def solids_GUI(compute_strains=False, plot_contours=True):
"""
Run a complete workflow for a Finite Element Analysis
Parameters
----------
compute_strains : Bool (optional)
Boolean variable to compute Strains and Stresses at nodes.
By default it is False.
plot_contours : Bool (optional)
Boolean variable to plot contours of the computed variables.
By default it is True.
Returns
-------
UC : ndarray (nnodes, 2)
Displacements at nodes.
E_nodes : ndarray (nnodes, 3), optional
Strains at nodes. It is returned when `compute_strains` is True.
S_nodes : ndarray (nnodes, 3), optional
Stresses at nodes. It is returned when `compute_strains` is True.
"""
folder = pre.initial_params()
start_time = datetime.now()
echo = False
#%% PRE-PROCESSING
nodes, mats, elements, loads = pre.readin(folder=folder)
if echo:
pre.echomod(nodes, mats, elements, loads, folder=folder)
DME , IBC , neq = ass.DME(nodes, elements)
print("Number of nodes: {}".format(nodes.shape[0]))
print("Number of elements: {}".format(elements.shape[0]))
print("Number of equations: {}".format(neq))
#%% SYSTEM ASSEMBLY
KG = ass.assembler(elements, mats, nodes, neq, DME)
RHSG = ass.loadasem(loads, IBC, neq)
#%% SYSTEM SOLUTION
UG = sol.static_sol(KG, RHSG)
if not(np.allclose(KG.dot(UG)/KG.max(), RHSG/KG.max())):
print("The system is not in equilibrium!")
end_time = datetime.now()
print('Duration for system solution: {}'.format(end_time - start_time))
#%% POST-PROCESSING
start_time = datetime.now()
UC = pos.complete_disp(IBC, nodes, UG)
E_nodes, S_nodes = None, None
if compute_strains:
E_nodes, S_nodes = pos.strain_nodes(nodes , elements, mats, UC)
if plot_contours:
pos.fields_plot(elements, nodes, UC, E_nodes=E_nodes, S_nodes=S_nodes)
end_time = datetime.now()
print('Duration for post processing: {}'.format(end_time - start_time))
print('Analysis terminated successfully!')
return UC, E_nodes, S_nodes if compute_strains else UC
def test_strain_nodes():
"""Tests for strain/stress calculation at nodes"""
# 2 x 2 mesh with axial load and rollers on the sides
mats = np.array([[8 / 3, 1 / 3]])
nodes = np.array([[0, -1, -1], [1, 0, -1], [2, 1, -1], [3, -1, 0],
[4, 0, 0], [5, 1, 0], [6, -1, 1], [7, 0, 1], [8, 1, 1]])
elements = np.array([[0, 1, 0, 0, 1, 4, 3], [1, 1, 0, 1, 2, 5, 4],
[2, 1, 0, 3, 4, 7, 6], [3, 1, 0, 4, 5, 8, 7]])
UC = np.array([[0, 0], [0, 0], [0, 0], [0, 1], [0, 1], [0, 1], [0, 2],
[0, 2], [0, 2]])
E_nodes, S_nodes = pos.strain_nodes(nodes, elements, mats, UC)
E_exact = np.zeros((9, 3))
E_exact[:, 1] = 1
S_exact = np.zeros((9, 3))
S_exact[:, 0] = 1
S_exact[:, 1] = 3
assert np.allclose(E_exact, E_nodes)
assert np.allclose(S_exact, S_nodes)
def solids_GUI(plot_contours=True, compute_strains=False, folder=None):
"""
Run a complete workflow for a Finite Element Analysis
Parameters
----------
plot_contours : Bool (optional)
Boolean variable to plot contours of the computed variables.
By default it is True.
compute_strains : Bool (optional)
Boolean variable to compute Strains and Stresses at nodes.
By default it is False.
folder : string (optional)
String with the path to the input files. If not provided
it would ask for it in a pop-up window.
Returns
-------
UC : ndarray (nnodes, 2)
Displacements at nodes.
E_nodes : ndarray (nnodes, 3), optional
Strains at nodes. It is returned when `compute_strains` is True.
S_nodes : ndarray (nnodes, 3), optional
Stresses at nodes. It is returned when `compute_strains` is True.
"""
if folder is None:
folder = pre.initial_params()
start_time = datetime.now()
echo = False
# Pre-processing
nodes, mats, elements, loads = pre.readin(folder=folder)
if echo:
pre.echomod(nodes, mats, elements, loads, folder=folder)
DME, IBC, neq = ass.DME(nodes, elements)
print("Number of nodes: {}".format(nodes.shape[0]))
print("Number of elements: {}".format(elements.shape[0]))
print("Number of equations: {}".format(neq))
# System assembly
KG = ass.assembler(elements, mats, nodes, neq, DME)
RHSG = ass.loadasem(loads, IBC, neq)
# System solution
UG = sol.static_sol(KG, RHSG)
if not (np.allclose(KG.dot(UG) / KG.max(), RHSG / KG.max())):
print("The system is not in equilibrium!")
end_time = datetime.now()
print('Duration for system solution: {}'.format(end_time - start_time))
# Post-processing
start_time = datetime.now()
UC = pos.complete_disp(IBC, nodes, UG)
E_nodes, S_nodes = None, None
if compute_strains:
E_nodes, S_nodes = pos.strain_nodes(nodes, elements, mats, UC)
if plot_contours:
pos.fields_plot(elements, nodes, UC, E_nodes=E_nodes, S_nodes=S_nodes)
end_time = datetime.now()
print('Duration for post processing: {}'.format(end_time - start_time))
print('Analysis terminated successfully!')
return (UC, E_nodes, S_nodes) if compute_strains else UC
t2=time.time()
print("system solution ", t2-t1)
end_time = dt.now()
#print('Duration for system solution: {}'.format(end_time - start_time))
# Post-processing
start_time = dt.now()
UC = pos.complete_disp(IBC, nodes, UG) # uc are x and y displacements
#UC2 = pos.complete_disp(IBC, nodes, UG2) # uc are x and y displacements
E_nodes, S_nodes = None, None
if compute_strains:
E_nodes, S_nodes = pos.strain_nodes(nodes, elements, mats, UC)
#E_nodes2,S_nodes2=pos.strain_nodes(nodes, elements, mats, UC2)
if plot_contours:
pos.fields_plot(elements, nodes, UC, E_nodes=E_nodes, S_nodes=S_nodes) # some matplotlib internal function to make it look smoother
end_time = dt.now()
# calculation of principal stresses
## are signes importnatn here???
# chek this and others
## https://wp.optics.arizona.edu/optomech/wp-content/uploads/sites/53/2016/10/OPTI_222_W21.pdf
sig_x=S_nodes[:,0]
sig_y=S_nodes[:,1]
tau_xy=S_nodes[:,2]
def solids_auto(data, plot_contours=True, compute_strains=False):
"""
Run a complete workflow for a Finite Element Analysis
Parameters
----------
data : dict
Simulation data composed of nodes, constrains, elements,
materials and loads.
plot_contours : Bool (optional)
Boolean variable to plot contours of the computed variables.
By default it is True.
compute_strains : Bool (optional)
Boolean variable to compute Strains and Stresses at nodes.
By default it is False.
Returns
-------
UC : ndarray (nnodes, 2)
Displacements at nodes.
E_nodes : ndarray (nnodes, 3), optional
Strains at nodes. It is returned when `compute_strains` is True.
S_nodes : ndarray (nnodes, 3), optional
Stresses at nodes. It is returned when `compute_strains` is True.
"""
# Retrieving data
nodes = data["nodes"]
cons = data["cons"]
elements = data["elements"]
mats = data["mats"]
loads = data["loads"]
# Pre-processing
assem_op, bc_array, neq = ass.DME(cons, elements)
print("Number of nodes: {}".format(nodes.shape[0]))
print("Number of elements: {}".format(elements.shape[0]))
print("Number of equations: {}".format(neq))
# System assembly
stiff_mat, _ = ass.assembler(elements, mats, nodes, neq, assem_op)
rhs_vec = ass.loadasem(loads, bc_array, neq)
# System solution
start_time = datetime.now()
disp = sol.static_sol(stiff_mat, rhs_vec)
if not np.allclose(
stiff_mat.dot(disp) / stiff_mat.max(), rhs_vec / stiff_mat.max()):
print("The system is not in equilibrium!")
end_time = datetime.now()
print('Duration for system solution: {}'.format(end_time - start_time))
# Post-processing
start_time = datetime.now()
disp_complete = pos.complete_disp(bc_array, nodes, disp)
strain_nodes, stress_nodes = None, None
if compute_strains:
strain_nodes, stress_nodes = pos.strain_nodes(nodes, elements, mats,
disp_complete)
if plot_contours:
pos.fields_plot(elements,
nodes,
disp_complete,
E_nodes=strain_nodes,
S_nodes=stress_nodes)
end_time = datetime.now()
print('Duration for post processing: {}'.format(end_time - start_time))
print('Analysis terminated successfully!')
if compute_strains:
return (disp_complete, strain_nodes, stress_nodes)
else:
return disp_complete
def solids_GUI(plot_contours=True, compute_strains=False, folder=None):
"""
Run a complete workflow for a Finite Element Analysis
Parameters
----------
plot_contours : Bool (optional)
Boolean variable to plot contours of the computed variables.
By default it is True.
compute_strains : Bool (optional)
Boolean variable to compute Strains and Stresses at nodes.
By default it is False.
folder : string (optional)
String with the path to the input files. If not provided
it would ask for it in a pop-up window.
Returns
-------
UC : ndarray (nnodes, 2)
Displacements at nodes.
E_nodes : ndarray (nnodes, 3), optional
Strains at nodes. It is returned when `compute_strains` is True.
S_nodes : ndarray (nnodes, 3), optional
Stresses at nodes. It is returned when `compute_strains` is True.
"""
if folder is None:
folder = pre.initial_params()
start_time = datetime.now()
echo = False
# Pre-processing
nodes, mats, elements, loads = pre.readin(folder=folder)
if echo:
pre.echomod(nodes, mats, elements, loads, folder=folder)
assem_op, bc_array, neq = ass.DME(nodes[:, -2:], elements)
print("Number of nodes: {}".format(nodes.shape[0]))
print("Number of elements: {}".format(elements.shape[0]))
print("Number of equations: {}".format(neq))
# System assembly
stiff_mat, _ = ass.assembler(elements, mats, nodes[:, :3], neq, assem_op)
rhs_vec = ass.loadasem(loads, bc_array, neq)
# System solution
disp = sol.static_sol(stiff_mat, rhs_vec)
if not np.allclose(
stiff_mat.dot(disp) / stiff_mat.max(), rhs_vec / stiff_mat.max()):
print("The system is not in equilibrium!")
end_time = datetime.now()
print('Duration for system solution: {}'.format(end_time - start_time))
# Post-processing
start_time = datetime.now()
disp_complete = pos.complete_disp(bc_array, nodes, disp)
strain_nodes, stress_nodes = None, None
if compute_strains:
strain_nodes, stress_nodes = pos.strain_nodes(nodes, elements, mats,
disp_complete)
if plot_contours:
pos.fields_plot(elements,
nodes,
disp_complete,
E_nodes=strain_nodes,
S_nodes=stress_nodes)
end_time = datetime.now()
print('Duration for post processing: {}'.format(end_time - start_time))
print('Analysis terminated successfully!')
if compute_strains:
return (disp_complete, strain_nodes, stress_nodes)
else:
return disp_complete
UG_sol, rx = custom_solver(
KG, RHSG, mask_area, verbose=True
) #solver with constratinst to zero translation and zero rotation
#UG=UG_sol[0]
#UG = sol.static_sol(KG, RHSG,nodes) #no constraints
#UG1,rx = sol.static_sol_cond(KG1, RHSG,mask_area) #solver with constratinst to zero translation and zero rotation
#norm1=np.sqrt(np.sum((RHSG-np.dot(KG.toarray(),UG[0]))**2)) # same norm as returned by sparse solver
#norm2=np.sqrt(np.sum((RHSG-np.dot(KG1,UG1[0]))**2))# same norm as returned by sparse solver
if not (np.allclose(KG.dot(UG_sol) / KG.max(), RHSG / KG.max())):
print("The system is not in equilibrium!")
UC = pos.complete_disp(IBC, nodes, UG_sol) # uc are x and y displacements
E_nodes, S_nodes = pos.strain_nodes(nodes, elements, mats,
UC) # stresses and strains
stress_tensor = calculate_stress_tensor(
S_nodes, nodes, dims=mask_area.shape) # assembling the stress tensor
#pos.fields_plot(elements, nodes, UC, E_nodes=E_nodes, S_nodes=S_nodes)
#####
# average shear and normal stress on the colony area
avg_shear, avg_normal_stress = calculate_mean_stress_measure(
mask_area, stress_tensor, ps_new)
### other possible stress measures, just for a nice picture
sigma_max, sigma_min, tau_max, phi_n, phi_shear, sigma_avg = all_stress_measures(
S_nodes, nodes, dims=mask_area.shape)
sigma_max_abs = np.maximum(
np.abs(sigma_min),
np.abs(sigma_max)) ### highest possible norm of the stress tensor