Hello,

while trying to solve a linear elasticity problem where pure bending condition is applied to the beam as follows

which should produce values for eps_xy and eps_yy equal to zero.

However, while plotting the deformation tensor i obtain the following results for the various components:

- eps_xy

- esp_yy

Here is the code used for the solution of the linear elasticity problem:

```
from dolfin import *
import ufl as uf
# --- Mesh
L, H = 1, 0.1
nel = 75
mesh = RectangleMesh(Point(0, 0), Point(L, H), 100, 10, 'crossed')
ndim = mesh.topology().dim()
# --- Material Parameter
E = Constant(70e3)
nu = Constant(0.)
lmbda = E*nu/(1+nu)/(1-2*nu)
mu = E/2./(1+nu)
k = lmbda + mu*2/3.
# --- Function Spaces
V = VectorElement("Lagrange", mesh.ufl_cell(), 1)
V_u = FunctionSpace(mesh, V)
u = Function(V_u)
du = TrialFunction(V_u)
v = TestFunction(V_u)
u.rename('u', 'u')
S3 = TensorFunctionSpace(mesh, 'DG', 0)
Eps = Function(S3)
Eps.rename('E', 'E')
# ---Boundaries
class Left(SubDomain):
def inside(self, x, on_boundary):
return near(x[0], 0.0)
left = Left()
class Right(SubDomain):
def inside(self, x, on_boundary):
return near(x[0], L)
right = Right()
# ---Measures
boundaries = MeshFunction("size_t", mesh, mesh.topology().dim() - 1)
boundaries.set_all(0)
left.mark(boundaries, 1)
right.mark(boundaries, 3)
# ---Displacement BC
u_R = Expression("t*(0.5-x[1]/H)", H=H, t=0.05, degree=1)
bcu_l = DirichletBC(V_u, Constant((0., 0.)), boundaries, 1)
bcu_r = DirichletBC(V_u.sub(0), u_R, boundaries, 3)
bcu = [bcu_r, bcu_l]
# ---Definitions
def eps(u):
return sym(grad(u))
def sigma(u):
return 2. * mu * (eps(u)) + lmbda * tr(eps(u)) * Identity(ndim)
# --- Energy functional
psi = 0.5 * inner(sigma(u), eps(u))*dx
E_u = derivative(psi, u, v)
E_du = uf.replace(E_u, {u: du})
problem_u = LinearVariationalProblem(lhs(E_du), rhs(E_du), u, bcu)
solver_u = LinearVariationalSolver(problem_u)
# --- Solver
solver_u.solve()
File('u.pvd') << u
Eps.assign(project(eps(u), S3))
File("E.pvd") << Eps
```

Am i making mistakes in the solution of the elasticity problem or is this problem tied to the projection of the deformation tensor for the output?

Thanks in advance