examples

Gofem – examples

Summary

1. dynamics_sgbook -- Solid dynamics. Examples from Smith, Griffiths and Margetts book [1].
2. rjoint_ex01_curved -- Rod-Joint model for reinforced concrete [2,3].
3. rjoint_ex06_pullout -- Pullout test in reinforced concrete [2,3].
4. seep_ex01_freesurf -- Transient simulation with seepage face. Rectangle domain. [4]
5. seep_ex02_freesurf -- Transient simulation with seepage face. Earthen Slope. [4]
6. seep_simple_flux -- Simple flux in a horizontal permeameter. 2D and 3D simulations with computation of water discharge.
7. spo751_pressurised_cylinder -- Internally pressurised cylinder. Plasticity problem number 7.5.1 (page 244) from Souza-Peric-Owen (SPO) book [5].
8. spo754_strip_footing_collapse -- Strip-footing collapse. Plasticity problem number 7.5.4 (page 252) from Souza-Peric-Owen (SPO) book [5].
9. up_3mcolumn_desiccation -- Desiccation of porous column. Unsaturated porous media simulation from [6].
10. up_indentation2d_unsat -- Indentation of unsaturated porous medium. Similar to example in [6].

References

1. Smith, Griffiths and Margetts (2013) Programming the Finite Element Method. 5th Edition. Wiley. ISBN: 978-1-119-97334-8. 682 pages.
2. Durand, Farias and Pedroso (2015) A rod-joint finite element for reinforced solids without the need for mesh compatibility.
3. Durand, Farias and Pedroso (2015) Computing intersections between non-compatible curves and finite elements. Computational Mechanics. doi:10.1007/s00466-015-1181-y.
4. Pedroso (2015) A solution to transient seepage in unsaturated porous media. Computer Methods in Applied Mechanics and Engineering. 285:791-816. doi:10.1016/j.cma.2014.12.009.
5. de Souza Neto, E. A., Peric, D., and Owen, D. R. J. (2008) Computational Methods for Plasticity: Theory and Applications. Wiley. 791 pages. doi:10.1002/9780470694626.
6. Pedroso (2015) A consistent u-p formulation for porous media with hysteresis. International Journal for Numerical Methods in Engineering. 101:606-634. doi:10.1002/nme.4808.

1 dynamics_sgbook -- Solid dynamics

1.1 Forced vibrations. Single beam element with dynamic load

See page 487 of [1].

1.1.1 Geometry, mesh and boundary conditions

1.1.2 Results

1.2 Forced vibrations. Solid element with dynamic load

See page 491 of [1].

1.2.1 Geometry, mesh and boundary conditions

1.2.2 Results

1.3 Plastic slab with impacting distributed load

See page 515 of [1].

1.3.1 Geometry, mesh and boundary conditions

1.3.2 Results

2 rjoint_ex01_curved -- Rod-Joint model for reinforced concrete

A curved rod is immersed in a parallelepiped and has a force applied to one of its end.

2.1 Mesh

2.2 Results

3 rjoint_ex06_pullout -- Pullout test in reinforced concrete

Pullout test in reinforced concrete block.

3.1 Mesh

3.2 Results

The plot shows the displacement of rod nodes for a number of time outputs. 'y' is the length of the rod starting from 0.20 because the rod is inside the beam.

4 seep_ex01_freesurf -- Transient simulation with seepage face

Modelling the seepage face using enriched element as proposed in [4]. The right hand side of a block of porous medium has the liquid pressure decreased thus inducing flow from left to right. See video of similar simulation here.

4.1 Mesh

4.2 Results

5 seep_ex02_freesurf -- Transient simulation with seepage face

Modelling the seepage face using enriched element as proposed in [4]. The right hand side of a earthen slope has the liquid pressure decreased thus inducing flow from left to right. See video of similar simulation here.

5.1 Mesh

5.2 Results

6 seep_simple_flux -- Simple flux in a horizontal permeameter

Cylinder with porous media under seepage only. With gravity. To the left hand side hydrostatic pressure is kept constant. To the right hand side, pressure is decrease by the following shift

hst specifies a shift of liquid pressure according to:

$$ pl(t,z) = pl_0(z) - shift(t) $$

hydrost must be true in stages

dvgctrl divergence control will reduce the time step in case divergence occurs

6.1 2D: Mesh

6.2 2D: Results

6.3 3D: Results

7 spo751_pressurised_cylinder -- Internally pressurised cylinder

See page 244 of [5]. Pressure is applied to the edge tagged with -10. The material is modelled using the von Mises model.

7.1 Mesh

7.2 Results

8 spo754_strip_footing_collapse -- Strip-footing collapse

See page 252 of [5]. Displacement is applied to the region corresponding to the footing at the left hand side. von Mises model is used.

8.1 Mesh

8.2 Results

TODO.

9 up_3mcolumn_desiccation -- Desiccation of porous column

Desiccation of a 3 metres high column of porous medium. The bottom of the column has pressure specified. This pressure varies causing desiccation of column.

9.1 Mesh

9.2 Decreasing and increasing the pressure.

9.3 Linearly decreasing the pressure to reach unsaturated state.

9.4 Wetting of initially unsaturated column.

10 up_indentation2d_unsat -- Indentation of unsaturated porous medium

This example shows the indentation of an unsaturated soil. First, the domain is made unsaturated by means of decreasing the pressure at the bottom. The next simulation the applies the indenter at the surface. Two ways of modelling this problem are considered:

• a and b simulations -- lower the pressure at bottom and apply the load
• c and d simulations -- dry the medium by means of flux prescribed at the surface then apply the load

10.1 Mesh

The size of the domain is 3 x 3 in units of length.

10.2 Results -- first stage by lowering pressure

10.3 Results -- first stage by drying surface