Thanks for your lecture! But there is a typo,,, In 8:2614:00, you have to time delta_t at the end. Becuase V(+dt) = V(t) + [(1-beta)... + (beta)...] * "delta_t". It was a helpful lecture. Thanks Again!!!
set \alpha = 0.25 and \delta = 0.5 (this will give constant average acceleration), \delta T is problem dependent - aim for 25 timesteps over the shortest period of interest
The time integration doesn't change for a nonlinear system, but you would need to incorporate an iteration loop to achieve convergence in an implicit scheme.
I hope to in the future, I have other priorities for courses at the moment. I'd definitely recommend the book 'Finite Element Procedures' by K J Bathe for details on how to implement these methods and restrictions on the time step size in explicit dynamics.
Thanks for your lecture! But there is a typo,,,
In 8:26 14:00, you have to time delta_t at the end.
Becuase V(+dt) = V(t) + [(1-beta)... + (beta)...] * "delta_t".
It was a helpful lecture. Thanks Again!!!
oops, yes 2nd eqn at these timestamps should have \Delta T after the square brackets. Hope the procedure was useful anyway.
Great video greetings from germany
Glad it was useful. I just use YT for video hosting content for my own students, but always glad to hear if they're of use to others.
how do we get thoses constants to calculate a1 a2 a3 ... ?
set \alpha = 0.25 and \delta = 0.5 (this will give constant average acceleration), \delta T is problem dependent - aim for 25 timesteps over the shortest period of interest
this is assuming that your dynamical system is linear and your M, K and D matrices does not change with time, correct?
The time integration doesn't change for a nonlinear system, but you would need to incorporate an iteration loop to achieve convergence in an implicit scheme.
Could you please tell, where do we perform Newton-Raphson iterations in this implicit algorithm.
This is just Newmark for time stepping linear problems only. You would need to have N-R loop inside of each time step for non-linear problems.
Sir, what about Explicit time integration? Are you going to post a lecture about that topic?
I hope to in the future, I have other priorities for courses at the moment. I'd definitely recommend the book 'Finite Element Procedures' by K J Bathe for details on how to implement these methods and restrictions on the time step size in explicit dynamics.
@@ProgrammedMechanics Tank You a lot!
@@ProgrammedMechanics Just wanted to reiterate that I would really love to see a similar video on explicit! Thank you!
Richard Ayoade is this you?
No my name is Maurice Moss ;-)
@@ProgrammedMechanics 😆