awolfgang
Civil/Environmental
- Jul 15, 2012
- 6
Hello,
I am not familiar with non-linear FEM, just learning on my own using text books, so apologies for this basic question.
I am trying to use a software which has a linear elastic analysis capability to convert it into a nonlinear elastic model. I could migrate to other programs which have the capability to solve nonlinear analysis but my model is not just to do with nonlinear elasticity.
I see that a nonlinear analysis requires solution of the following equation (assuming modified N-R method).
K(t)*delta_U(i) = R(t+delta_t) - F(t+delta_t,(i-1))
(R=ext load, F=int forces, i=iteration in a given load step, delta_U=incremental displacement)
The existing software gives me the global (no element level) K and R vectors. But no access to internal force vector, F. So my question is how to compute internal force vector for the next iteration.
I thought of the following procedure. Is this correct?
For the first iteration, I solve for delta_U as:
Equation 1 -- K(t)*delta_U(i) = R(t+delta_t) (because F is zero, assuming no initial displacements or stresses)
Equation 2 -- U(i)=U0+delta_U(i) (i=1, of course U0 = 0, in the first iteration)
For the second iteration, I would need to have F(i-1) (internal forces) vector, which I calculate as:
Equation 3 -- F(i-1) = K(t)*U(i-1) (i=2; in other words U(1) above)
But I guess from the F(i-1) vector I should take away reaction forces (at constraint points or edges). I am not sure.
And so on....
Of course, when I look at many free nonlinear FEM programs, I see that the internal force vector is computed at the end of each iteration at the element level first and then assembled at the global level. Why don't they simply use Equation 3 that I show above.
I am may be totally wrong.
Can anyone please help me.
Regards
Albion
I am not familiar with non-linear FEM, just learning on my own using text books, so apologies for this basic question.
I am trying to use a software which has a linear elastic analysis capability to convert it into a nonlinear elastic model. I could migrate to other programs which have the capability to solve nonlinear analysis but my model is not just to do with nonlinear elasticity.
I see that a nonlinear analysis requires solution of the following equation (assuming modified N-R method).
K(t)*delta_U(i) = R(t+delta_t) - F(t+delta_t,(i-1))
(R=ext load, F=int forces, i=iteration in a given load step, delta_U=incremental displacement)
The existing software gives me the global (no element level) K and R vectors. But no access to internal force vector, F. So my question is how to compute internal force vector for the next iteration.
I thought of the following procedure. Is this correct?
For the first iteration, I solve for delta_U as:
Equation 1 -- K(t)*delta_U(i) = R(t+delta_t) (because F is zero, assuming no initial displacements or stresses)
Equation 2 -- U(i)=U0+delta_U(i) (i=1, of course U0 = 0, in the first iteration)
For the second iteration, I would need to have F(i-1) (internal forces) vector, which I calculate as:
Equation 3 -- F(i-1) = K(t)*U(i-1) (i=2; in other words U(1) above)
But I guess from the F(i-1) vector I should take away reaction forces (at constraint points or edges). I am not sure.
And so on....
Of course, when I look at many free nonlinear FEM programs, I see that the internal force vector is computed at the end of each iteration at the element level first and then assembled at the global level. Why don't they simply use Equation 3 that I show above.
I am may be totally wrong.
Can anyone please help me.
Regards
Albion
