ib = InteriorBasis(m, e, intorder=4)
Ib = InteriorBasis(M, E, intorder=4)
mapping = MappingMortar.init_2D(m, M, m.boundaries['contact'],
M.facets_satisfying(lambda x: x[0] == 1.0),
np.array([0.0, 1.0]))
mb = [
FacetBasis(m, e, mapping=mapping, intorder=4, side=0),
FacetBasis(M, E, mapping=mapping, intorder=4, side=1),
]
# define bilinear forms
E = 1000.0
nu = 0.3
Lambda, Mu = lame_parameters(E, nu)
weakform1 = linear_elasticity(Lambda, Mu)
weakform2 = linear_elasticity(Lambda, Mu)
C = linear_stress(Lambda, Mu)
alpha = 1000
limit = 0.3
# assemble the stiffness matrices
K1 = asm(weakform1, ib)
K2 = asm(weakform2, Ib)
K = [[K1, 0.], [0., K2]]
f = [None] * 2
weak form of the linear elasticity problem is defined in
:func:`skfem.models.elasticity.linear_elasticity`.
"""
import numpy as np
from skfem import *
from skfem.models.elasticity import linear_elasticity, lame_parameters
m = MeshHex()
m.refine(3)
e1 = ElementHex1()
e = ElementVectorH1(e1)
ib = InteriorBasis(m, e, MappingIsoparametric(m, e1), 3)
K = asm(linear_elasticity(*lame_parameters(1e3, 0.3)), ib)
dofs = {
'left' : ib.get_dofs(lambda x: x[0] == 0.0),
'right': ib.get_dofs(lambda x: x[0] == 1.0),
}
u = np.zeros(K.shape[0])
u[dofs['right'].nodal['u^1']] = 0.3
I = ib.complement_dofs(dofs)
u = solve(*condense(K, 0*u, I=I, x=u))
sf = 1.0
m.p += sf * u[ib.nodal_dofs]
"""
from skfem import *
from skfem.models.elasticity import linear_elasticity,\
lame_parameters
import numpy as np
from pathlib import Path
m = MeshTet.load(Path(__file__).parent / 'meshes' / 'beams.msh')
e1 = ElementTetP2()
e = ElementVectorH1(e1)
ib = Basis(m, e)
K = asm(linear_elasticity(*lame_parameters(200.0e9, 0.3)), ib)
rho = 8050.0
@BilinearForm
def mass(u, v, w):
from skfem.helpers import dot
return dot(rho * u, v)
M = asm(mass, ib)
L, x = solve(
*condense(K, M, D=ib.find_dofs()["fixed"]), solver=solver_eigen_scipy_sym()
)
]
mapping = MappingMortar.init_2D(m, M,
m.boundaries['contact'],
M.facets_satisfying(lambda x: x[0] == 1.0),
np.array([0.0, 1.0]))
mb = [
MortarFacetBasis(m, e, mapping=mapping, intorder=4, side=0, dofs=dofs1),
MortarFacetBasis(M, E, mapping=mapping, intorder=4, side=1, dofs=dofs2),
]
# define bilinear forms
youngs_modulus = 1000.0
poisson_ratio = 0.3
Lambda, Mu = lame_parameters(youngs_modulus, poisson_ratio)
weakform = linear_elasticity(Lambda, Mu)
C = linear_stress(Lambda, Mu)
alpha = 1000
limit = 0.3
# mortar forms
@BilinearForm
def bilin_mortar(u, v, w):
# jumps
ju = (-1.) ** w.idx[0] * dot(u, w.n)
jv = (-1.) ** w.idx[1] * dot(v, w.n)
nxn = prod(w.n, w.n)
mu = .5 * ddot(nxn, C(sym_grad(u)))
