
3 |
4 |
5 |
| 0 |
0.0 |
-0.016180 |
-0.020235 |
-0.026011 |
-0.054760 |
-0.068836 |
| 1 |
0.0 |
-0.004619 |
-0.005641 |
-0.006943 |
-0.013000 |
-0.016213 |
| 2 |
0.0 |
0.025365 |
0.030523 |
0.039657 |
0.080000 |
0.102720 |
| 3 |
0.0 |
-0.001066 |
-0.001211 |
0.000051 |
0.003645 |
0.005404 |
| 4 |
0.0 |
0.000290 |
0.000409 |
0.000051 |
-0.006000 |
-0.008272 |
