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pendulo_duplo.py
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pendulo_duplo.py
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# -*- coding: utf-8 -*-
"""
Created on Thu Oct 7 07:00:49 2021
@author: lbaru
"""
from nachbagauer3Dc import beamANCF3Dquadratic, node
from materialsc import linearElasticMaterial
from bodiesc import flexibleBody
import numpy as np
from matplotlib.pyplot import plot
np.seterr('raise')
'''
TESTE DOS ELEMENTOS EM PÊNDULO DUPLO
'''
steel = linearElasticMaterial('Steel', 207e6, 0.3, 7.85e3)
penA = flexibleBody('Pêndulo A', steel)
penB = flexibleBody('Pêndulo B', steel)
LpenA = 400.0e-3
LpenB = 400.0e-3
altura = 20.0e-3
largura = 30.0e-3
g = [0, 0, -9.810]
nel = 2
nodesA = [0]*(nel*3-1)*4
nodesB = [0]*(nel*3-1)*4
for i in range(nel+1):
nodesA[i] = node([LpenA * i/nel, 0.0, 0.0,
0.0, 1.0, 0.0,
0.0, 0.0, 1.0])
nodesB[i] = node([LpenA + LpenB * i/nel, 0.0, 0.0,
0.0, 1.0, 0.0,
0.0, 0.0, 1.0])
elemA = [0]*nel
elemB = [0]*nel
for i in range(nel):
elemA[i] = beamANCF3Dquadratic(nodesA[i], nodesA[i+1], altura, largura)
elemB[i] = beamANCF3Dquadratic(nodesB[i], nodesB[i+1], altura, largura)
penA.addElement(elemA)
penB.addElement(elemB)
# número total de graus de liberdade nodais
gdlA = penA.totalDof
gdlB = penB.totalDof
gdls = gdlA + gdlB
'''RESTRIÇÕES'''
'COM O SOLO'
pin1 = [0, 1]
'ENTRE BARRAS'
# x em A x em B y em A y em B
pin2 = [[gdlA-4, gdlA], [gdlA-3, gdlA+1]]
'MATRIZ DE RESTRIÇÕES'
Phi = np.zeros([len(pin1)+len(pin2), gdls])
phiLine = 0
for rdof in pin1:
Phi[phiLine, rdof] = 1
phiLine += 1
for rdof in pin2:
Phi[phiLine, rdof[0]] = 1
Phi[phiLine, rdof[1]] = -1
phiLine += 1
'''SOLVER'''
finalTime = 1.0
h = 2.5e-5 # timestep
t = [0]
# LHS matrix
lhs = np.zeros([2*gdls+Phi.shape[0], 2*gdls+Phi.shape[0]])
MA = penA.assembleMassMatrix()
MB = penB.assembleMassMatrix()
In = np.eye(gdls)
lhs[0:gdlA, 0:gdlA] = MA
lhs[gdlA:gdls, gdlA:gdls] = MB
lhs[0:gdls, 2*gdls:] = -h*Phi.T
lhs[gdls:2*gdls, 0:gdls] = -h * In
lhs[gdls:2*gdls, gdls:2*gdls] = In
lhs[2*gdls:, gdls:2*gdls] = Phi
lhsInv = np.linalg.inv(lhs)
''' CONDIÇÕES INICIAIS '''
z = [np.zeros([2*gdls+len(pin1)+len(pin2)])]
outFlag = 0
rhs = np.zeros([2*gdls+len(pin1)+len(pin2)])
jac = np.array([0.]*gdls)
CA = 0.00 * penA.assembleTangentStiffnessMatrix()
CB = 0.00 * penB.assembleTangentStiffnessMatrix()
WA = penA.assembleWeightVector(g)
WB = penB.assembleWeightVector(g)
print('##\nStarting simulation for {} s with timestep {} s\n##'.format(finalTime, h))
def getForces(body):
return (-body.assembleElasticForceVector().A1)
while t[-1] < finalTime:
# Prediction step
rhs = 0.0 * rhs
jac[0:gdlA] = getForces(penA) + WA + np.dot(CA, z[-1][0:gdlA])
jac[gdlA:gdls] = getForces(penB) + WB + np.dot(CB, z[-1][gdlA:gdls])
rhs[0:gdlA] = np.dot(MA, z[-1][0:gdlA]) + jac[0:gdlA] * h
rhs[gdlA:gdls] = np.dot(MB, z[-1][gdlA:gdls]) + jac[gdlA:gdls] * h
rhs[gdls:2*gdls] = z[-1][gdls:2*gdls]
zPred = np.dot(lhsInv, rhs)
# update nodal positions
xA = zPred[gdls:gdls+gdlA]
xB = zPred[gdls+gdlA:2*gdls]
penA.updateDisplacements(xA)
penB.updateDisplacements(xB)
# Correction step
jac[0:gdlA] = 0.5 * (jac[0:gdlA] + getForces(penA) +
WA + np.dot(CA, z[-1][0:gdlA]))
jac[gdlA:gdls] = 0.5 * \
(jac[gdlA:gdls] + getForces(penB) + WB + np.dot(CB, z[-1][gdlA:gdls]))
rhs[0:gdlA] = np.dot(MA, z[-1][0:gdlA]) + jac[0:gdlA] * h
rhs[gdlA:gdls] = np.dot(MB, z[-1][gdlA:gdls]) + jac[gdlA:gdls] * h
z.append(np.dot(lhsInv, rhs))
xA = z[-1][gdls:gdls+gdlA]
xB = z[-1][gdls+gdlA:2*gdls]
penA.updateDisplacements(xA)
penB.updateDisplacements(xB)
t.append(t[-1] + h)
outFlag += 1
if outFlag == 100:
print('{0:1.6f}'.format(t[-1]))
# penA.plotPositions(show=True)
# penB.plotPositions(show=True)
outFlag = 0
z = np.asmatrix(z)
vA = z[:, 0:gdlA]
vB = z[:, gdlA:gdls]
qA = z[:, gdls:gdls+gdlA]
qB = z[:, gdls+gdlA:2*gdls]
f = z[:, 2*gdls:]