def scatter(DME, UG, ne, neq, elements):
"""Scatter the nodal displacements vector `UG` over each element
Parameters
----------
DME : ndarray (int)
Array that shows the connectivity of degrees of freedom.
UG : ndarray (float)
Array with the computed displacements.
ne : int
Number of elements.
neq : int
Number of equations (degrees of freedom).
elements : ndarray (int)
Array with the node number for the nodes that correspond to each
element.
Returns
-------
UU : ndarray (float)
Array with the displacements. This one contains both, the
computed and imposed values.
"""
iet = elements[0, 1]
ndof, nnodes, ngpts = fe.eletype(iet)
UU = np.zeros([ne, ndof], dtype=np.float)
for i in range(ne):
for ii in range(ndof):
kk = DME[i, ii]
if kk != -1:
UU[i, ii] = UG[kk]
return UU
def eleDisp(Up, iet, dme, i):
"""
This function find displacements of element i. Returns 1D array
with x, y and rotation displacements values in each node.
Parameters
----------
Up : Displacement al time t + dtaT (not converged).
iet : Element i type
dme : Assembly operator that indicates degrees of freedom correspondence of the element.
i : Element indicator
"""
ndof, nnodes, ngpts = fem.eletype(iet)
ele_disp = np.zeros((ndof,))
#
for j in range (ndof):
ID_dof = dme[j]
if ID_dof == -1:
ele_disp[j] = 0.0
else:
ele_disp[j] = Up[ID_dof]
# End if
#End for
return ele_disp
def scatter(DME, UG, ne, neq, elements):
"""Scatter the nodal displacements vector `UG` over each element
Parameters
----------
DME : ndarray (int)
Array that shows the connectivity of degrees of freedom.
UG : ndarray (float)
Array with the computed displacements.
ne : int
Number of elements.
neq : int
Number of equations (degrees of freedom).
elements : ndarray (int)
Array with the node number for the nodes that correspond to each
element.
Returns
-------
UU : ndarray (float)
Array with the displacements. This one contains both, the
computed and imposed values.
"""
iet = elements[0, 1]
ndof, nnodes, ngpts = fe.eletype(iet)
UU = np.zeros([ne, ndof], dtype=np.float)
for i in range(ne):
for ii in range(ndof):
kk = DME[i, ii]
if kk != -1:
UU[i, ii] = UG[kk]
return UU
def strainGLO(IELCON, UU, ne, COORD, elements):
"""Compute the strain solution for all the elements
Computes the strain solution for all the elements
in the domain and the physical coordinates of the complete
domain integration points. It then assembles all the element strains
into a global strains vector EG[].
Parameters
----------
IELCON : ndarray (int)
Array with the nodes numbers for each element.
UU : ndarray (float)
Array with the displacements. This one contains both, the
computed and imposed values.
ne : int
Number of elements.
COORD : ndarray (float).
Array with nodes coordinates.
elements : ndarray (int)
Array with the node number for the nodes that correspond to each
element.
Returns
-------
EG : ndarray (float)
Array that contains the strain solution for each integration
point in physical coordinates.
XS : ndarray (float)
Array with the coordinates of the integration points.
"""
iet = elements[0, 1]
ndof, nnodes, ngpts = fe.eletype(iet)
XS = np.zeros([ngpts * ne, 2], dtype=np.float)
elcoor = np.zeros([nnodes, 2], dtype=np.float)
EG = np.zeros([ngpts * ne, 3], dtype=np.float)
ul = np.zeros([ndof], dtype=np.float)
for i in range(ne):
for j in range(nnodes):
elcoor[j, 0] = COORD[IELCON[i, j], 0]
elcoor[j, 1] = COORD[IELCON[i, j], 1]
for j in range(ndof):
ul[j] = UU[i, j]
if iet == 1:
epsG, xl = fe.str_el4(elcoor, ul)
elif iet == 2:
epsG, xl = fe.str_el6(elcoor, ul)
elif iet == 3:
epsG, xl = fe.str_el3(elcoor, ul)
for j in range(ngpts):
XS[ngpts * i + j, 0] = xl[j, 0]
XS[ngpts * i + j, 1] = xl[j, 1]
for k in range(3):
EG[ngpts * i + j, k] = epsG[j, k]
return EG, XS
def strainGLO(IELCON, UU, ne, COORD, elements):
"""Compute the strain solution for all the elements
Computes the strain solution for all the elements
in the domain and the physical coordinates of the complete
domain integration points. It then assembles all the element strains
into a global strains vector EG[].
Parameters
----------
IELCON : ndarray (int)
Array with the nodes numbers for each element.
UU : ndarray (float)
Array with the displacements. This one contains both, the
computed and imposed values.
ne : int
Number of elements.
COORD : ndarray (float).
Array with nodes coordinates.
elements : ndarray (int)
Array with the node number for the nodes that correspond to each
element.
Returns
-------
EG : ndarray (float)
Array that contains the strain solution for each integration
point in physical coordinates.
XS : ndarray (float)
Array with the coordinates of the integration points.
"""
iet = elements[0, 1]
ndof, nnodes, ngpts = fe.eletype(iet)
XS = np.zeros([ngpts*ne, 2], dtype=np.float)
elcoor = np.zeros([nnodes, 2], dtype=np.float)
EG = np.zeros([ngpts*ne, 3], dtype=np.float)
ul = np.zeros([ndof], dtype=np.float)
for i in range(ne):
for j in range(nnodes):
elcoor[j, 0] = COORD[IELCON[i, j], 0]
elcoor[j, 1] = COORD[IELCON[i, j], 1]
for j in range(ndof):
ul[j] = UU[i, j]
if iet == 1:
epsG, xl = fe.str_el4(elcoor, ul)
elif iet == 2:
epsG, xl = fe.str_el6(elcoor, ul)
elif iet == 3:
epsG, xl = fe.str_el3(elcoor, ul)
for j in range(ngpts):
XS[ngpts*i + j, 0] = xl[j, 0]
XS[ngpts*i + j, 1] = xl[j, 1]
for k in range(3):
EG[ngpts*i + j, k] = epsG[j, k]
return EG, XS
def retriever(elements , mats , nodes , i, uel=None):
"""Computes the elemental stiffness matrix of element i
Parameters
----------
elements : ndarray
Array with the number for the nodes in each element.
mats : ndarray.
Array with the material profiles.
nodes : ndarray.
Array with the nodal numbers and coordinates.
i : int.
Identifier of the element to be assembled.
Returns
-------
kloc : ndarray (float)
Array with the local stiffness matrix.
ndof : int.
Number of degrees of fredom of the current element.
"""
IELCON = np.zeros([9], dtype=np.integer)
iet = elements[i, 1]
ndof, nnodes, ngpts = fem.eletype(iet)
elcoor = np.zeros([nnodes, 2])
im = np.int(elements[i, 2])
par0, par1 = mats[im, :]
for j in range(nnodes):
IELCON[j] = elements[i, j+3]
elcoor[j, 0] = nodes[IELCON[j], 1]
elcoor[j, 1] = nodes[IELCON[j], 2]
if uel is None:
if iet == 1:
kloc = ue.uel4nquad(elcoor, par1, par0)
elif iet == 2:
kloc = ue.uel6ntrian(elcoor, par1, par0)
elif iet == 3:
kloc = ue.uel3ntrian(elcoor, par1, par0)
elif iet == 5:
kloc = ue.uelspring(elcoor, par1, par0)
elif iet == 6:
kloc = ue.ueltruss2D(elcoor, par1, par0)
elif iet == 7:
kloc = ue.uelbeam2DU(elcoor, par1, par0)
else:
kloc, ndof, iet = uel(elcoor, par1, par0)
return kloc, ndof, iet
def DME(nodes, elements):
"""Counts active equations, creates BCs array IBC[]
and the assembly operator DME[]
Parameters
----------
nodes : ndarray.
Array with the nodal numbers and coordinates.
elements : ndarray
Array with the number for the nodes in each element.
Returns
-------
DME : ndarray (int)
Assembly operator.
IBC : ndarray (int)
Boundary conditions array.
neq : int
Number of active equations in the system.
"""
nels = elements.shape[0]
IELCON = np.zeros([nels, 9], dtype=np.integer)
DME = np.zeros([nels, 18], dtype=np.integer)
neq, IBC = eqcounter(nodes)
for i in range(nels):
iet = elements[i, 1]
ndof, nnodes, ngpts = fem.eletype(iet)
for j in range(nnodes):
IELCON[i, j] = elements[i, j+3]
kk = IELCON[i, j]
for l in range(2):
DME[i, 2*j+l] = IBC[kk, l]
return DME , IBC , neq
def DME(IBC, ne, elements):
"""Create the assembly operator
Create the assembly operator DME and processes the element
connectivity array IELCON
Parameters
----------
IBC : ndarray
Array that maps the nodes with number of equations.
ne : int
Number of elements.
elements : ndarray
Array with the number for the nodes in each element.
Returns
-------
DME : ndarray (int)
Assembly operator.
IELCON : ndarray (int)
Element connectivity.
"""
IELCON = np.zeros([ne, 9], dtype=np.integer)
DME = np.zeros([ne, 18], dtype=np.integer)
for i in range(ne):
iet = elements[i, 1]
ndof, nnodes, ngpts = fem.eletype(iet)
for j in range(nnodes):
IELCON[i, j] = elements[i, j + 3]
kk = IELCON[i, j]
for l in range(2):
DME[i, 2 * j + l] = IBC[kk, l]
return DME, IELCON
def DME(IBC, ne, elements):
"""Create the assembly operator
Create the assembly operator DME and processes the element
connectivity array IELCON
Parameters
----------
IBC : ndarray
Array that maps the nodes with number of equations.
ne : int
Number of elements.
elements : ndarray
Array with the number for the nodes in each element.
Returns
-------
DME : ndarray (int)
Assembly operator.
IELCON : ndarray (int)
Element connectivity.
"""
IELCON = np.zeros([ne, 9], dtype=np.integer)
DME = np.zeros([ne, 18], dtype=np.integer)
for i in range(ne):
iet = elements[i, 1]
ndof, nnodes, ngpts = fem.eletype(iet)
for j in range(nnodes):
IELCON[i, j] = elements[i, j+3]
kk = IELCON[i, j]
for l in range(2):
DME[i, 2*j+l] = IBC[kk, l]
return DME, IELCON
def readin(folder):
"""Read the input files"""
inipar = np.loadtxt(folder + '01_Inipar.txt', ndmin=2, usecols=(0), skiprows=6)
nodes = np.loadtxt(folder + '03_Nodes.txt' , ndmin=2, skiprows=3)
loads = np.loadtxt(folder + '05_Nodal_loads.txt' , ndmin=2, skiprows=3)
#
# -------------------------------------------------------------------------------------
# Read constraints file and identify if there is any diaphfragm or constraint
const = np.loadtxt(folder + '07_DOF_Constraints.txt' , ndmin=2, skiprows=9)
DPH_flag = 0
CST_flag = 0
#
if len(const) != 0:
if max(const[:,1]) >= 0:
DPH_flag = 1
if min(const[:,1]) < 0:
CST_flag = 1
# End if
#End if
const = list(const)
const.insert(0,CST_flag)
const.insert(0,DPH_flag)
#
# -------------------------------------------------------------------------------------
#
NLSTA = int(inipar[5,0])
NLDYNA = int(inipar[6,0])
#
if (NLSTA == 1) and (NLDYNA == 0):
Seismo_signal = []
elif (NLSTA == 0) and (NLDYNA == 1):
Seismo_signal = np.loadtxt(folder + '06_Seismo_signal.txt' , skiprows=5)
elif (NLSTA == 1) and (NLDYNA == 1):
Seismo_signal = np.loadtxt(folder + '06_Seismo_signal.txt' , skiprows=5)
# End if
#
# -------------------------------------------------------------------------------------
# Read material - parameters file
mat_file = open(folder + '02_Mater.txt', 'r')
#
mats = []
matflag = 0
for line in mat_file:
if matflag == 1:
l = np.array(line.split(), dtype = float)
mats.append(l)
# End if
if line == 'PARAMETERS INFORMATION\n':
matflag = 1
#End if
#End for
#
# -------------------------------------------------------------------------------------
# Read elements file
eles_file = open(folder + '04_Eles.txt', 'r')
#
elements = []
eleflag = 0
for line in eles_file:
if eleflag == 1:
l = np.array(line.split(), dtype = int)
elements.append(l)
#End if
if line == 'ELEMENTS\n':
eleflag = 1
#End if
#End for
#
# -------------------------------------------------------------------------------------
# Initialize Msvar (List where state variables of each element will be stocked)
Msvar = []
ILF = []
nele = len(elements)
#
for i in range (nele):
#
iet = elements[i][1]
ndof, nnodes, ngpts = fem.eletype(iet)
#
if iet == 0: # Linear - 1D Spring
nsvar = 1
if iet == 1: # Linear - Simple frame
nsvar = 1
if iet == 2: # Linear - Full frame
nsvar = 1
if iet == 3: # Linear - 2D Truss
nsvar = 1
if iet == 4: # NonLin - 4 noded plate (Rutinas de Jefe)
nsvar = 88
if iet == 5: # NonLin - 1D Spring
nsvar = 5
if iet == 6: # Lin - 2D shear-rotational Spring
nsvar = 1
if iet == 7: # Lin - 1D rotational Spring
nsvar = 1
if iet == 8: # NonLin - 1D rotational Spring
nsvar = 5
if iet == 9: # NonLin - 1D pile spring for stiff soils
nsvar = 4
if iet == 10: # Linear - 3D full frame bending ans shear effects
nsvar = 1
# End if
#
ele_svar = np.zeros((nsvar))
ele_ilf = np.zeros((ndof))
Msvar.append(ele_svar)
ILF.append(ele_ilf)
# End for
# -------------------------------------------------------------------------------------
return inipar, nodes, mats, elements, loads, Msvar, ILF, Seismo_signal, const
def strain_nodes(IELCON, UU, ne, COORD, elements, mats):
"""Compute averaged strains and stresses at nodes
First, the variable is extrapolated from the Gauss
point to nodes for each element. Then, these values are averaged
according to the number of element that share that node. The theory
for this technique can be found in [1]_.
Parameters
----------
IELCON : ndarray (int)
Array with the nodes numbers for each element.
UU : ndarray (float)
Array with the displacements. This one contains both, the
computed and imposed values.
ne : int
Number of elements.
COORD : ndarray (float).
Array with nodes coordinates.
elements : ndarray (int)
Array with the node number for the nodes that correspond to each
element.
Returns
-------
E_nodes : ndarray
Strains evaluated at the nodes.
References
----------
.. [1] O.C. Zienkiewicz and J.Z. Zhu, The Superconvergent patch
recovery and a posteriori error estimators. Part 1. The
recovery technique, Int. J. Numer. Methods Eng., 33,
1331-1364 (1992).
"""
iet = elements[0, 1]
ndof, nnodes, ngpts = fe.eletype(iet)
elcoor = np.zeros([nnodes, 2])
E_nodes = np.zeros([COORD.shape[0], 3])
S_nodes = np.zeros([COORD.shape[0], 3])
el_nodes = np.zeros([COORD.shape[0]], dtype=int)
ul = np.zeros([ndof])
for i in range(ne):
young, poisson = mats[elements[i, 2], :]
shear = young/(2*(1 + poisson))
fact1 = young/(1 - poisson**2)
fact2 = poisson*young/(1 - poisson**2)
for j in range(nnodes):
elcoor[j, 0] = COORD[IELCON[i, j], 0]
elcoor[j, 1] = COORD[IELCON[i, j], 1]
for j in range(ndof):
ul[j] = UU[i, j]
if iet == 1:
epsG, xl = fe.str_el4(elcoor, ul)
extrap0 = interp2d(xl[:, 0], xl[:,1], epsG[:, 0])
extrap1 = interp2d(xl[:, 0], xl[:,1], epsG[:, 1])
extrap2 = interp2d(xl[:, 0], xl[:,1], epsG[:, 2])
elif iet == 2:
epsG, xl = fe.str_el6(elcoor, ul)
extrap0 = interp2d(xl[:, 0], xl[:,1], epsG[:, 0])
extrap1 = interp2d(xl[:, 0], xl[:,1], epsG[:, 1])
extrap2 = interp2d(xl[:, 0], xl[:,1], epsG[:, 2])
elif iet == 3:
epsG, xl = fe.str_el3(elcoor, ul)
extrap0 = lambda x, y: epsG[0, 0]
extrap1 = lambda x, y: epsG[0, 1]
extrap2 = lambda x, y: epsG[0, 2]
for node in IELCON[i, :]:
x, y = COORD[node, :]
E_nodes[node, 0] = E_nodes[node, 0] + extrap0(x, y)
E_nodes[node, 1] = E_nodes[node, 1] + extrap1(x, y)
E_nodes[node, 2] = E_nodes[node, 2] + extrap2(x, y)
S_nodes[node, 0] = S_nodes[node, 0] + fact1*extrap0(x, y) \
+ fact2*extrap1(x, y)
S_nodes[node, 1] = S_nodes[node, 1] + fact2*extrap0(x, y) \
+ fact1*extrap1(x, y)
S_nodes[node, 2] = S_nodes[node, 2] + shear*extrap2(x, y)
el_nodes[node] = el_nodes[node] + 1
E_nodes[:, 0] = E_nodes[:, 0]/el_nodes
E_nodes[:, 1] = E_nodes[:, 1]/el_nodes
E_nodes[:, 2] = E_nodes[:, 2]/el_nodes
S_nodes[:, 0] = S_nodes[:, 0]/el_nodes
S_nodes[:, 1] = S_nodes[:, 1]/el_nodes
S_nodes[:, 2] = S_nodes[:, 2]/el_nodes
return E_nodes, S_nodes
def matassem(IBC, mats, elements, nn, ne, neq, COORD, DME, IELCON):
"""Assembles the global stiffness matrix KG
Parameters
----------
IBC : ndarray (int)
Array that maps the nodes with number of equations.
mats : ndarray
Material properties.
elements : ndarray
Array with the number for the nodes in each element.
nn : int
Number of nodes.
ne : int
Number of elements.
neq : int
Number of equations in the system after removing the nodes
with imposed displacements.
COORD : ndarray
Coordinates of the nodes.
DME : ndarray (int)
Assembly operator.
IELCON : ndarray (int)
Element connectivity.
Returns
-------
KG : ndarray
Global stiffness matrix.
"""
KG = np.zeros([neq, neq])
for i in range(ne):
iet = elements[i, 1]
ndof, nnodes, ngpts = fem.eletype(iet)
elcoor = np.zeros([nnodes, 2])
kloc = np.zeros([ndof, ndof])
im = elements[i, 2]
emod = mats[im, 0]
enu = mats[im, 1]
dme = np.zeros([ndof], dtype=np.integer)
for j in range(nnodes):
elcoor[j, 0] = COORD[IELCON[i, j], 0]
elcoor[j, 1] = COORD[IELCON[i, j], 1]
if iet == 1:
kloc = ue.uel4nquad(elcoor, enu, emod)
elif iet == 2:
kloc = ue.uel6ntrian(elcoor, enu, emod)
elif iet == 3:
kloc = ue.uel3ntrian(elcoor, enu, emod)
for ii in range(ndof):
dme[ii] = DME[i, ii]
for ii in range(ndof):
kk = dme[ii]
if kk != -1:
for jj in range(ndof):
ll = dme[jj]
if ll != -1:
KG[kk, ll] = KG[kk, ll] + kloc[ii, jj]
return KG
def strain_nodes(nodes, elements, mats, UC):
"""Compute averaged strains and stresses at nodes
First, the variable is extrapolated from the Gauss
point to nodes for each element. Then, these values are averaged
according to the number of element that share that node. The theory
for this technique can be found in [1]_.
Parameters
----------
nodes : ndarray (float).
Array with nodes coordinates.
elements : ndarray (int)
Array with the node number for the nodes that correspond
to each element.
mats : ndarray (float)
Array with material profiles.
UC : ndarray (float)
Array with the displacements. This one contains both, the
computed and imposed values.
Returns
-------
E_nodes : ndarray
Strains evaluated at the nodes.
References
----------
.. [1] O.C. Zienkiewicz and J.Z. Zhu, The Superconvergent patch
recovery and a posteriori error estimators. Part 1. The
recovery technique, Int. J. Numer. Methods Eng., 33,
1331-1364 (1992).
"""
ne = elements.shape[0]
nn = nodes.shape[0]
iet = elements[0, 1]
ndof, nnodes, _ = fe.eletype(iet)
elcoor = np.zeros([nnodes, 2])
E_nodes = np.zeros([nn, 3])
S_nodes = np.zeros([nn, 3])
el_nodes = np.zeros([nn], dtype=int)
ul = np.zeros([ndof])
IELCON = elements[:, 3:]
for i in range(ne):
young, poisson = mats[np.int(elements[i, 2]), :]
shear = young / (2 * (1 + poisson))
fact1 = young / (1 - poisson**2)
fact2 = poisson * young / (1 - poisson**2)
for j in range(nnodes):
elcoor[j, 0] = nodes[IELCON[i, j], 1]
elcoor[j, 1] = nodes[IELCON[i, j], 2]
ul[2 * j] = UC[IELCON[i, j], 0]
ul[2 * j + 1] = UC[IELCON[i, j], 1]
if iet == 1:
epsG, _ = fe.str_el4(elcoor, ul)
elif iet == 2:
epsG, _ = fe.str_el6(elcoor, ul)
elif iet == 3:
epsG, _ = fe.str_el3(elcoor, ul)
for cont, node in enumerate(IELCON[i, :]):
E_nodes[node, 0] = E_nodes[node, 0] + epsG[cont, 0]
E_nodes[node, 1] = E_nodes[node, 1] + epsG[cont, 1]
E_nodes[node, 2] = E_nodes[node, 2] + epsG[cont, 2]
S_nodes[node, 0] = S_nodes[node, 0] + fact1*epsG[cont, 0] \
+ fact2*epsG[cont, 1]
S_nodes[node, 1] = S_nodes[node, 1] + fact2*epsG[cont, 0] \
+ fact1*epsG[cont, 1]
S_nodes[node, 2] = S_nodes[node, 2] + shear * epsG[cont, 2]
el_nodes[node] = el_nodes[node] + 1
E_nodes[:, 0] = E_nodes[:, 0] / el_nodes
E_nodes[:, 1] = E_nodes[:, 1] / el_nodes
E_nodes[:, 2] = E_nodes[:, 2] / el_nodes
S_nodes[:, 0] = S_nodes[:, 0] / el_nodes
S_nodes[:, 1] = S_nodes[:, 1] / el_nodes
S_nodes[:, 2] = S_nodes[:, 2] / el_nodes
return E_nodes, S_nodes
def retriever(Up, svar, dme, ac, elements , mats , nodes , i, uel=None):
"""Computes the elemental stiffness matrix of element i
Parameters
----------
Up : ndarray
Array with the nodal displacement at time t
svar : python list
List with the state variables of the element of the last converged increment.
dme : ndarray (int)
Assembly operator that indicates degrees of freedom correspondence of the element.
ac : 1D array
Integration constants
elements : ndarray
Array with the number for the nodes in each element.
mats : ndarray.
Array with the material profiles.
nodes : ndarray.
Array with the nodal numbers and coordinates.
i : int.
Identifier of the element to be assembled.
Returns
-------
kloc : ndarray (float)
Array with the local stiffness matrix.
mloc : ndarray (float)
Array with the local mass matrix.
cloc : ndarray (float)
Array with the local damping matrix.
svar : Python list
List with the state variables of the current element.
ndof : int.
Number of degrees of freedom of the current element.
"""
#
iet = elements[i][1]
#
ndof, nnodes, ngpts = fem.eletype(iet)
iele_disp = eleDisp(Up, iet, dme, i)
#
elcoor = np.zeros([nnodes, 3])
im = np.int(elements[i][2])
par = mats[im]
for j in range(nnodes):
IELCON = elements[i][j+3] # Index of each node of the element
elcoor[j, 0] = nodes[IELCON, 1] # X coordinate of the node
elcoor[j, 1] = nodes[IELCON, 2] # X coordinate of the node
elcoor[j, 2] = nodes[IELCON, 3] # X coordinate of the node
# End for j
#
if uel is None:
if iet == 0:
kloc , mloc , cloc , svar, ilf = ue.L_1Dspring(iele_disp, elcoor, par, svar)
if iet == 1:
kloc , mloc , cloc , svar, ilf = ue.L_sframe(iele_disp, elcoor, par, svar)
elif iet == 2:
kloc , mloc , cloc , svar, ilf = ue.L_fframe(iele_disp, elcoor, par, svar)
elif iet == 3:
kloc , mloc , cloc , svar, ilf = ue.L_2Dtruss(iele_disp, elcoor, par, svar)
elif iet == 4:
kloc , mloc , cloc , svar, ilf = slds.uel4nquad_PLK(elcoor, par, svar, iele_disp)
elif iet == 5:
kloc , mloc , cloc , svar, ilf = ue.NL_1Dspring(iele_disp, elcoor, par, svar)
elif iet == 6:
kloc , mloc , cloc , svar, ilf = ue.L_2DRotspg(iele_disp, elcoor, par, svar)
elif iet == 7:
kloc , mloc , cloc , svar, ilf = ue.L_1DRotspg(iele_disp, elcoor, par, svar)
elif iet == 8:
kloc , mloc , cloc , svar, ilf = ue.NL_1DRotspg(iele_disp, elcoor, par, svar)
elif iet == 9:
kloc , mloc , cloc , svar, ilf = ue.NL_1DPileRCK(iele_disp, elcoor, par, svar)
elif iet == 10:
kloc , mloc , cloc , svar, ilf = ue.L_3Dfframe(iele_disp, elcoor, par, svar)
else:
kloc, ndof, iet = uel(elcoor, par)
return kloc, mloc, cloc, svar, ndof, ilf
def DME(nodes, elements):
"""Counts active equations, creates BCs array IBC[]
and the assembly operator DME[]
Parameters
----------
nodes : ndarray.
Array with the nodal numbers and coordinates.
elements : ndarray
Array with the number for the nodes in each element.
iet : int (This is not an input for this function)
Type of element. These are:
0. Linear - 1D Spring in X direction.
1. Linear - Simple frame.
2. Linear - Full frame.
3. Linear - 2D Truss.
4. NonLin - 4 noded plate.
5. NonLin - 1D Spring in X direction.
6. Linear - 2D Shear-Rotational spring.
7. Linear - 1D Rotational spring.
8. NonLin - 1D Rotational spring.
9. NonLin - 1D pile spring P-Y curve for stiff soil
10. Linear - 3D full frame bending and shear effects
Returns
-------
DME : ndarray (int)
Assembly operator.
IBC : ndarray (int)
Boundary conditions array.
neq : int
Number of active equations in the system.
"""
nels = len(elements)
IELCON = np.zeros([nels, 4], dtype=np.integer) # 4 por que es el máximo numero de nodos que conforman un elemento
DME = []
neq, IBC = eqcounter(nodes)
for i in range(nels):
dme = []
iet = elements[i][1]
ndof, nnodes, ngpts = fem.eletype(iet)
for j in range(nnodes):
IELCON[i, j] = elements[i][j+3]
kk = IELCON[i, j]
#
if iet == 0:
dme.append(IBC[kk, 0])
elif iet == 1:
dme.append(IBC[kk, 0])
dme.append(IBC[kk, 1])
dme.append(IBC[kk, 5])
elif iet == 2:
dme.append(IBC[kk, 0])
dme.append(IBC[kk, 1])
dme.append(IBC[kk, 5])
elif iet == 3:
dme.append(IBC[kk, 0])
dme.append(IBC[kk, 1])
elif iet == 4:
dme.append(IBC[kk, 0])
dme.append(IBC[kk, 1])
elif iet == 5:
dme.append(IBC[kk, 0])
elif iet == 6:
dme.append(IBC[kk, 1])
dme.append(IBC[kk, 5])
elif iet == 7:
dme.append(IBC[kk, 5])
elif iet == 8:
dme.append(IBC[kk, 5])
elif iet == 9:
dme.append(IBC[kk, 0])
elif iet == 10:
dme.append(IBC[kk, 0])
dme.append(IBC[kk, 1])
dme.append(IBC[kk, 2])
dme.append(IBC[kk, 3])
dme.append(IBC[kk, 4])
dme.append(IBC[kk, 5])
#End if
# End for j
DME.append(dme)
# ENd for i
return DME, IBC, neq
def strain_nodes(IELCON, UU, ne, COORD, elements, mats):
"""Compute averaged strains and stresses at nodes
First, the variable is extrapolated from the Gauss
point to nodes for each element. Then, these values are averaged
according to the number of element that share that node. The theory
for this technique can be found in [1]_.
Parameters
----------
IELCON : ndarray (int)
Array with the nodes numbers for each element.
UU : ndarray (float)
Array with the displacements. This one contains both, the
computed and imposed values.
ne : int
Number of elements.
COORD : ndarray (float).
Array with nodes coordinates.
elements : ndarray (int)
Array with the node number for the nodes that correspond to each
element.
Returns
-------
E_nodes : ndarray
Strains evaluated at the nodes.
References
----------
.. [1] O.C. Zienkiewicz and J.Z. Zhu, The Superconvergent patch
recovery and a posteriori error estimators. Part 1. The
recovery technique, Int. J. Numer. Methods Eng., 33,
1331-1364 (1992).
"""
iet = elements[0, 1]
ndof, nnodes, ngpts = fe.eletype(iet)
elcoor = np.zeros([nnodes, 2])
E_nodes = np.zeros([COORD.shape[0], 3])
S_nodes = np.zeros([COORD.shape[0], 3])
el_nodes = np.zeros([COORD.shape[0]], dtype=int)
ul = np.zeros([ndof])
for i in range(ne):
young, poisson = mats[elements[i, 2], :]
shear = young / (2 * (1 + poisson))
fact1 = young / (1 - poisson**2)
fact2 = poisson * young / (1 - poisson**2)
for j in range(nnodes):
elcoor[j, 0] = COORD[IELCON[i, j], 0]
elcoor[j, 1] = COORD[IELCON[i, j], 1]
for j in range(ndof):
ul[j] = UU[i, j]
if iet == 1:
epsG, xl = fe.str_el4(elcoor, ul)
extrap0 = interp2d(xl[:, 0], xl[:, 1], epsG[:, 0])
extrap1 = interp2d(xl[:, 0], xl[:, 1], epsG[:, 1])
extrap2 = interp2d(xl[:, 0], xl[:, 1], epsG[:, 2])
elif iet == 2:
epsG, xl = fe.str_el6(elcoor, ul)
extrap0 = interp2d(xl[:, 0], xl[:, 1], epsG[:, 0])
extrap1 = interp2d(xl[:, 0], xl[:, 1], epsG[:, 1])
extrap2 = interp2d(xl[:, 0], xl[:, 1], epsG[:, 2])
elif iet == 3:
epsG, xl = fe.str_el3(elcoor, ul)
extrap0 = lambda x, y: epsG[0, 0]
extrap1 = lambda x, y: epsG[0, 1]
extrap2 = lambda x, y: epsG[0, 2]
for node in IELCON[i, :]:
x, y = COORD[node, :]
E_nodes[node, 0] = E_nodes[node, 0] + extrap0(x, y)
E_nodes[node, 1] = E_nodes[node, 1] + extrap1(x, y)
E_nodes[node, 2] = E_nodes[node, 2] + extrap2(x, y)
S_nodes[node, 0] = S_nodes[node, 0] + fact1*extrap0(x, y) \
+ fact2*extrap1(x, y)
S_nodes[node, 1] = S_nodes[node, 1] + fact2*extrap0(x, y) \
+ fact1*extrap1(x, y)
S_nodes[node, 2] = S_nodes[node, 2] + shear * extrap2(x, y)
el_nodes[node] = el_nodes[node] + 1
E_nodes[:, 0] = E_nodes[:, 0] / el_nodes
E_nodes[:, 1] = E_nodes[:, 1] / el_nodes
E_nodes[:, 2] = E_nodes[:, 2] / el_nodes
S_nodes[:, 0] = S_nodes[:, 0] / el_nodes
S_nodes[:, 1] = S_nodes[:, 1] / el_nodes
S_nodes[:, 2] = S_nodes[:, 2] / el_nodes
return E_nodes, S_nodes
def matassem(IBC, mats, elements, nn, ne, neq, COORD, DME, IELCON):
"""Assembles the global stiffness matrix KG
Parameters
----------
IBC : ndarray (int)
Array that maps the nodes with number of equations.
mats : ndarray
Material properties.
elements : ndarray
Array with the number for the nodes in each element.
nn : int
Number of nodes.
ne : int
Number of elements.
neq : int
Number of equations in the system after removing the nodes
with imposed displacements.
COORD : ndarray
Coordinates of the nodes.
DME : ndarray (int)
Assembly operator.
IELCON : ndarray (int)
Element connectivity.
Returns
-------
KG : ndarray
Global stiffness matrix.
"""
KG = np.zeros([neq, neq])
for i in range(ne):
iet = elements[i, 1]
ndof, nnodes, ngpts = fem.eletype(iet)
elcoor = np.zeros([nnodes, 2])
kloc = np.zeros([ndof, ndof])
im = elements[i, 2]
emod = mats[im, 0]
enu = mats[im, 1]
dme = np.zeros([ndof], dtype=np.integer)
for j in range(nnodes):
elcoor[j, 0] = COORD[IELCON[i, j], 0]
elcoor[j, 1] = COORD[IELCON[i, j], 1]
if iet == 1:
kloc = ue.uel4nquad(elcoor, enu, emod)
elif iet == 2:
kloc = ue.uel6ntrian(elcoor, enu, emod)
elif iet == 3:
kloc = ue.uel3ntrian(elcoor, enu, emod)
for ii in range(ndof):
dme[ii] = DME[i, ii]
for ii in range(ndof):
kk = dme[ii]
if kk != -1:
for jj in range(ndof):
ll = dme[jj]
if ll != -1:
KG[kk, ll] = KG[kk, ll] + kloc[ii, jj]
return KG
