def solver(mesh_name, material, body_forces, traction_imposed,
displacement_imposed, period, steps, u0, v0,
plot_undeformed, plot_stress, plot_deformed):
mesh = gmsh.parse(mesh_name)
s = mesh.surfaces
mat_dic = {s[i]: material[j] for i, j in enumerate(material)}
k_ele = element2dof.stiffness(mesh, mat_dic)
p0q_ele = element2dof.body_forces(mesh, body_forces)
m_ele = element2dof.mass(mesh, mat_dic)
k = assemble2dof.global_matrix(k_ele, mesh)
m = assemble2dof.global_matrix(m_ele, mesh)
p0q = assemble2dof.global_vector(p0q_ele, mesh)
p0t = boundaryconditions2dof.neumann(mesh, traction_imposed)
p0 = p0q + p0t
km, p0m = boundaryconditions2dof.dirichlet(k, p0, mesh,
displacement_imposed)
mm, p0m = boundaryconditions2dof.dirichlet(m, p0, mesh, displacement_imposed)
timestep.iterations(period, steps, u0, v0, mesh, mat_dic, km, mm, p0m, interval=1)
'''
def solver(mesh_name, material, body_forces, traction_imposed,
displacement_imposed, period, steps, u0, v0, plot_undeformed,
plot_stress, plot_deformed):
mesh = gmsh.parse(mesh_name)
s = mesh.surfaces
mat_dic = {s[i]: material[j] for i, j in enumerate(material)}
k_ele = element2dof.stiffness(mesh, mat_dic)
p0q_ele = element2dof.body_forces(mesh, body_forces)
m_ele = element2dof.mass(mesh, mat_dic)
k = assemble2dof.global_matrix(k_ele, mesh)
m = assemble2dof.global_matrix(m_ele, mesh)
p0q = assemble2dof.global_vector(p0q_ele, mesh)
p0t = boundaryconditions2dof.neumann(mesh, traction_imposed)
p0 = p0q + p0t
km, p0m = boundaryconditions2dof.dirichlet(k, p0, mesh,
displacement_imposed)
mm, p0m = boundaryconditions2dof.dirichlet(m, p0, mesh,
displacement_imposed)
timestep.iterations(period,
steps,
u0,
v0,
mesh,
mat_dic,
km,
mm,
p0m,
interval=1)
'''
def neumann(mesh, traction):
"""Apply Neumann BC.
Computes the integral from the weak form with the boundary term.
.. note::
How its done:
1. Define an array with the Gauss points for each path, each path will
have 2 sets of two gauss points. One of the gp is fixed, which indicates
that its going over an specific boundary of the element.
Gauss points are defines as::
gp = [gp, -1 1st path --> which has 2 possibilities for gp.
1, gp 2nd path
gp, 1 3rd
-1, gp] 4th
2. A loop over the elements on the boundary extracting also the side
where the boundary is located on this element.
.. note::
Edge elements are necessary because we need to extract the nodes
from the connectivity. Then we can create a T for this element.
Args:
traction: Function with the traction and the line where the traction
is applied.
mesh: Object with the mesh attributes.
Returns:
T: Traction vector with size equals the dof.
"""
Tele = np.zeros((8, mesh.num_ele))
gp = np.array([[[-1.0/math.sqrt(3), -1.0],
[1.0/math.sqrt(3), -1.0]],
[[1.0, -1.0/math.sqrt(3)],
[1.0, 1.0/math.sqrt(3)]],
[[-1.0/math.sqrt(3), 1.0],
[1.0/math.sqrt(3), 1.0]],
[[-1.0, -1.0/math.sqrt(3)],
[-1.0, 1.0/math.sqrt(3)]]])
for line in traction(1,1).keys():
if line[0] == 'line':
for ele, side, l in mesh.boundary_elements:
if l == line[1]:
for w in range(2):
mesh.basisFunction2D(gp[side, w])
mesh.eleJacobian(mesh.nodes_coord[mesh.ele_conn[ele, :]])
x1_o_e1e2, x2_o_e1e2 = mesh.mapping(ele)
t = traction(x1_o_e1e2, x2_o_e1e2)
dL = mesh.ArchLength[side]
Tele[0, ele] += mesh.phi[0]*t[line][0]*dL
Tele[1, ele] += mesh.phi[0]*t[line][1]*dL
Tele[2, ele] += mesh.phi[1]*t[line][0]*dL
Tele[3, ele] += mesh.phi[1]*t[line][1]*dL
Tele[4, ele] += mesh.phi[2]*t[line][0]*dL
Tele[5, ele] += mesh.phi[2]*t[line][1]*dL
Tele[6, ele] += mesh.phi[3]*t[line][0]*dL
Tele[7, ele] += mesh.phi[3]*t[line][1]*dL
T = assemble2dof.global_vector(Tele, mesh)
for n in traction(1, 1).keys():
if n[0] == 'node':
t = traction(1,1)
T[2*n[1]] = t[n][0]
T[2*n[1]+1] = t[n][1]
return T
