janoskias
Aerospace
- Apr 29, 2021
- 2
Hey guys,
I'm new in FEM and stuck with the following problem (TLTR: question is if 2B is theoretically correct?, I am grateful for thoughts about the other ones (1 and 2A)):
I have a (geometric) non-linear 2D analysis (lets say a pulled rope) and I want to use TRUSS elements.
-----------------------------------------
Problem:
Let's consider a very simple case A |>o------o B, single TRUSS element, where A is fixed and B is moving.
I want B to move along a prescribed curve lets say c(x) = [x, f(x)].
I am not interested in the dynamics, only the equilibrium.
I struggle with the appropriate boundary condition. I have basically 2 ideas in my mind.
------------------------------------------
1. Instead of using the conventional truss element stiffness matrix, derive one with different shape function, which matches with c(x). I haven't tried it yet, and I want my trusses only carry axial loads,
it might also bring some non axial loads in? And it also should be recalculated for each curve.
2. Use the conventional stiffness matrix for the truss. (Geometric stiffness is also calculated and incremental force is added, c is linearized around B_x0, so c(x) = (x, n*x))
Then my calculation basically becomes:
Possibilities that come in my mind:
Thanks in advance.
I'm new in FEM and stuck with the following problem (TLTR: question is if 2B is theoretically correct?, I am grateful for thoughts about the other ones (1 and 2A)):
I have a (geometric) non-linear 2D analysis (lets say a pulled rope) and I want to use TRUSS elements.
-----------------------------------------
Problem:
Let's consider a very simple case A |>o------o B, single TRUSS element, where A is fixed and B is moving.
I want B to move along a prescribed curve lets say c(x) = [x, f(x)].
I am not interested in the dynamics, only the equilibrium.
I struggle with the appropriate boundary condition. I have basically 2 ideas in my mind.
------------------------------------------
1. Instead of using the conventional truss element stiffness matrix, derive one with different shape function, which matches with c(x). I haven't tried it yet, and I want my trusses only carry axial loads,
it might also bring some non axial loads in? And it also should be recalculated for each curve.
2. Use the conventional stiffness matrix for the truss. (Geometric stiffness is also calculated and incremental force is added, c is linearized around B_x0, so c(x) = (x, n*x))
Then my calculation basically becomes:
K*b = F_B
The A corresponding elements disappear, because A is fixed, so I have [k11,k12; k21,k22]*[bx; by] = [f_Bx; f_By] (1)Possibilities that come in my mind:
2A
Prescribe a condition for f_Bx/f_By = 1/n, this is not so good, because the B coordinates also modify the force components, so I need more iteration
Prescribe a condition for f_Bx/f_By = 1/n, this is not so good, because the B coordinates also modify the force components, so I need more iteration
2B
Modify K before inverting. If I write (1), and use that k12 = k21 then after a short derivation, if k12 = (f_By*k11-n*f_Bx*k22)/(f_Bx-n*f_By) then the solution for b will be [x, nx], so my condition is basically filled. But I don't know if my approach is right, or if there is a standard method for a problem like that.
Modify K before inverting. If I write (1), and use that k12 = k21 then after a short derivation, if k12 = (f_By*k11-n*f_Bx*k22)/(f_Bx-n*f_By) then the solution for b will be [x, nx], so my condition is basically filled. But I don't know if my approach is right, or if there is a standard method for a problem like that.
Thanks in advance.