Greetings researchers!
I am using FEM to obtain the time response of the nonlinear forced vibration of plates. I am using plate elements based on Reddy's HSDT and Newmark time integration in conjunction with the Newton-Raphson iteration to obtain the time response.
It is well known that multiple steady-state solutions can exist in the case of nonlinear forced vibrations. Also, all steady-state solutions are not stable. In practice, unstable solutions are not realizable and the system assumes any one of the stable solutions depending on the initial conditions.
I was curious to know whether the FEM predicts only stable steady-state solutions. Or does it predict stable and unstable solutions and the stability of the predicted solutions needs to be determined through other means?
Thank you for your valuable time.
With best regards,
Jatin
Jatin Poojary Can you share your finite element model in an appropriate format?
Nils Wagner sir, I am sorry but since it is an in-house code and still under development, I am unable to share it presently.
Time integration will give only steady solutions. In case you need to trace unsteady use continuation techniques.
Thank you Praveen Krishna I R sir for your answer. However, I could not understand the reason behind your statement that time integration will give only steady-state solutions.
The finite element approximation results in a system of ordinary differential equations in time. Through time integration, one obtains the response of the system as time progresses. Therefore, if I am not mistaken, it should consist of both the transient component as well as the steady-state component.
If possible, could you kindly elaborate on the same?
I think Praveen meant stable solutions and not steady. To get unstable solutions you can integrate backward in time or use continuation methods to trace steady-state stable and unstable solutions including bifurcations.
Thank you Chandramouli Padmanabhan sir and Praveen Krishna I R sir for the clarification.
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