A collection of different numerical examples implemented in deal.ii

"A numerical example is worth a thousand equations." [Frans Paul VAN DER MEER, Dissertation-Propositions]

... and takes about as many lines of code.

Proposal for updated standard:

• group additional parameter
• create standalone make_grid, with all parameters are explicit input argument

Still being implemented consistently: From the 04.01.2021 we obey a new standard (numExS11).

• contain member variable named body_dimensions (see Bar_model), which contains characteristic dimensions (length, width, thickness) and maybe also some for paths (e.g. the location of the evaluation path);
• incorporating contact and many more numerical examples (updated soon)

Major changes:

• clean-up
• contact
• member variable named body_dimensions, which contains characteristic dimensions (length, width, thickness)

From the 24.07.2020 we obey a new standard (numExS07).

Major changes:

• clean-up of boundary ids
• option to specify the loading direction and the loaded faces

• add the enumerator_list
• add an exemplary call to make_constraints, make_grid
• change the interfaces of the make_grid functions to obtain the same setup as the deal.ii geometries (all dimensions and parameters as explicit input arguments)
• add a note on the difference between the qplate and the infinite plate (maybe add analytical solution code from PA)
• add a few pictures of the meshes here
• add a documentation (input arguments, interface)
• update the QPlate grid with the new deal.ii function plate_with_a_hole
• add optional parameters/switches (e.g. apply z-sym on pos z-face) as global variables into a standardised framework

*** @todo *** document the interfaces

• make_grid(*):

    QuarterHyperCube_Merged::make_grid<dim> ( triangulation, parameter );
    loading_direction = QuarterHyperCube_Merged::loading_direction;
    boundary_id_collection[enums::id_primary_load] = QuarterHyperCube_Merged::id_boundary_load;
    boundary_id_collection[enums::id_secondary_load] = QuarterHyperCube_Merged::id_boundary_secondaryLoad;

Creates the triangulation (2D or 3D), requires additional parameters (can also be hardcoded into the function) and boundary ids (std::vector<enums::enum_boundary_ids> boundary_id_collection).

• make_constraints(*):

			QuarterHyperCube_Merged::make_constraints<dim> ( constraints, fe, n_components, dof_handler_ref, apply_dirichlet_bc,
															 load_increment, parameter);

Apply the boundary conditions onto the faces, e.g. symmetry BC.

The names try to be as general as possible. Look closely, there are many options, so e.g. the HyperRectangle is not just a rectangle, but can be notched multiple times by defined round notches.

By setting the number of global refinements to zero, you obtain the one-element test. For number of global refinements equal to 1 (in 3D) you obtain 8 Elements arranged as a cube, which can also be distorted internally (overall still a cube, but distorted but matching elements inside). With the option (twitch) the Dis8El version can also be twitched, so it is no longer a cube

@todo add picture of OET and distored OET

For the bar or sheet strip (just a matter of the width) initial inhomogenous refinements are available. For finite plasticity, we recommend making the finer mesh part approximately a square to also capture the shear bands (develop for isotropy at 55°).

Parameters

Be aware that you can also choose the geometry of the notch (round, sharp), which might affect your results.

• Total length of the rod
• Radius of the cylindrical part
• length of the notch
• Radius of the leftover material in the notch (or specify the tool radius)
• Number of elements in the notched area in y-direction (number of repetitions)
• Number of elements in the cylindrical part in y-direction

It's parameterised so you can also change the geometry.

For this example to work you require the assemble routines for contact that are NOT yet available online.

Bending of a notched beam

!!! Not developed anymore, version frozen in March 2020 !!!