def __init__(self, p1, p2, crosssection, x, number=0, gnn=(0, 0), stiffness=sTruss, dimension="3D"):
self.Number = number # number in a global geometric system
self.GlobalNodeNumbers = gnn # global node numbers
self.P1 = p1 # 1st Point of the beam
self.P2 = p2 # 2nd Point of the beam
self.Dimension = dimension
self.BeamType = "{}{}".format(stiffness, self.Dimension)
self.DoFPerNode = self.__dof_per_node_mapping[self.BeamType]
self.DOFS = dict() # global degree of freedoms according to the beam number in a global system
# just needed if there is a global system
# is a dictionary with entries for both nodes of the beam
if self.Number > 0:
self.DOFS.update(get_dofs_from_node(self.GlobalNodeNumbers[0], self.DoFPerNode))
self.DOFS.update(get_dofs_from_node(self.GlobalNodeNumbers[1], self.DoFPerNode))
if self.Dimension == "3D":
self.Datum = Datum3D(self.P1, self.P2)
elif self.Dimension == "2D":
self.Datum = Datum2D(self.P1, self.P2) # datum object for the beam; both points are required for creation
# detailed description in datum class file
self.Geometry = Geometry(p1, p2, crosssection, x) # Geometry object; requires both points to calculate
# the length, the cross section's type and the characteristic value for the corresponding cross section
self.Material = Material # create the Material object; now: nothing else is required because E and
# rho are constant
self.Mass = self.calculatemass_a(self.Geometry.CrossSection.A) # calculate mass of the beam
# select the stiffness type; now: only Truss stiffness is available
if stiffness == "Truss":
self.Stiffness = TrussStiffness(self, stiffness)
elif stiffness == "Beam":
self.Stiffness = BeamStiffness(self, stiffness)
else:
self.Stiffness = None
def __get_2d_beam_matrix(_gm, _d2, _x=1):
# _a = (pi/4) ** _d ** 2
_ndofs = len(_gm.Nodes) * _gm.DoFsPerNode
_k = [0] * _ndofs
for _n in range(_ndofs):
_k[_n] = [0] * _ndofs
for _b in _gm.Beams:
cb = _gm.Beams[_b]
ek = get_beam_element_submatrix(cb, _d2[_b])
dl = cb.DOFS[list(cb.DOFS.keys())[0]] + cb.DOFS[list(
cb.DOFS.keys())[1]]
dl = [i - 1 for i in dl]
for i in range(2 * _gm.DoFsPerNode):
for j in range(2 * _gm.DoFsPerNode):
_k[int(dl[i])][int(dl[j])] += ek[i][j] # * _x[_b]
for _node in _gm.Bounds:
_bd = get_dofs_from_node(_node, _gm.DoFsPerNode, zerobased=True)
for _n in _bd[_node]:
for _i in range(len(_k)):
_k[int(_i)][int(_n)] = 0
for _j in range(len(_k[int(_n)])):
_k[int(_n)][int(_j)] = 0
_k[int(_n)][int(_n)] = 1
return _k
def get_matrix(_gm, _a, _x):
_ndofs = len(_gm.Nodes) * _gm.DoFsPerNode
_k = make_zeros(_ndofs)
for _n in range(_ndofs):
_k[_n] = make_zeros(_ndofs)
for _b in _gm.Beams:
cb = _gm.Beams[_b]
# ek = cb.Stiffness.K_dof.tolist()
ek = get_beam_element_submatrix(cb, _a[_b])
dl = cb.DOFS[list(cb.DOFS.keys())[0]] + cb.DOFS[list(
cb.DOFS.keys())[1]]
dl = [i - 1 for i in dl]
for i in range(2 * _gm.DoFsPerNode):
for j in range(2 * _gm.DoFsPerNode):
_k[int(dl[i])][int(dl[j])] += ek[i][j] * _x[_b]
for _node in _gm.Bounds:
_bd = get_dofs_from_node(_node, _gm.DoFsPerNode, zerobased=True)
for _n in _bd[_node]:
for _i in range(len(_k)):
_k[int(_i)][int(_n)] = 0
for _j in range(len(_k[int(_n)])):
_k[int(_n)][int(_j)] = 0
_k[int(_n)][int(_n)] = 1
return _k
def __init__(self, _nodes, _beams, _bounds, _loads, _eletype=sTruss):
self.ElementType = _eletype
self.DoFsPerNode = self.__dof_per_node_mapping[self.ElementType]
self.deletionindices = list()
self.Nodes = _nodes
self.Beams = _beams
self.Bounds = _bounds
self.Loads = _loads
self.BoundedNodes, self.FreeNodes = self.__get_nodes_types()
self.Calculationindices = list()
for node in self.FreeNodes:
self.Calculationindices.extend(get_dofs_from_node(node, self.DoFsPerNode, zerobased=False)[node])
self.Kglob = get_complete_stiffness(self.Nodes, self.Beams, self.DoFsPerNode, self.ElementType)
self.F = self.get_force_vector()
_myU, _myK = self.__get_u()
self.U = np.array(_myU)
self.Kcal = _myK
pass
def get_force_vector(self):
_f = np.zeros((len(self.Nodes) * self.DoFsPerNode))
_myMap = dict()
for node in self.Loads:
_f_indices = (get_dofs_from_node(node, self.DoFsPerNode, zerobased=True))[node]
_f_vals = self.Loads[node]
_j = 0
for _i in _f_indices:
_f[int(_i)] = _f_vals[_j]
_j += 1
return _f
def __get_truss_matrix(_gm, _d, _x=1):
# _a = (pi/4) * _d
__nnodes = len(_gm.Nodes)
__ndofs = __nnodes * _gm.DoFsPerNode
_bk = dict() # k_alpha dict for every beam in geometric system
for _b in _gm.Beams:
_bk[_b] = get_truss_sub_matrix(_gm.Beams[_b], _d[_b])
_k = list()
for i in range(__ndofs):
_k.append([0] * __ndofs)
def _fill_k(__k, _b, __sub_k):
for __i in _b.DOFS:
for __j in _b.DOFS:
_igd = _b.DOFS[__i]
_jgd = _b.DOFS[__j]
_it = 0
for ___i in _igd:
_jt = 0
for ___j in _jgd:
if __i == __j:
__k[int(___i) - 1][int(___j) -
1] += __sub_k[_it][_jt] # * __x
else:
__k[int(___i) - 1][int(___j) -
1] -= __sub_k[_it][_jt] # * __x
_jt += 1
_it += 1
return __k
for _b in _bk:
_k = _fill_k(_k, _gm.Beams[_b], _bk[_b])
for _node in _gm.Bounds:
_bd = get_dofs_from_node(_node, _gm.DoFsPerNode, zerobased=True)
for _n in _bd[_node]:
for _i in range(len(_k)):
_k[int(_i)][int(_n)] = 0
for _j in range(len(_k[int(_n)])):
_k[int(_n)][int(_j)] = 0
_k[int(_n)][int(_n)] = 1
return _k
def __get_u(self):
_k = np.array(self.Kglob)
_f = np.array(self.F)
for _node in self.Bounds:
_bd = get_dofs_from_node(_node, self.DoFsPerNode, zerobased=True)
for __di in _bd[_node]:
_k[int(__di), :] = 0
_k[:, int(__di)] = 0
for __dj in _bd[_node]:
if __di == __dj:
_k[int(__dj), int(__dj)] = 1
_u = np.linalg.solve(_k, _f)
return _u, _k
def get_displacement_vector(self):
_k = self.Kglob
_f = self.F
_u = np.zeros((len(self.Nodes) * self.DoFsPerNode, 1))
_indices = list()
for node in self.Bounds:
_indices = get_dofs_from_node(node, self.DoFsPerNode, zerobased=True)
self.deletionindices.extend(_indices[node])
_f = np.delete(_f, self.deletionindices, axis=0)
_k = np.delete(_k, self.deletionindices, axis=0)
_k = np.delete(_k, self.deletionindices, axis=1)
self.Kcal = _k
self.Fcal = _f
_k = np.round(_k, 3)
_f = np.round(_f, 3)
_u_cal = np.linalg.solve(_k, _f)
self.Ucal = _u_cal
_z = 0
for _i in self.Calculationindices:
_u[int(_i-1)] = _u_cal[_z]
_z += 1
# get a translation dict for u and u_cal
_u_mapping = dict() # key: u_cal, value: u_glob
_z = 1
for i in self.Calculationindices:
_u_mapping[_z] = int(i)
_z += 1
return _u, _u_mapping