Beam Model Simulation in GETFEM

Questions and issues
1

Hello everyone,

I want to ask if it’s possible to do a beam model simulation in GetFEM? I’ve tried to search in the Documentation but I couldn’t find it.

Thank you and have a great day.

Best regards,

2

Hello,

If you mean to model a beam with solid elements, this is quite easy.

If you mean to use beam elements to model a larger structure, GetFEM is not very good at it. It is possible but it is probably easier for you to model the beam elements directly.

Could you please clarify a bit more which of the two cases you are interested in?

3

Hello,

Thank you for your response.

The beam model I’m talking about is the center line model of a complex beam structure. The theory for this model which is well known is the Euler-Bernoulli beam theory.

Can we launch the simulation for this kind of model in GetFEM.

Thank you

4

I don’t think that GetFEM is your best option for making a model consisting of beam elements. It will just make your modeling more complicated without offering you any other significant advantages.

The basic idea of GetFEM is to make difficult problems easy, but if you have an already rather simple problem at hand it is not the best option.

5

Do you know a way to implement the beam elements into GetFEM ?

I choose getFEM because right now its adapted to almost everything i need. It just doesn’t have beam element. And i couldn’t find another FEA open source has beam element also.

Thank you.

6

it is possible to define beam elements using Hermite shape functions for the bending part and linear element for the axial deformations. These two components will give you the same local element stiffness matrix as in the usual beam theory. If the beam elements are in arbitrary orientations in 2D or 3D space you will need to do the local to global coordinate transformation and the coupling between the elements manually.

There is a previous discussion about beam elements here
https://lists.gnu.org/archive/html/getfem-users/2017-11/msg00026.html

Based on Jean Francois’ code from this reference, defining beam elements using only Hermite shape functions would look something like this (but still the code does not yield correct results, needs some debugging)

#!/usr/bin/env python

import getfem as gf
RG_FIXED = 99;
m = gf.Mesh("import", "structured",
               f"GT='GT_PK(1,1)';ORG=[0.];SIZES=[5.];NSUBDIV=[10]")
#m.transform([[1.],[0.5]]) # inclined beam
m.transform([[1.],[0.]]) # horizontal beam
m.set_region(RG_FIXED, m.outer_faces_in_box([-1e-5,-1e-5], [1e-5,1e-5], 1)) # select lower left corner
m.export_to_vtu("mesh.vtu")
mfu = gf.MeshFem(m,2)
mfu.set_fem(gf.Fem("FEM_HERMITE(1)"))
mfl = gf.MeshFem(m,1)
mfl.set_fem(gf.Fem("FEM_PK(1,1)"))
mim = gf.MeshIm(m,2)
mimd = gf.MeshImData(mim,-1,2) # "-1" means the entire domain
md = gf.Model("real")
md.add_fem_variable("u",mfu)
md.add_im_data("Tvec", mimd)
md.add_im_data("Nvec", mimd)
md.add_macro("Tvecdef", "Normalized(element_K)")
md.add_macro("Nvecdef", "[0,-1;1,0]*Normalized(element_K)")
md.set_variable("Tvec", md.interpolation("Tvecdef", mimd))
md.set_variable("Nvec", md.interpolation("Nvecdef", mimd))
md.add_linear_term(mim,"0.5*sqr((Grad(u)*Tvec)).Tvec")
md.add_linear_term(mim,"0.5*sqr(((Hess(u).Tvec).Tvec).Nvec)")
md.add_linear_term(mim,"0.01*Test_u(2)") # uniform vertical load
md.add_Dirichlet_condition_with_multipliers(mim,"u",mfu,RG_FIXED)
#md.add_linear_term(mim,"1e6*u.Test_u", RG_FIXED) # fixed position left node by penalization
md.add_filtered_fem_variable("lag_slope", mfl, RG_FIXED)
md.add_linear_term(mim,"lag_slope*Nvecdef.Grad(u).Tvecdef", RG_FIXED)
md.solve()
mfu.export_to_vtu("beam.vtu","ascii",mfu,md.variable("u"),"u")