def apply(f, coords):
x, y = symbols("x y")
return lambdify((x, y), f.subs({R.x: x, R.y: y}))(*coords)
u_exact = 1 + R.x + 2 * R.y # exact solution
f = -divergence(q(u_exact) * gradient(u_exact)) # manufactured RHS
mesh = MeshTri()
mesh.refine(3)
V = InteriorBasis(mesh, ElementTriP1())
boundary = V.get_dofs().all()
interior = V.complement_dofs(boundary)
@LinearForm
def load(v, w):
return v * apply(f, w.x)
b = asm(load, V)
@BilinearForm
def diffusion_form(u, v, w):
return sum(v.grad * (q(w["w"]) * u.grad))
L = 1.0
W = 0.2
mu = 1.0
rho = 1.0
delta = W / L
gamma = 0.4 * delta**2
beta = 1.25
lambda_ = beta
g = gamma
mesh = MeshTet.init_tensor(np.linspace(0, L, 10 + 1), np.linspace(0, W, 3 + 1),
np.linspace(0, W, 3 + 1))
basis = InteriorBasis(mesh, ElementVectorH1(ElementTetP1()))
clamped = basis.get_dofs(lambda x: x[0] == 0.0).all()
free = basis.complement_dofs(clamped)
K = asm(linear_elasticity(lambda_, mu), basis)
@LinearForm
def load(v, w):
return -rho * g * v.value[2]
f = asm(load, basis)
u = solve(*condense(K, f, I=free))
deformed = MeshTet(mesh.p + u[basis.nodal_dofs], mesh.t)