Modeling doubly curved surfaces

Problem/Question #

Can we model doubly curved surfaces using the AxisVM program?

In the program, the finite element method’s specific properties make defining a domain for curved surfaces impossible. The condition for defining a domain is that all its points are in one plane.

Explanation/Solution #

As it has been said, we cannot directly define such surfaces; we must use a certain kind of approximation in AxisVM to model such a structure. The first input condition for this is that we need a triangular mesh.

Triangular mesh #

We need the triangular mesh because the triangle is the simplest form in which, no matter how they stand, they will always designate a plane from the 3D space. Of course, by changing the size of the triangles, we can approximate our desired curved surface more and more, thus clarifying the results.

We can get this mesh from:

  • Given by the contractor, other disciplines (architectural, e.g.)
  • Manually (in an external program)
  • Parametrically (in an external program)

Of course, the most favorable option is to produce the network parametrically. In this way, the size of the triangulation can also be easily changed, which can increase the accuracy of the approximation. A program that can be used for this is the Rhino/Grasshopper pair, from where it can be perfectly transferred to AxisVM, any triangular network of any kind. And after importing the triangle mesh, we can define domains directly.

The network, of course, can be a . dxf import also or any kind of drawing file. Creating such a network of lines within the program is technically possible, but this is strongly not recommended. The next step is creating domains/interfaces if we have the network. Since there are two ways to proceed and only one is recommended in such a case, they will be discussed further.

Traditional – Domains #

In the traditional way, you create domains. This way, the program automatically meshes the surfaces according to the set parameters. This is not the best solution for curved surfaces where we work from a triangular mesh.

Advanced – finite element areas directly #

The program has an option that can be turned on, with which extra buttons appear on the toolbar. With these extra functions, we can skip the domain “level” and directly define a finite element area with the given properties.  These areas will not be meshed later by the software.

The switch for these buttons can be found at:

 

The functions that appear in the ‘Geometry’ and ‘Elements’ tabs are:

 

With the right-most function in the first image, we can find the enclosed surfaces (triangles, in our case) and make the software recognize them as areas for finite elements. Then, in the second image, we can set properties directly for these finite element areas.

Conclusion #

It can be said that it is possible to model curved surfaces, but for this to go smoothly and quickly, we will always need an external source. This is better for a parametric, dynamic connection to an external program such as Grasshopper, or it can be an imported drawing file.

It is important that triangulation should not be refined by defining domains on the triangular areas and then meshing them with smaller finite element mesh. The inner nodes of the FEM mesh will not be placed on the curved surface but formed in the plane of the triangles. Thus, the finite-element mesh will no longer be a model of the original, curved surface but of a surface consisting of flat “sheets” touching the original surface. The triangles meshed in their plane will be softer than the edges, so they will have local problems.