def ex_ball():
h = 0.3
g = 1
n_bounces = 3
T = n_bounces * 2 * np.sqrt(2 * h / g)
rho = 10
nu = 0.3
E = 1000
N_frames = 500
K = 1e-3
dt = K * np.sqrt(rho / E)
N = np.ceil(T / dt).astype(int)
if N < N_frames:
frame_skip = 1
else:
frame_skip = np.floor(N / N_frames).astype(int)
lambda_, mu = proj.calc_lame_parameters(E, nu)
b = np.array((0, -g)) * rho
x, y, simplices, cvs = fvm.load_cvs_mat('ball.mat')
y = y - (4 - h)
t = np.zeros(2)
boundary_mask = np.ones(x.size) == 1
t_mask = ~boundary_mask
points, E_pot, E_kin, E_str, momentum = proj.simulate(x,
y,
simplices,
cvs,
dt,
N,
lambda_,
mu,
b,
t,
rho,
t_mask,
boundary_mask,
y0=0)
E_pot = E_pot * g
np.savez('ball_stuff', *[points, E_pot, E_kin, E_str])
x_all = points[:, :, 0].flatten()
y_all = points[:, :, 1].flatten()
xmax = np.amax(x_all)
xmin = np.amin(x_all)
ymin = np.amin(y_all)
ymax = np.amax(y_all)
limits = np.array(((xmin, xmax), (ymin, ymax)))
proj.make_animation(points,
simplices,
dt, [E_pot, E_kin, E_str],
y0=0,
lims=limits,
frame_skip=frame_skip,
fps=60,
outfile='ball.mp4',
save=True)
def ex_hex():
h = 0.8
T = 10
K = 1e-3
N_frames = 500
E, nu = 1e3, 0.3
rho = 10
lambda_, mu = proj.calc_lame_parameters(E, nu)
dt = K * np.sqrt(rho / E)
N = np.ceil(T / dt).astype(int)
b = np.array((0, -1)) * rho
if N < N_frames:
frame_skip = 1
else:
frame_skip = np.floor(N / N_frames).astype(int)
x = np.array((0, 1, 3 / 2, 1 / 2, 1, 0, -1 / 2)) - (1 / 2)
y = np.array((0, 0, np.sqrt(3) / 2, np.sqrt(3) / 2, np.sqrt(3), np.sqrt(3),
np.sqrt(3) / 2)) + h
simp = Delaunay(np.array((x, y)).T).simplices
cvs = None
y0 = 0
# lims = np.array(((np.amin(x), np.amax(x)), (np.amax(y))))
t = np.zeros(2)
boundary_mask = x != 10
points, E_pot, E_kin, _, _ = proj.simulate(x, y, simp, cvs, dt, N, lambda_,
mu, b, t, rho, boundary_mask,
boundary_mask, y0)
x_all = points[:, :, 0].flatten()
y_all = points[:, :, 1].flatten()
xmax = np.amax(x_all)
xmin = np.amin(x_all)
ymin = np.amin(y_all)
ymax = np.amax(y_all)
limits = np.array(((xmin, xmax), (ymin, ymax)))
proj.make_animation(points,
simp,
dt, [E_pot, E_kin],
y0=y0,
lims=limits,
frame_skip=frame_skip,
fps=60,
outfile='hex3.mp4')
def ex_steel(dt=1, N=10, frameskip=1):
rho = 8100
E = 200e9
nu = 0.3
lambda_, mu = proj.calc_lame_parameters(E, nu)
b = np.zeros(2)
t = 1e-2 * np.array((0, -1)) * rho
x, y, simplices, cvs = fvm.load_cvs_mat('control_volumes2.mat')
points = proj.simulate(x, y, simplices, cvs, dt, N, lambda_, mu, b, t, rho)
np.save('bent', points[-1])
t_mask = x == np.amax(x)
De0, _, _, _ = proj.calc_intial_stuff(x, y, simplices, b, rho, t_mask, t)
fig, ax = plt.subplots()
X, Y = points[-1].T
Pe = proj.calc_Pe(X, Y, simplices, De0, lambda_, mu, True)
ax.triplot(x, y, simplices)
ax.triplot(X, Y, simplices)
fig.tight_layout()
plt.show()
def ex_simple():
rho = 10
E = 1000
nu = 0.3
T = 7
K = 1e-3
dt = K * np.sqrt(rho / E)
N = np.ceil(T / dt).astype(int)
N_frames = 500
if N < N_frames:
frame_skip = 1
else:
frame_skip = np.floor(N / N_frames).astype(int)
lambda_, mu = proj.calc_lame_parameters(E, nu)
b = np.zeros(2)
t = 1e0 * np.array((0, -1)) * rho
x, y, simplices, cvs = fvm.load_cvs_mat('control_volumes2.mat')
# points, E_pot, E_kin, E_str, momentum = proj.simulate(
# x, y, simplices, cvs, dt, N, lambda_, mu, b, t, rho, T_stopt=0.5)
# np.savez('bar_stuff', *[points, E_pot, E_kin, E_str])
points, E_pot, E_kin, E_str = np.load('bar_stuff.npz').values()
x_all = points[:, :, 0].flatten()
y_all = points[:, :, 1].flatten()
xmax = np.amax(x_all)
xmin = np.amin(x_all)
ymin = np.amin(y_all)
ymax = np.amax(y_all)
limits = np.array(((xmin, xmax), (ymin, ymax)))
# fig, ax = plt.subplots()
# x, y = points[-1].T
# ax.triplot(x, y, simplices)
# plt.show()
proj.make_animation(points,
simplices,
dt, [None, E_kin, E_str],
lims=limits,
frame_skip=frame_skip,
fps=60,
outfile='bar.mp4',
save=True)
def ex_debug():
X = np.array((0, 1, 0.5))
Y = np.array((0, 0, np.sqrt(3) / 2))
T = np.array((0, 1, 2)).reshape((1, 3))
I = np.array((X.sum(), Y.sum())) / 3
tris = mesh.all_triangles(T, X, Y)
area = mesh.calc_areas(tris)
a = 1.1
i = a * I
x = a * X
y = a * Y
v = I - i
x = x + v[0]
y = y + v[1]
i = i + v
X2 = X - I[1]
Y2 = Y - I[1]
# lims = np.array(((np.amin(x), np.amax(x)), (np.amin(y), np.amax(y))))
E, nu = 1e3, 0.3
rho = 10
b = np.zeros(2)
t = b
mask = np.zeros(3) == 1
bmask = ~mask
cvs = None
De0inv, m, f_ext, ft = proj.calc_intial_stuff(X, Y, T, b, rho, mask, t)
m = m.reshape((3, 1))
lambda_, mu = proj.calc_lame_parameters(E, nu)
fe = proj.calc_all_fe(x, y, T, cvs, De0inv, lambda_, mu)
k = 1 / 2 * (a * a + 1) * (lambda_ + mu)
T0 = 1
K = 5e-3
dt = K * np.sqrt(rho / E)
N = np.ceil(T0 / dt).astype(int)
v = np.zeros((3, 2))
p = np.array((x, y)).T
points = np.zeros((N, 3, 2))
E_kin = np.zeros(N)
E_pot = np.zeros(N)
E_str = np.zeros(N)
E_kin[0] = proj.calc_kin_energy(m, v)
E_pot[0] = calc_pot_energy_tri(np.array((x[0], y[0])), np.zeros(2), k)
E_pot[0] = proj.calc_pot_energy(m, y)
E_str[0] = proj.calc_strain_energy(x, y, T, De0inv, lambda_, mu, area)
points[0] = p
fes = np.zeros((N, 3, 2))
bar = Bar('Simulating', max=N)
bar.next()
for n in range(1, N):
x, y = points[n - 1].T
fe = proj.calc_all_fe(x, y, T, cvs, De0inv, lambda_, mu)
f_total = fe
fes[n] = f_total
points[n], v = proj.calc_next_time_step(points[n - 1], v, m, f_total,
dt, bmask)
E_kin[n] = proj.calc_kin_energy(m, v)
x, y = points[n].T
E_str[n] = proj.calc_strain_energy(x, y, T, De0inv, lambda_, mu, area)
E_pot[n] = calc_pot_energy_tri(np.array((x[0], y[0])), np.zeros(2), k)
E_pot[n] = proj.calc_pot_energy(m, y)
bar.next()
bar.finish()
N_frames = 500
if N < N_frames:
frame_skip = 1
else:
frame_skip = np.floor(N / N_frames).astype(int)
x_all = points[:, :, 0].flatten()
y_all = points[:, :, 1].flatten()
xmax = np.amax(x_all)
xmin = np.amin(x_all)
ymin = np.amin(y_all)
ymax = np.amax(y_all)
limits = np.array(((xmin, xmax), (ymin, ymax)))
outfile = 'triangle4.mp4'
dpi = 200
fps = 60
padding = 0.2
xlims, ylims = limits
padding = np.array((-padding, padding))
xlims = xlims + padding
ylims = ylims + padding
Times = np.cumsum(dt * np.ones(N))
fig, (ax, ax2) = plt.subplots(nrows=2,
gridspec_kw={'height_ratios': [2, 1]})
ax2.plot(Times, E_kin + E_pot + E_str, label='$E_{total}$')
ax2.plot(Times, E_pot, label='$E_{pot}$')
ax2.plot(Times, E_kin, label='$E_{kin}$')
ax2.plot(Times, E_str, label='$E_{str}$')
ax2.legend()
plt.show()
import fvm
import project as proj
#%%
# Initial mesh
X = np.array((0, 1, 3 / 2, 1 / 2, 1, 0, -1 / 2)) - (1 / 2)
Y = np.array((0, 0, np.sqrt(3) / 2, np.sqrt(3) / 2, np.sqrt(3), np.sqrt(3),
np.sqrt(3) / 2))
T = Delaunay(np.array((X, Y)).T).simplices
points = np.load('bent_hex.npy')
x, y = points[-1].T
y0 = Y[4] - y[4]
y = y + y0
E, nu = 1e3, 0.4
lambda_, mu = proj.calc_lame_parameters(E, nu)
rho = 10
boundary_mask = x != 10
t = np.zeros(0)
b = np.array((0, -1)) * rho
De0inv, m, f_ext, _ = proj.calc_intial_stuff(X, Y, T, b, rho, boundary_mask, t)
fe = proj.calc_all_fe(x, y, T, None, De0inv, lambda_, mu)
Ft = f_ext + fe
for t, e in zip(f_ext, fe):
print(t[1], e[1])
fig, ax = plt.subplots()
ax.triplot(x, y, T)
ax.quiver(x, y, Ft[:, 0], Ft[:, 1], color='r')
#%%