From: bangerth Date: Fri, 3 Jun 2011 02:24:16 +0000 (+0000) Subject: Turn one paragraph into a @note. Fix a formatting problem. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=fafb70e79c4e73984a5c592e8f98d1f2f8a89668;p=dealii-svn.git Turn one paragraph into a @note. Fix a formatting problem. git-svn-id: https://svn.dealii.org/trunk@23782 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-18/doc/intro.dox b/deal.II/examples/step-18/doc/intro.dox index 9f56d3a0a2..10940ee4cd 100644 --- a/deal.II/examples/step-18/doc/intro.dox +++ b/deal.II/examples/step-18/doc/intro.dox @@ -554,6 +554,7 @@ The program text will reveal more about how to implement this situation, and the results section will show what displacement pattern comes out of this simulation. +

Possible directions for extensions

The program as is does not really solve an equation that has many applications @@ -563,7 +564,9 @@ more interesting experiments, and that indeed was the initial motivation for writing it. Here are some suggestions of what the program is missing and in what direction it may be extended: -
Plasticity models
The most obvious extension is to use a more +
Plasticity models
+ + The most obvious extension is to use a more realistic material model for large-scale quasistatic deformation. The natural choice for this would be plasticity, in which a nonlinear relationship between stress and strain replaces equation [stress-strain]. Plasticity @@ -596,7 +599,9 @@ elastoplasticity: I. Mixed displacement-pressure formulation” pp. 3559-3586, 2004). -
Stabilization issues
The formulation we have chosen, i.e. using +
Stabilization issues
+ +The formulation we have chosen, i.e. using piecewise (bi-, tri-)linear elements for all components of the displacement vector, and treating the stress as a variable dependent on the displacement is appropriate for most materials. However, this so-called displacement-based @@ -627,7 +632,9 @@ elasticity” (Computer Methods in Applied Mechanics and Engineering, vol. 1 pp. 1093-1112, 2005). -
Refinement during timesteps
In the present form, the program +
Refinement during timesteps
+ +In the present form, the program only refines the initial mesh a number of times, but then never again. For any kind of realistic simulation, one would want to extend this so that the mesh is refined and coarsened every few time steps instead. This is not hard to do, @@ -658,7 +665,9 @@ different kind of problem, giving indications on how to approach the problem for time-dependent adaptivity as well. -
Ensuring mesh regularity
At present, the program makes no attempt +
Ensuring mesh regularity
+ +At present, the program makes no attempt to make sure that a cell, after moving its vertices at the end of the time step, still has a valid geometry (i.e. that its Jacobian determinant is positive and bounded away from zero everywhere). It is, in fact, not very hard @@ -671,21 +680,7 @@ sophisticated version definitely should employ some sort of heuristic defining what amount of deformation of cells is acceptable, and what isn't. -

Compiling the program

- -Finally, just to remind everyone: the program runs in 3d (see the definition -of the elastic_problem variable in main(), unlike almost -all of the other example programs. While the compiler doesn't care what -dimension it compiles for, the linker has to know which library to link with. -And as explained in other places, this requires slight changes to the Makefile -compared to the other tutorial programs. In particular, everywhere where the -2d versions of libraries are mentioned, one needs to change this to 3d, -although this is already done in the distributed version of the Makefile. -Conversely, if you want to run the program in 2d (after making the necessary -changes to accommodate for a 2d geometry), you have to change the Makefile -back to allow for 2d. - -There is an additional caveat: PETSc appears not to co-operate well when using +@note PETSc appears not to co-operate well when using threads and the program crashes when deal.II is compiled in its usual mode supporting multithreading. The program can therefore only be compiled and run if multithreading is disabled upon configuration of deal.II using the