1. Lukasz Kaczmarczyk Avatar Lukasz Kaczmarczyk
  2. Project created by Lukasz
  3. mofem-joseph

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mofem-joseph / Cantilever Beam

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For the purpose of establishing the validity of moFEM's output a simple 2D linear elastic problem was constructed for which an an exact solution can be found.

Analytical Solution

The 2D cantilever shown below has an analytical solution for the displacement and stress profile. The material is isotropic with a Young's modulus (E) 106 N/m2 and the analysis uses the Euler–Bernoulli beam theory. Results are given to 6 significant figures.

2D Cantilever

Vertical displacement at end: 0.0400000m

Maximum stress at support: 6000.000 N 2

moFEM

Below is the geometry used for meshing the 3D beam and the corresponding mesh generated for it complete with boundary conditions. Differing levels of polynomial order were used to test the change in accuracy; the results of which can be found in the table.

Number of DOFs: 507 Number of elements: 316 Mesh scheme:TetMesh in Cubit Element type:Tetrahedral

3D Cantilever

test.

3D Mesh
Polynomial Order 1
Polynomial Order 5
moFEM Results
Poly Order Disp @ tip Stress @ support top
1 -0.00330253  
2 -0.0399973  
3 -0.0400024  
4 -0.0400024  
5 -0.0400024  

Conclusion

Shear stresses change Convergence to exact solution

Updated