def giveElemVolume(elem, elemType):
mat_id = elem["MaterialId"] - 1
material = globalvars.data["Materials"][mat_id]
if (elemType == "BR02" or elemType == "TRUSS02"):
area = material["Area"]
node1 = elem["Connectivities"][0] - 1
x1 = globalvars.data["Mesh"]["Nodes"][node1]["x"]
y1 = globalvars.data["Mesh"]["Nodes"][node1]["y"]
node2 = elem["Connectivities"][1] - 1
x2 = globalvars.data["Mesh"]["Nodes"][node2]["x"]
y2 = globalvars.data["Mesh"]["Nodes"][node2]["y"]
length = math.sqrt((x2 - x1)**2 + (y2 - y1)**2)
volume = area * length
elif (elemType == "TR03" or elemType == "QU04"):
thickness = 1.0
if (material["Plane_Type"] == "Plane_Stress"):
thickness = material["Thickness"]
ngauss = Set_Ngauss(elemType)
Nodes = globalvars.data["Mesh"]["Nodes"]
pos_pg, W = GaussQuadrature(elemType)
area = 0.0
for igauss in range(ngauss):
det_Jac, _ = derivCartesian(elem, elemType, Nodes, pos_pg[igauss])
area += det_Jac * W[igauss]
volume = area * thickness
return volume
def CalcMassMatrix(ElemType, elem):
nnodes = GiveNnodes(ElemType)
ngauss = Set_Ngauss(ElemType)
mat_id = elem["MaterialId"] - 1
material = globalvars.data["Materials"][mat_id]
Nodes = globalvars.data["Mesh"]["Nodes"]
pos_pg, W = GaussQuadrature(ElemType)
if (globalvars.data["ProblemType"] == "Thermal"):
rho = material["Specific_Heat"]
nrows = nnodes
ncols = nnodes
ngl = 1
elif (globalvars.data["ProblemType"] == "Structural_Mechanics"):
rho = material["Density"]
if (ElemType == "BAR02"):
nrows = nnodes
ncols = nnodes
ngl = 1
else:
nrows = nnodes * 2
ncols = nnodes * 2
ngl = 2
if (ElemType == "BAR02" or ElemType == "TRUSS02"):
rho *= material["Area"]
elif (ElemType == "TR03" or ElemType == "TR06" or ElemType == "QU04"
or ElemType == "QU08" or ElemType == "QU09"):
thickness = 1.0
if (material["Plane_Type"] == "Plane_Stress"):
thickness = material["Thickness"]
rho *= thickness
massMatrix = np.zeros((nrows, ncols), dtype=float)
localMat = np.zeros((ngl, ngl), dtype=float)
massMatrix_pg = np.zeros((ngl, ngl), dtype=float)
for inode in range(nnodes):
for jnode in range(nnodes):
irow_ini = inode * ngl
irow_end = irow_ini + ngl
icol_ini = jnode * ngl
icol_end = icol_ini + ngl
for igauss in range(ngauss):
fform = FuncForm(ElemType, pos_pg, igauss)
for igl in range(ngl):
localMat[igl, igl] = fform[inode] * fform[jnode]
det_Jac, _ = derivCartesian(elem, ElemType, Nodes,
pos_pg[igauss])
massMatrix_pg[:ngl, :ngl] = localMat[:ngl, :ngl] * rho * W[
igauss] * det_Jac
massMatrix[irow_ini:irow_end,
icol_ini:icol_end] += massMatrix_pg[:ngl, :ngl]
return massMatrix
def Smooth_Forces():
num_nodes = len(globalvars.data["Mesh"]["Nodes"])
nodal_Forces = np.zeros((num_nodes, 3), dtype=float)
node_counter = np.zeros((num_nodes), dtype=int)
ProblemType = globalvars.data["ProblemType"]
ElemType = globalvars.data["Mesh"]["ElemType"]
nnode = GiveNnodes(ElemType)
ngauss = Set_Ngauss(ElemType)
ncomp = GiveNComp(ElemType, ProblemType)
Eps_vec = np.zeros((ncomp, ngauss), dtype=float)
Sigma_vec = np.zeros((ncomp, ngauss), dtype=float)
Forces_vec = np.zeros((ncomp, ngauss), dtype=float)
ielem = 0
for elem in globalvars.data["Mesh"]["Elements"]:
mat_id = elem["MaterialId"] - 1
material = globalvars.data["Materials"][mat_id]
factor = 1.0
if (ElemType == "TR03" or ElemType == "TR06" or ElemType == "QU04"
or ElemType == "QU08" or ElemType == "QU09"):
if (material["Plane_Type"] == "Plane_Stress"):
factor = material["Thickness"]
elif (ElemType == "TRUSS02" or ElemType == "BAR02"
or ElemType == "BAR03"):
factor = material["Area"]
if (ElemType == "TR03"):
Sigma_vec_TR03 = Stress_TR03(elem)
Forces_vec[:ncomp, :] = Sigma_vec_TR03[:ncomp] * factor
else:
for igauss in range(ngauss):
if (len(globalvars.Sigma_elem_vec[0]) == 0):
Eps_vec[:, igauss] = Strain_Solid(elem, ElemType,
ProblemType, igauss)
Sigma_vec[:,
igauss] = Stress_Solid(elem, ElemType,
Eps_vec[:, igauss])
else:
for icomp in range(ncomp):
Sigma_vec[icomp,
igauss] = globalvars.Sigma_elem_vec[icomp][
ielem, igauss]
Forces_vec[:, igauss] = Sigma_vec[:, igauss] * factor
ielem += 1
for inode in range(nnode):
id_node = elem["Connectivities"][inode] - 1
node_counter[id_node] += 1
nodal_Forces[id_node, :ncomp] += Forces_vec[:ncomp, inode]
for inode in range(num_nodes):
nodal_Forces[inode, :ncomp] /= node_counter[inode]
return nodal_Forces
def Smooth_Stresses():
num_nodes = len(globalvars.data["Mesh"]["Nodes"])
nodal_Sigma = np.zeros((num_nodes, 3), dtype=float)
node_counter = np.zeros((num_nodes), dtype=int)
ProblemType = globalvars.data["ProblemType"]
ElemType = globalvars.data["Mesh"]["ElemType"]
nnode = GiveNnodes(ElemType)
ngauss = Set_Ngauss(ElemType)
ncomp = GiveNComp(ElemType, ProblemType)
Eps_vec = np.zeros((ncomp, ngauss), dtype=float)
Sigma_vec = np.zeros((ncomp, ngauss), dtype=float)
num_elems = len(globalvars.data["Mesh"]["Elements"])
for icomp in range(ncomp):
globalvars.Sigma_elem_vec[icomp] = np.zeros((num_elems, ngauss),
dtype=float)
ielem = 0
for elem in globalvars.data["Mesh"]["Elements"]:
if (ElemType == "TR03"):
Sigma_vec_TR03 = Stress_TR03(elem)
for igauss in range(ngauss):
Sigma_vec[:ncomp, igauss] = Sigma_vec_TR03[:ncomp]
else:
for igauss in range(ngauss):
if (len(globalvars.Eps_elem_vec[0]) == 0):
Eps_vec[:, igauss] = Strain_Solid(elem, ElemType,
ProblemType, igauss)
else:
for icomp in range(ncomp):
Eps_vec[icomp,
igauss] = globalvars.Eps_elem_vec[icomp][
ielem, igauss]
Sigma_vec[:, igauss] = Stress_Solid(elem, ElemType,
Eps_vec[:, igauss])
for igauss in range(ngauss):
for icomp in range(ncomp):
globalvars.Sigma_elem_vec[icomp][ielem,
igauss] = Sigma_vec[icomp,
igauss]
ielem += 1
for inode in range(nnode):
id_node = elem["Connectivities"][inode] - 1
node_counter[id_node] += 1
nodal_Sigma[id_node, :ncomp] += Sigma_vec[:ncomp, inode]
for inode in range(num_nodes):
nodal_Sigma[inode, :ncomp] /= node_counter[inode]
return nodal_Sigma
def stiffnessMatCalc(elem, ElemType, ProblemType, Dmat):
ngauss = Set_Ngauss(ElemType)
Nodes = globalvars.data["Mesh"]["Nodes"]
ndof = GiveNdof(ElemType, ProblemType)
nnodes = GiveNnodes(ElemType)
size = nnodes * ndof
rigimat = np.zeros((size,size), dtype=float)
pos_pg, W = GaussQuadrature(ElemType)
for igauss in range(ngauss):
det_Jac, derivCart = derivCartesian(elem, ElemType, Nodes, pos_pg[igauss])
Bmat = Calc_Bmat(ElemType, derivCart, ProblemType)
DxBmat = np.matmul(Dmat, Bmat)
rigimat_pg = np.matmul(Bmat.transpose(), DxBmat) * det_Jac * W[igauss]
rigimat += rigimat_pg
return rigimat