Transient Dynamic Time integration scheme

[zhnanli]

Dear everyone,
 
I have some questions about the time integration schemes of transient dynamics.
 
1. For the Newmark family of methods with predictor-corrector, are they explicit time integration schemes? 

2. From Prof. Hughes, "There are no unconditionally stable predictor-corrector schemes", then what are the advantages of the methods with predictor-corrector over the standard methods.

3. For low speed dynamics, is it more appropriate to apply the time integration schemes without predictor-corrector format. The principal use of time integration schemes with predictor-corrector format is for problems like wave propagation and impact problems.

Hope for help!

Best wishes,
zhnanli

[Prof. R.L. Taylor]

We do not implement predictor-corrector methods.  In FEAP Newmark is implemented in both explicit and implicit form.  In some cases a problem may be split to use explicit for some elements and implicit for others.

The advantages or disadvantages of a time integration scheme often depends on the specific class of problems being considered.

[zhnanli]

Thanks for your reply! I found the predictor-corrector methods is not suitable for transient dynamic analysis considering geometric nonlinearity, such as rubber materials(large strain elasticity). During the calculation, the Jacobian of the finite elements sometimes has negative values, or need more iterations than the Newmark family of methods without predictor-corrector.

[zhnanli]

Dear Prof. Taylor,
In FEAP Theory Manual,"For an implicit solution it is best to select the initial value for the iterate as shown in Figure 1. Any other choice may perturb the displacements in such a way to cause false inelastic values, especially near boundaries, which impede convergence of the Newton method".

In the article"Implicit-explicit finite elements in nonlinear transient analysis" and other articles about implicit-explicit finite elements in transient analysis by Prof. Hughes, the initial value is selected as shown in Figure 2. It involves a predictor phase and a corrector phase. As feap theory says, it may perturb the displacements and impede convergence of the Newton method.

As I know, the predictor-corrector methods are often used in multiphysics problems, like FSI.

Do the predictor-corrector methods have advantages in solid nonlinear finite element analysis?

Best wishes
zhnanli

[Prof. S. Govindjee]

I do not think that it is possible to make blanket statements about whether or not P-C algorithms are a good idea or not a good idea.  Such matters are very problem dependent.  Thus one needs to try the algorithms out and then select the one that performs best on one's problems of interest.

No single algorithm is always the best algorithm.

[zhnanli]

Dear Prof. S. Govindjee,

I will keep these two formats in my own finite element program and test them in more engineering cases.

[alphayash]

I do not think that it is possible to make blanket statements about whether or not P-C algorithms are a good idea or not a good idea.  Such matters are very problem dependent.  Thus one needs to try the algorithms out and then select the one that performs best on one's problems of interest. Momix VidMate

No single algorithm is always the best algorithm.

I totally agree with your statement as I personally think there is no 1 perfect algorithms that solves everything, in fact for the same problems different people prefer different solution or has different needs which can be solved by different algorithms respectively