# Problems implementing the linear elasticity tutorial on Google Colab **URL:** \ **Category:** General\ **Created:** [November 23, 2023, 6:29pm UTC](https://fenicsproject.discourse.group/t/problems-implementing-the-linear-elasticity-tutorial-on-google-colab/12843 "2023-11-23T18:29:18Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![Jpalma](https://avatars.discourse-cdn.com/v4/letter/j/c67d28/32.png) [@Jpalma](https://fenicsproject.discourse.group/u/Jpalma)\ **Post date:** [November 23, 2023, 6:29pm UTC](https://fenicsproject.discourse.group/t/problems-implementing-the-linear-elasticity-tutorial-on-google-colab/12843/1 "2023-11-23T18:29:18Z")
I’ve been trying to implement the [linear elasticity tutorial](https://jsdokken.com/dolfinx-tutorial/chapter2/linearelasticity_code.html) on Google Colab using a [FEM on Colab](https://fem-on-colab.github.io/packages.html) installation of dolfinx 0.8.0.0. So far I have been unable to properly set a constant vector for the Dirichlet boundary condition of the problem. So far I’ve been using the exact code of the implementation, except for the use of `fem.functionspace` instead of `fem.VectorFunctionSpace` This is the code I’ve been using so far ```auto from dolfinx import mesh, fem, default_scalar_type from mpi4py import MPI import ufl import numpy as np L = 1 W = 0.2 domain = mesh.create_box(MPI.COMM_WORLD, [np.array([0, 0, 0]), np.array([L, W, W])], [20, 6, 6], cell_type=mesh.CellType.hexahedron) V = fem.functionspace(domain, ("Lagrange", 1)) def clamped_boundary(x): return np.isclose(x[0], 0) fdim = domain.topology.dim - 1 boundary_facets = mesh.locate_entities_boundary(domain, fdim, clamped_boundary) u_D = np.array([0, 0, 0], dtype=default_scalar_type) bc = fem.dirichletbc(u_D, fem.locate_dofs_topological(V, fdim, boundary_facets), V) ``` However, I always get the following error ```auto --------------------------------------------------------------------------- TypeError Traceback (most recent call last) /usr/local/lib/python3.10/dist-packages/dolfinx/fem/bcs.py in dirichletbc(value, dofs, V) 174 try: --> 175 bc = bctype(_value, dofs, V) 176 except TypeError: TypeError: __init__ (): incompatible function arguments. The following argument types are supported: 1. __init__ (self, g: ndarray[dtype=float64, writable=False, order='C'], dofs: ndarray[dtype=int32, writable=False, shape=(*), order='C'], V: dolfinx.cpp.fem.FunctionSpace_float64) -> None 2. __init__ (self, g: dolfinx.cpp.fem.Constant_float64, dofs: ndarray[dtype=int32, writable=False, shape=(*), order='C'], V: dolfinx.cpp.fem.FunctionSpace_float64) -> None 3. __init__ (self, g: dolfinx.cpp.fem.Function_float64, dofs: ndarray[dtype=int32, writable=False, shape=(*), order='C']) -> None 4. __init__ (self, g: dolfinx.cpp.fem.Function_float64, dofs: list[ndarray[dtype=int32, writable=False, shape=(*), order='C']], V: dolfinx.cpp.fem.FunctionSpace_float64) -> None Invoked with types: dolfinx.cpp.fem.DirichletBC_float64, ndarray, ndarray, dolfinx.fem.function.FunctionSpace During handling of the above exception, another exception occurred: RuntimeError Traceback (most recent call last) 1 frames /usr/local/lib/python3.10/dist-packages/dolfinx/fem/bcs.py in dirichletbc(value, dofs, V) 175 bc = bctype(_value, dofs, V) 176 except TypeError: --> 177 bc = bctype(_value, dofs, V._cpp_object) 178 else: 179 bc = bctype(_value, dofs) RuntimeError: Rank mis-match between Constant and function space in DirichletBC ``` This error can be bypassed by using `u_D = default_scalar_type(0)`. However, this generates issues with the dimension of the boundary condition latter on. Can anybody help me understand what is going wrong with this impementation? ---
**Author:** ![nate](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/nate/32/17_2.png) [@nate](https://fenicsproject.discourse.group/u/nate)\ **Post date:** [November 23, 2023, 6:36pm UTC](https://fenicsproject.discourse.group/t/problems-implementing-the-linear-elasticity-tutorial-on-google-colab/12843/2 "2023-11-23T18:36:00Z")
You likely need to provide shape to your function space. Something like ```python V = fem.functionspace(domain, ("Lagrange", 1, (mesh.geometry.dim,))) ``` ---
**Author:** ![Jpalma](https://avatars.discourse-cdn.com/v4/letter/j/c67d28/32.png) [@Jpalma](https://fenicsproject.discourse.group/u/Jpalma)\ **Post date:** [November 23, 2023, 7:26pm UTC](https://fenicsproject.discourse.group/t/problems-implementing-the-linear-elasticity-tutorial-on-google-colab/12843/3 "2023-11-23T19:26:04Z")
Thanks for the answer. I’ve tried the suggested code and it solved my issue. However I do not quite understand why the shape is provided in the form `(shape, )` Anyways, thank you very much! ---
**Author:** ![dokken](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/dokken/32/1560_2.png) [@dokken](https://fenicsproject.discourse.group/u/dokken)\ **Post date:** [November 23, 2023, 9:39pm UTC](https://fenicsproject.discourse.group/t/problems-implementing-the-linear-elasticity-tutorial-on-google-colab/12843/4 "2023-11-23T21:39:15Z")
> [@Jpalma](#): > > However I do not quite understand why the shape is provided in the form `(shape, )` In the old version of dolfinx, you had the Notion of a vector Finite element space. That is a space where a single basis function is repeated over multiple dimensions (such as a vector or tensor), with unique coefficients per dimension). In the 0.8.0 code, UFL has removed the Notion of such elements, and we Therefore provide a triplet to define the Finite element: 1. The family, here Lagrange 2. The degree of the element, here 1 3. how it should be repeated over multiple dimensions. Default is a single dimension (a scalar), and otherwise you send in a tensor of the appropriate shape, in your case a (3,) vector, which can be generalized by the geometrical dimension of your mesh. ---
**Author:** ![Jpalma](https://avatars.discourse-cdn.com/v4/letter/j/c67d28/32.png) [@Jpalma](https://fenicsproject.discourse.group/u/Jpalma)\ **Post date:** [November 24, 2023, 3:03pm UTC](https://fenicsproject.discourse.group/t/problems-implementing-the-linear-elasticity-tutorial-on-google-colab/12843/5 "2023-11-24T15:03:47Z")
Thanks, that makes it a lot clearer to me!