Importing general curved shell mesh in FEniCS

General
1

Hi FEniCS family,

I wanted to use FEniCS shells for 8 noded shell element mesh imported externally like Abaqus (.inp).

  1. The examples shown in documentation created their own shell mesh through 2D rec mesh and projecting the coordinates. (ref: Clamped semi-cylindrical Naghdi shell under point load — fenics-shells,
    But, for general mesh, how can I import it and is it similar to previous case of converting to xml from msh.

  2. What shape functions are used to interpolate the shell coordintes in xyz physical space to 2 curviliinear coordinates. In demo, a bubble function is used which I do not understand. Aren’t there any specific shape functions like Lagrange/Hermite like (N1 = 0.25*(1- eta)(1-xi)(-1-eta-xi), upto N8).
    Can you give me the details of shape functions usage (FEM) related to shell elements ?

Any help is greatly appreciated.

2

The model you refer to in FEniCS-Shells, which used DOLFINx, relies on an explicit map between the parametric and real shell geometry. The finite elements you are referring to in 2. are the ones used to approximate the field variables, not the geometry (we are not using an isoparametric formulation where field variables and geometry are approximated using the same interpolation).

With my colleagues here at University of Luxembourg we have a new shell formulation implementation for DOLFINx where the geometry is approximated using a mesh of arbitrary order using Lagrangian basis functions. I need to organise getting it into our repository: GitHub - FEniCS-Shells/fenicsx-shells: A FEniCS Project-based library for simulating thin structures It will probably not be till after Christmas though…

1 Like
3

Thanks @jackhale for your response. I greatly appreciate for giving your valuable time.

  1. When you say “geometry is approximated”, Can I understand it as any arbitrary geometry like complex wind turbine blades where we know only nodes and connectivity in physical space xyz?

  2. I am glad to know that you are working on using lagrangian functions.
    When you say, “mesh of arbitrary order of Lagrangian basis functions”, can I know the basis functions expressions in terms of curvilinear coordinates? This would help me to verify numerically (over known cylinder /spherical shell) that, the basis functions are exactly interpolating the shell geometry to build confident.

Can same basis functions be used to interpolate displacement and rotations?