np.set_printoptions(precision=5)
# Results from Abaqus
abaqus_data = pickle.load(open('neutral_line.p', 'rb'))
# Beam properties
bp = properties()
bc = boundary_conditions(load=np.array([
[0, -1],
]))
EB_solution = bc.concentrated_load[0][1]/(6*bp.young*bp.inertia) * \
np.array([0, 0, 3, -1])
mesh = mesh_1D(mesh_n=11, alpha=[1, 1], alpha_nodes=[0, 1])
curve_parent = poly(a=[0, 0, 0, 0])
curve_child = poly(a=EB_solution)
beam = structure(curve_parent, curve_child, mesh, bp, bc)
beam.calculate_position()
eulerBernoulle = beam.r_c
# Find stable solution
bounds = np.array(((-0.02, 0.02), (-0.02, 0.02)))
x, fun = beam.find_stable(beam.g_c.a[2:4],
bounds=bounds,
input_type='Geometry',
loading_condition='plane_stress',
input_function=input_function)
beam.g_c.a = input_function(x)
from aeropy.geometry.parametric import poly, frame
import matplotlib.pyplot as plt
import matplotlib.cm as cm
from matplotlib.colors import Normalize
import numpy as np
curve = poly()
z1 = np.linspace(0, 1)
z2 = curve.z2(z1)
colors = ['r', 'g', 'k', 'b', 'm']
plt.figure()
plt.plot(z1, z2, label='geometry')
r1 = curve.r(z1, diff=[0, 1, 0, 0])
r2 = curve.r(z1, diff=[0, 0, 1, 0])
plt.plot(r1[0], r1[1], label='a1')
plt.plot(r2[0], r2[1], label='a2')
z1 = np.linspace(.1, 1, 6)
i = 0
x1 = curve.x1(z1)
for x2 in np.linspace(-.3, .3, 5):
g1 = curve.g(1, z1, x2)
g2 = curve.g(2, z1, x2)
r = curve.r(z1, x2)
Q = plt.quiver(r[0],
r[1],
g1[0],
g1[1],
coefficients = np.array([0, 0, 0, 0])
beam_properties = properties()
bc = boundary_conditions(load=np.array([
[0, 0],
]))
analytical_solution = bc.concentrated_load[0][0] / (beam_properties.young *
beam_properties.area)
mesh = mesh_1D(alpha=[
1 + analytical_solution, 1 + analytical_solution, 1 + analytical_solution
],
alpha_nodes=[0, .5, 1],
mesh_n=10)
curve_parent = poly(coefficients)
curve_child = poly(coefficients)
beam = structure(curve_parent, curve_child, mesh, beam_properties, bc)
strain = beam.strain()
stress = beam.stress()
n = 10
problem = DOE(levels=n, driver='Full Factorial')
problem.add_variable('a1', lower=0, upper=.001, type=float)
problem.add_variable('a2', lower=0, upper=.001, type=float)
problem.define_points()
print(problem.domain)
strain_matrix = np.array(
list(zip(problem.domain['a1'], problem.domain['a2'],
)))
abq_x, abq_y, abq_u1, abq_u2 = abaqus_data.T
abq_y = -abq_y + .005
abq_u2 = -abq_u2
# Convert log strains into engineering strain
abaqus_secondary['LE11'] = np.exp(np.array(abaqus_secondary['LE11'])) - 1
abaqus_secondary['LE12'] = np.exp(np.array(abaqus_secondary['LE12'])) - 1
abaqus_secondary['LE22'] = np.exp(np.array(abaqus_secondary['LE22'])) - 1
coefficients = np.array([0, 0, 0, 0])
bp = properties()
bc = boundary_conditions(load=np.array([[0, -1]]))
analytical_solution = bc.concentrated_load[0][1]/(6*bp.young*bp.inertia) * \
np.array([-1, 3, 0, 0])
mesh = mesh_1D(mesh_n=10)
curve_parent = poly(a=[0, 0, 0, 0])
curve_child = poly(a=analytical_solution)
beam = structure(curve_parent, curve_child, mesh, bp, bc)
beam.calculate_position()
strain = beam.strain()
stress = beam.stress(loading_condition='plane_stress')
# Plot beam results
plt.figure()
u = beam.u()
u1 = beam.u(diff='x1')
u2 = beam.u(diff='x2')
plt.plot(beam.r_p[0], beam.r_p[1], label='parent')
plt.scatter(beam.r_p[0], beam.r_p[1], label='parent')
plt.plot(beam.r_c[0], beam.r_c[1], label='child')
def __init__(self, curve=poly(), frame='Frenet-Serret',
z1=np.linspace(0, 1, 11)):
self.curve = poly()
self.frame = frame
self.z1 = z1
self.z2 = self.curve.z2(z1)
x2 = 0
b = 0.01
h = 0.01
P = 10000
L = 1
E = 70e9
Area = h * b
Inertia = b * h**3 / 12.
# For Euler Bernouille
# a = P/(6*E*Inertia)*np.array([-1, 3*L, 0, 0])
# For axial deformation
a = np.array([0, 0, 0, 0])
alpha = [1 + P / Area / E]
curve_parent = poly(a, config='parent')
curve_child = poly(a, alpha, config='child')
r_p = curve_parent.r(x1, x2)
r_c = curve_child.r(x1, x2)
beam = structure(curve_parent, curve_child, area=Area, young=E, load=P)
u = beam.u(x1)
strain = beam.strain(x1)
stress = beam.stress()
# print('strain', strain)
# print('target', beam.load/beam.area/beam.young)
#
# plt.figure()
# plt.plot(r_p[0], r_p[1], label='parent', color='r')
# plt.plot(r_c[0], r_c[1], label='child', color='b')
# Q = plt.quiver(r_p[0], r_p[1], u[0], u[1], angles='xy', scale_units='xy',
# scale=1, width=0.005, color='0.5')