Clamped Beam under the End Load Problem

1

Hello, the program in the link is not working.

https://fenicsproject.org/qa/13149/clamped-beam-under-the-end-load-problem/
I tired to use the suggestion in there
class PointLoad(Expression):
def init(self, **kwargs):
self.point = kwargs[‘point’]
self.value = kwargs[‘value’]
def eval(self, value, x):
if near (x[0], self.point[0]) and near(x[1], self.point[1]):
value[0] = self.value[0]
value[1] = self.value[1]
else: # Reset the input variable because it’s likely to be reused
values[0] = 0
values[1] = 0
def value_shape(self):
return (2,)

This part is giving an error.
T = PointLoad(point=(1.0,.2), value=(0,-10), degree=0)

RecursionError Traceback (most recent call last)
in ()
----> 1 T = PointLoad(point=(L,.2), value=(-1), degree=0)

How can I solve this problem? I want to add a point force at the end

2

This is due to a change in User-interface for Expression. See for instance: RecursionError: maximum recursion depth exceeded in the ft11_magnetostatics.py example of the "Solving PDEs in Python - The FEniCS tutorial Part 1" or Problem defining initial conditions : Expression problem?

3

Thank you, The code is like this now, I got this error.
AttributeError: ‘PointLoad’ object has no attribute ‘_ufl_shape’

    from dolfin import *
    from ufl import nabla_div

    # Load mesh and define function space
    L = 10.
    W = 1.
    # Mesh for cantilever beam
    Omega = BoxMesh(Point(0, 0, 0), Point(L, W, W),100, 3, 3)
    Omega.init()
    V = VectorFunctionSpace(Omega, "CG", 1)
    tol = 1.e-8 # tolerance
    # Left boundary
    class Left(SubDomain):
        def inside(self, x, on_boundary):
            return near(x[0], 0.0)
    # Right boundary
    class Right(SubDomain):
        def inside(self, x, on_boundary):
            return near(x[0], L)
    class PointLoad(UserExpression):
        def __init__(self, **kwargs):
            self.point = kwargs['point']
            self.value = kwargs['value']
        def eval(self, value, x):
            if near (x[0], self.point[0]) and near(x[1], self.point[1]):
                value[0] = self.value[0]
                value[1] = self.value[1]
            else:  # Reset the input variable because it's likely to be reused
                values[0] = 0
                values[1] = 0
        def value_shape(self):
            return (2,)
    # Point (8,0.5,0.5) at which load is added
    #class point(SubDomain):
     #   def inside(self, x, on_boundary):
      #      return near(x[0],L) and near(x[1],0.8,1e-5) and near(x[2],0.8,1e-5)
    ## dokken: @0.5 no dof 
        
    #class point(SubDomain):
     #   def inside(self, x, on_boundary):
      #      return on_boundary and  abs(x[0]-L) < 0.2 and abs(x[1]-0.5) < 0.2  and abs(x[1]-0.5) < 0.2 
     #Boundary segments
    left = Left()
    pt = point()
    right = Right()
    boundaries = MeshFunction("size_t", Omega,0)
    boundaries.set_all(0)
    left.mark(boundaries, 1)
    pt.mark(boundaries, 2)
    u = TrialFunction(V)
    v = TestFunction(V)
    f = Constant((0.0, 0.0, -1e-3))
    # Elasticity parameters
    E = 1e5
    nu = 0.3
    mu, lmbda = Constant(E/(2*(1 + nu))), Constant(E*nu/((1 + nu)*(1 - 2*nu)))
    # Strain
    def eps(u):
        return sym(grad(u))
    model = "plane_stress"
    mu = E/2/(1+nu)
    lmbda = E*nu/(1+nu)/(1-2*nu)
    if model == "plane_stress":
        lmbda = 2*mu*lmbda/(lmbda+2*mu)
    def sigma(u):
        return lmbda*tr(eps(u))*Identity(3) + 2.0*mu*eps(u)
    # Define variational problem

    ds= Measure("ds", domain=Omega, subdomain_data=boundaries)
    #g_T= Constant((0.0, 0.0, -0))`Preformatted text`
T = PointLoad(point=(L,.2), value=(0,-10), degree=0)
a = inner(sigma(u), grad(v))*dx

left_end_displacement = Constant((0.0, 0.0, 0.0))
bc = [DirichletBC(V, left_end_displacement, left)]
l=  dot(f, v)*dx +dot(v,T)*ds
# Compute solution
u = Function(V)
solve(a == l, u, bc)
print("Maximal deflection:", -u(L,1,1)[2])
4

Dear Amy, please search through the forum before posting every new error message. Then you can find it for instance in: Subdomains with different material properties