Tutorials

Before you do anything else, please just read through the list of Keywords on the Help page. Else the below is going to make very little sense.

2D problems

Tutorial 1

NOTE:- This is a work in progress, check back again soon, I should have it finished in the next two weeks or so.

Problem

Two loads acting on a 30x30 square area, supported at two locations at the bottom. What is the stiffest structure I can place inside the area to resist the two loads?

Note that the bottom left constraint can 'slide' in the horizontal direction (along the X-axis).

Trivial solution

The stiffest possible structure we can place in our 30x30 domain (region/area) is simply to put material everywhere in the domain, but that's exactly what we don't want to do.

ToPy solution (non-trivial)

Solution for limited material usage

Assume we don't have material to fill the 30x30 area, let's say we only have 20x20 (400) elements that we need to place in the 900 possible locations in our grid, but where to place them to obtain an optimally stiff structure? The solution to this problem is topology optimisation.

Approach

We start with a 30x30 grid, with loading (forces at nodes) and constraints (fixtures at nodes) as shown in the figure above (the red arrows are the loads) applied at the relevant node numbers. Note that the node numbering is from top left corner downwards -- all 2d ToPy problems must follow this numbering scheme. The mesh was created using ToPy's create_2d_msh function, the mesh is viewed in Gmsh.

The mesh was created by using ToPy's create_2d_msh function that is defined in the visualisation module: >> create_2d_msh(30, 30, 'tut1')

This will create a file named 'tut1.msh' that can be opened and viewed with Gmsh.

Define the TPD file

Open a text editor, for example Notepad on Windows. The first line of a TPD file [ToPy Problem Definition File v2007]