def solve(self):
"""Solve problem"""
self.updateGeometry()
self.updateMesh()
self.ep = [self.ptype, self.t]
self.D = cfc.hooke(self.ptype, self.E, self.v)
cfu.info("Assembling system matrix...")
nDofs = np.size(self.dofs)
ex, ey = cfc.coordxtr(self.edof, self.coords, self.dofs)
K = np.zeros([nDofs, nDofs])
for eltopo, elx, ely in zip(self.edof, ex, ey):
Ke = cfc.planqe(elx, ely, self.ep, self.D)
cfc.assem(eltopo, K, Ke)
cfu.info("Solving equation system...")
f = np.zeros([nDofs, 1])
bc = np.array([], 'i')
bcVal = np.array([], 'i')
bc, bcVal = cfu.applybc(self.bdofs, bc, bcVal, 5, 0.0, 0)
cfu.applyforce(self.bdofs, f, 7, 10e5, 1)
self.a, self.r = cfc.solveq(K, f, bc, bcVal)
cfu.info("Computing element forces...")
ed = cfc.extractEldisp(self.edof, self.a)
self.vonMises = []
# For each element:
for i in range(self.edof.shape[0]):
# Determine element stresses and strains in the element.
es, et = cfc.planqs(ex[i, :], ey[i, :], self.ep, self.D, ed[i, :])
# Calc and append effective stress to list.
self.vonMises.append(
sqrt(
pow(es[0], 2) - es[0] * es[1] + pow(es[1], 2) + 3 * es[2]))
def step(K, C, a, bc, bcval, dt, T, Tnr):
"""
Compute the capacity matrix C for a 2D-element with 3 nodes.
Parameters:
K = Stiffness matrix
C = Capacity matrix
a = Stress distrubution at time t=0
bc = Nodes with prescribed values
bcval = Prescribed nodal values
dt = Time increment size
Tvec = Vector containing times for which the stress distrubution should be displayed
Returns:
avec Excess pore water pressure at given times (Tvec) in all nodes, dim(avec)= ndof x Tvec
"""
n = int(T / dt)
ndt = np.floor(T / dt / Tnr)
Tvec = np.arange(ndt, n, ndt)
Tvec = np.append(Tvec, n)
theta = 1
avec = a
Kt = K
Ct = C
for i in range(n):
Kt = Ct + dt * Kt
f = (Ct + (1 - theta) * Kt) * a
a, r = cfc.solveq(Kt, f, bc)
if (i + 1) in Tvec:
avec = np.hstack((avec, a))
return avec, Tvec
for eltopo, elx, ely in zip(edof, ex, ey):
Ke = cfc.planqe(elx, ely, ep, D)
cfc.assem(eltopo, K, Ke)
bc = np.array([], 'i')
bcVal = np.array([], 'f')
bc, bcVal = cfu.applybc(bdofs, bc, bcVal, left_support, 0.0, 0)
bc, bcVal = cfu.applybc(bdofs, bc, bcVal, right_support, 0.0, 2)
f = np.zeros([nDofs, 1])
cfu.applyforcetotal(bdofs, f, top_line, -10e5, 2)
a, r = cfc.solveq(K, f, bc, bcVal)
ed = cfc.extractEldisp(edof, a)
vonMises = []
for i in range(edof.shape[0]):
es, et = cfc.planqs(ex[i, :], ey[i, :], ep, D, ed[i, :])
vonMises.append(
sqrt(pow(es[0], 2) - es[0] * es[1] + pow(es[1], 2) + 3 * es[2]))
# ----- Draw geometry
cfv.drawGeometry(g)
# ----- Draw the mesh.
else:
if numElementNodes == 3:
# core version of plante /tri3el
K_el, f_el = cfc.plante(ex[iel], ey[iel], ep, Dmat, eq)
# Transpose so correct dim for assem
f_el = f_el.T
elif numElementNodes == 4:
# Number of intergration points. 1, 2 or 3
n = 2
ep = np.array([ep[0], ep[1], n])
K_el, f_el = cfc.plani4e(ex[iel], ey[iel], ep, Dmat, eq)
f_el = f_el.T
cfc.assem(eldofs[iel], K, K_el, R, f_el)
r, R0 = cfc.solveq(K, R, bc)
nodMiddle = numNodesY//2 + 1 # Mid nod on right edge
xC = r[-(nodMiddle*2), 0] # 2 dofs per node, so this is the middle dof on end
# 2 dofs per node, so this is the middle dof on end
yC = r[-(nodMiddle*2)+1, 0]
print("Element: ", numElementNodes)
print(
"Displacement center node right end, x:{:12.3e} y:{:12.3e}".format(xC, yC))
# Sum uf reaction forces
R0Sum = np.zeros(2, 'f')
for i in range(0, (numNodesY*2), 2):
R0Sum[0] += R0[i, 0]
R0Sum[1] += R0[i+1, 0]
# from Ddict and depends on which region (which marker) the element is in.
Ke = cfc.flw2i8e(elx, ely, ep, Ddict[elMarker])
cfc.assem(eltopo, K, Ke)
print("Solving equation system...")
f = np.zeros([n_dofs, 1])
bc = np.array([], 'i')
bc_val = np.array([], 'i')
bc, bc_val = cfu.applybc(bdofs, bc, bc_val, 2, 30.0)
bc, bc_val = cfu.applybc(bdofs, bc, bc_val, 3, 0.0)
a, r = cfc.solveq(K, f, bc, bc_val)
# ---- Compute element forces -----------------------------------------------
print("Computing element forces...")
ed = cfc.extractEldisp(edof, a)
for i in range(np.shape(ex)[0]):
es, et, eci = cfc.flw2i8s(
ex[i, :], ey[i, :], ep, Ddict[elementmarkers[i]], ed[i, :])
# Do something with es, et, eci here.
# ---- Visualise results ----------------------------------------------------
ey = np.array([[2., 2.], [0., 0.], [2., 2.], [0., 0.], [0., 2.], [0., 2.],
[0., 2.], [0., 2.], [2., 0.], [2., 0.]])
# ----- Create element stiffness matrices Ke and assemble into K -
for elx, ely, eltopo in zip(ex, ey, Edof):
Ke = cfc.bar2e(elx, ely, ep)
cfc.assem(eltopo, K, Ke)
print("Stiffness matrix K:")
print(K)
# ----- Solve the system of equations ----------------------------
bc = np.array([1, 2, 3, 4])
a, r = cfc.solveq(K, f, bc)
print("Displacements a:")
print(a)
print("Reaction forces r:")
print(r)
# ----- Element forces -------------------------------------------
ed = cfc.extractEldisp(Edof, a)
N = np.zeros([Edof.shape[0]])
print("Element forces:")
i = 0
def solve(self):
"""Löser ett system av kontinuerliga balkar"""
# Kontrollera att vi har materialegenskaper
E = 2.1e9
A = 0.1 * 0.1
I = 0.1 * (0.1**3) / 12
if self.properties == None:
self.properties = []
for i in enumerate(self.segments):
self.properties.append([E, A, I])
# Beräkna antal element och frihetsgrader
self.n_dofs = 0
self.n_elements = 0
for n in self.segments:
self.n_dofs += n * 3
self.n_elements += n
self.n_dofs += 3
# Global styvhetsmatris och lastvektor
K = np.zeros((self.n_dofs, self.n_dofs), float)
f = np.zeros((self.n_dofs, 1), float)
# Elementtopologimatris. Varje rad representerar
# ett element och dess frihetsgradskopplingar.
edof = np.zeros((self.n_elements, 6), int)
# Elementkoordinatsmatriser. Varje rad
# anger koordinaterna för varje element
ex = np.zeros((self.n_elements, 2), float)
ey = np.zeros((self.n_elements, 2), float)
# Elementegenskapsmatris. Anger elementegenskaperna
# för varje element.
ep = np.zeros((self.n_elements, 3), float)
# Elementlastvektor. Anger elementlasten för varje
# element.
eq = np.zeros((self.n_elements, 2), float)
# X-koordinat för varje beräkningspunkt.
self.x = np.zeros((self.n_elements + 1), float)
# Assemblera styvhetsmatrisen
dof = 1 # Räknare för frihetsgrader
el = 0 # Elementräknare
self.support_dofs = [] # Randvillkor för varje upplag
x = 0.0 # Aktuell x-koordinat för element
for l, n, q, p in zip(self.lengths, self.segments, self.loads,
self.properties):
l_n = l / n
self.support_dofs.append([dof, dof + 1, dof + 2])
for i in range(n):
# Tilldela elementkoordinater
ex[el, :] = [x, x + l_n]
ey[el, :] = [0.0, 0.0]
ep[el, :] = p
eq[el, :] = [0.0, q]
x += l_n
# Beräkna element styvhet
Ke, fe = cfc.beam2e(ex[el, :], ey[el, :], ep[el, :], eq[el, :])
# Tilldela elementtopologi
etopo = np.array(
[dof, dof + 1, dof + 2, dof + 3, dof + 4, dof + 5])
dof += 3
# Assemblera in element i global styvhetsmatris
cfc.assem(etopo, K, Ke, f, fe)
edof[el, :] = etopo
el += 1
# Lägg till randvillkor för sista upplaget
self.support_dofs.append([dof, dof + 1, dof + 2])
# Tillämpa randvillkor
bc_prescr = []
bc_val = []
for dofs, support in zip(self.support_dofs, self.supports):
if support == BeamModel.FIXED_Y:
bc_prescr.append(dofs[1])
bc_val.append(0.0)
elif support == BeamModel.FIXED_XY:
bc_prescr.append(dofs[0])
bc_val.append(0.0)
bc_prescr.append(dofs[1])
bc_val.append(0.0)
elif support == BeamModel.FIXED_XYR:
bc_prescr.append(dofs[0])
bc_val.append(0.0)
bc_prescr.append(dofs[1])
bc_val.append(0.0)
bc_prescr.append(dofs[2])
bc_val.append(0.0)
# Lösning av ekvationssystem
a, _ = cfc.solveq(K, f, np.asarray(bc_prescr), np.asarray(bc_val))
# Tilldela resultatvariabler
self.y_displ = a[1::3]
self.x_displ = a[0::3]
self.rot = a[2::3]
# Beräkna inre krafter och förskjutningar
ed = cfc.extractEldisp(edof, a)
# Skapa matris för de inre krafterna
self.NVM = np.zeros((self.y_displ.shape[0], 3), float)
# Beräkna elementkrafter
i = 0
for el_displ, el_x, el_y, el_ep, el_eq in zip(ed, ex, ey, ep, eq):
es = cfc.beam2s(el_x, el_y, el_ep, el_displ, el_eq)
self.NVM[i, :] = es[0][0]
self.x[i] = el_x[0]
i += 1
# Sista positionen måste också tilldelas
self.NVM[i, :] = es[0][1]
self.x[i] = el_x[1]
ep = np.array([E, A, I])
ex = np.array([0., 3.])
ey = np.array([0., 0.])
Ke = cfc.beam2e(ex, ey, ep)
print(Ke)
# ----- Assemble Ke into K ---------------------------------------
K = cfc.assem(Edof, K, Ke)
# ----- Solve the system of equations and compute support forces -
bc = np.array([1, 2, 11])
(a, r) = cfc.solveq(K, f, bc)
# ----- Section forces -------------------------------------------
Ed = cfc.extractEldisp(Edof, a)
es1, ed1, ec1 = cfc.beam2s(ex, ey, ep, Ed[0, :], nep=10)
es2, ed2, ec2 = cfc.beam2s(ex, ey, ep, Ed[1, :], nep=10)
es3, ed3, ec3 = cfc.beam2s(ex, ey, ep, Ed[2, :], nep=10)
# ----- Results --------------------------------------------------
print("a=")
print(a)
print("r=")
print(r)
# ----- Generate FE-mesh -----
#clf; eldraw2(Ex,Ey,[1 3 0],Edof(:,1));
#disp('PRESS ENTER TO CONTINUE'); pause; clf;
# ----- Create and assemble element matrices -----
for i in range(8):
Ke = cfc.flw2qe(Ex[i], Ey[i], ep, D)
K = cfc.assem(Edof[i], K, Ke)
# ----- Solve equation system -----
bcPrescr = np.array([1, 2, 3, 4, 7, 10, 13, 14, 15])
bcVal = np.array([0, 0, 0, 0, 0, 0, 0.5e-3, 1e-3, 1e-3])
a, r = cfc.solveq(K, f, bcPrescr, bcVal)
# ----- Compute element flux vector -----
Ed = cfc.extractEldisp(Edof, a)
Es = np.zeros((8, 2))
for i in range(8):
Es[i], Et = cfc.flw2qs(Ex[i], Ey[i], ep, D, Ed[i])
# ----- Draw flux vectors and contourlines -----
print(Ex)
print(Ey)
cfv.eldraw2_mpl(Ex, Ey, [1, 2, 1], range(1, Ex.shape[0] + 1))
cfv.eliso2_mpl(Ex, Ey, Ed)
def execute(self):
# ------ Transfer model variables to local variables
self.inputData.updateparams()
version = self.inputData.version
units = self.inputData.units
v = self.inputData.v
ep = self.inputData.ep
E = self.inputData.E
mp = self.inputData.mp
fp = self.inputData.fp
bp = self.inputData.bp
ep[1] = ep[1] * U2SI[units][0]
E = E * U2SI[units][2]
for i in range(len(fp[0])):
fp[1][i] = fp[1][i] * U2SI[units][1]
for i in range(len(bp[0])):
bp[1][i] = bp[1][i] * U2SI[units][0]
# Get most updated dxf dimensions and import model geometry to calfem format
self.inputData.dxf.readDXF(self.inputData.dxf_filename)
for dim in self.inputData.d:
("Adjusting Dimension {0} with val {1}".format(
dim[0], dim[1] * U2SI[units][0]))
self.inputData.dxf.adjustDimension(dim[0], dim[1] * U2SI[units][0])
self.inputData.dxf.adjustDimension(
self.inputData.c['aName'], self.inputData.c['a'] * U2SI[units][0])
self.inputData.dxf.adjustDimension(
self.inputData.c['bName'], self.inputData.c['b'] * U2SI[units][0])
dxf = self.inputData.dxf
if self.inputData.refineMesh:
geometry, curve_dict = dxf.convertToGeometry(max_el_size=mp[2])
else:
geometry, curve_dict = dxf.convertToGeometry()
# Generate the mesh
meshGen = cfm.GmshMeshGenerator(geometry)
meshGen.elSizeFactor = mp[2] # Max Area for elements
meshGen.elType = mp[0]
meshGen.dofsPerNode = mp[1]
meshGen.returnBoundaryElements = True
coords, edof, dofs, bdofs, elementmarkers, boundaryElements = meshGen.create(
)
# Add the force loads and boundary conditions
bc = np.array([], int)
bcVal = np.array([], int)
nDofs = np.size(dofs)
f = np.zeros([nDofs, 1])
for i in range(len(bp[0])):
bc, bcVal = cfu.applybc(bdofs, bc, bcVal, dxf.markers[bp[0][i]],
bp[1][i])
for i in range(len(fp[0])):
xforce = fp[1][i] * np.cos(np.radians(fp[2][i]))
yforce = fp[1][i] * np.sin(np.radians(fp[2][i]))
cfu.applyforce(bdofs,
f,
dxf.markers[fp[0][i]],
xforce,
dimension=1)
cfu.applyforce(bdofs,
f,
dxf.markers[fp[0][i]],
yforce,
dimension=2)
# ------ Calculate the solution
print("")
print("Solving the equation system...")
# Define the elements coordinates
ex, ey = cfc.coordxtr(edof, coords, dofs)
# Define the D and K matrices
D = (E / (1 - v**2)) * np.matrix([[1, v, 0], [v, 1, 0],
[0, 0, (1 - v) / 2]])
K = np.zeros([nDofs, nDofs])
# Extract element coordinates and topology for each element
for eltopo, elx, ely in zip(edof, ex, ey):
Ke = cfc.plante(elx, ely, ep, D)
cfc.assem(eltopo, K, Ke)
# Solve the system
a, r = cfc.solveq(K, f, bc, bcVal)
# ------ Determine stresses and displacements
print("Computing the element forces")
# Extract element displacements
ed = cfc.extractEldisp(edof, a)
# Determine max displacement
max_disp = [[0, 0], 0] # [node idx, value]
for idx, node in zip(range(len(ed)), ed):
for i in range(3):
disp = math.sqrt(node[2 * i]**2 + node[2 * i + 1]**2)
if disp > max_disp[1]:
max_disp = [[idx, 2 * i], disp]
# Determine Von Mises stresses
vonMises = []
max_vm = [0, 0] # [node idx, value]
for i in range(edof.shape[0]):
es, et = cfc.plants(ex[i, :], ey[i, :], ep, D, ed[i, :])
try:
vonMises.append(
math.sqrt(
pow(es[0, 0], 2) - es[0, 0] * es[0, 1] +
pow(es[0, 1], 2) + 3 * es[0, 2]))
if vonMises[-1] > max_vm[1]:
max_vm = [i, vonMises[-1]]
except ValueError:
vonMises.append(0)
print("CAUGHT MATH EXCEPTION with es = {0}".format(es))
# Note: es = [sigx sigy tauxy]
# ------ Store the solution in the output model variables
self.outputData.disp = ed
self.outputData.stress = vonMises
self.outputData.geometry = geometry
self.outputData.a = a
self.outputData.coords = coords
self.outputData.edof = edof
self.outputData.mp = mp
self.outputData.meshGen = meshGen
self.outputData.statistics = [
max_vm, max_disp, curve_dict, self.inputData.dxf.anchor,
self.inputData.dxf.wh
]
if self.inputData.paramFilename is None:
print("Solution completed.")
def execute(self):
# --- Överför modell variabler till lokala referenser
ep = self.inputData.ep
E = self.inputData.E
v = self.inputData.v
Elementsize = self.inputData.Elementsize
# --- Anropa InputData för en geomtetribeskrivning
geometry = self.inputData.geometry()
# --- Nätgenerering
elType = 3 # <-- Fyrnodselement flw2i4e
dofsPerNode = 2
meshGen = cfm.GmshMeshGenerator(geometry)
meshGen.elSizeFactor = Elementsize # <-- Anger max area för element
meshGen.elType = elType
meshGen.dofsPerNode = dofsPerNode
meshGen.returnBoundaryElements = True
coords, edof, dof, bdofs, elementmarkers, boundaryElements = meshGen.create(
)
self.outputData.topo = meshGen.topo
#Solver
bc = np.array([], 'i')
bcVal = np.array([], 'i')
D = cfc.hooke(1, E, v)
nDofs = np.size(dof)
ex, ey = cfc.coordxtr(edof, coords, dof) #Coordinates
K = np.zeros([nDofs, nDofs])
#Append Boundary Conds
f = np.zeros([nDofs, 1])
bc, bcVal = cfu.applybc(bdofs, bc, bcVal, 30, 0.0, 0)
cfu.applyforce(bdofs, f, 20, 100e3, 1)
qs_array = []
qt_array = []
for x, y, z in zip(ex, ey, edof):
Ke = cfc.planqe(x, y, ep, D)
cfc.assem(z, K, Ke)
asolve, r = cfc.solveq(K, f, bc, bcVal)
ed = cfc.extractEldisp(edof, asolve)
for x, y, z in zip(ex, ey, ed):
qs, qt = cfc.planqs(x, y, ep, D, z)
qs_array.append(qs)
qt_array.append(qt)
vonMises = []
stresses1 = []
stresses2 = []
# For each element:
for i in range(edof.shape[0]):
# Determine element stresses and strains in the element.
es, et = cfc.planqs(ex[i, :], ey[i, :], ep, D, ed[i, :])
# Calc and append effective stress to list.
vonMises.append(
np.sqrt(
pow(es[0], 2) - es[0] * es[1] + pow(es[1], 2) + 3 * es[2]))
## es: [sigx sigy tauxy]
# sigmaij = np.array([[es(i,1),es(i,3),0],[es(i,3),es(i,2),0],[0,0,0]])
sigmaij = np.array([[es[0], es[2], 0], [es[2], es[1], 0],
[0, 0, 0]])
[v, w] = np.linalg.eig(sigmaij)
stresses1.append(v[0] * w[0])
stresses2.append(v[1] * w[1])
# --- Överför modell variabler till lokala referenser
self.outputData.vonMises = vonMises
self.outputData.edof = edof
self.outputData.coords = coords
self.outputData.stresses1 = stresses1
self.outputData.stresses2 = stresses2
self.outputData.geometry = geometry
self.outputData.asolve = asolve
self.outputData.r = r
self.outputData.ed = ed
self.outputData.qs = qs_array
self.outputData.qt = qt_array
self.outputData.dofsPerNode = dofsPerNode
self.outputData.elType = elType
self.outputData.calcDone = True
