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
def gap(x):
"""Initial gap between the bodies."""
return (1. - np.sqrt(1. - x[1]**2))
M = asm(mass, gb)
D = gb.find_dofs({'left': m.facets_satisfying(lambda x: x[0] == 0.)})
y = gb.zeros()
I = gb.complement_dofs(D)
L, x = solve(*condense(K, M, I=I),
solver=solver_eigen_scipy_sym(k=6, sigma=0.0))
y = x[:, 4]
# calculate stress
sgb = gb.with_element(ElementVector(e))
C = linear_stress(lam, mu)
yi = gb.interpolate(y)
@LinearForm
def proj(v, _):
return ddot(C(sym_grad(yi)), v)
sigma = projection(proj, sgb, gb)
if __name__ == "__main__":
from skfem.visuals.matplotlib import plot, draw, show
M = MeshQuad(np.array(m.p + y[gb.nodal_dofs]), m.t)
ax = draw(M)
plot(M, sigma[sgb.nodal_dofs[0]], ax=ax, colorbar=True)
show()