second order mid-point scheme

[Xuannamdo-danang]

Dear Admin,

I currently would like to solve a dynamic problem by second order mid-point scheme. Howerver, in Feap only the first order generalized midpoint method is available. Thus, I have been looking for some ducuments to understand computational procedure implemented by second order mid-point scheme (the effective stiffness matrix, mass matrix and so on). However, none of them presented this scheme.

Could you please explain to me about the second order mid-point scheme or tell mE any document in which the second order mid-point schem is shown?

Thank you so much and I am waiting for your reply

Yours sincerely,
DO XUAN NAM

[Prof. R.L. Taylor]

What is the mid-point algorithm you are seeking?  Do you have a reference?  There are implementations for the "alpha" and "hht" forms, but they do not use the mid-point.  The "cons" method is mid-point but generally not applicable to general problems.

[Xuannamdo-danang]

Dear Professor Taylor,

Thank you so much for your reply

I use implicit second order midpoint scheme like a picture 11, which is captured from textbook of Professor Adnan IBRAHIMBEGOVIC, in attached file.

Because there is no more details like Newmark scheme or Wilson theta method (see also attached file) I really do not know how the effective stiffness matrix/mass matrix is and then what/how needs to updated in dyna.f subroutine (I intend to write a new dyna.f for the second mid-point scheme)

Hope to receive your explain and advice

Yours sincerely,
DO XUAN NAM

[Prof. R.L. Taylor]

Did you look at the report on implementing the Wilson theta method?

http://faculty.ce.berkeley.edu/sanjay/FEAP/ucb_semm_2010_07.pdf

[Xuannamdo-danang]

Dear Professor Taylor,

Yes, I looked at and even read carefully Wilson theta method.

How can I apply Wilson theta method to become a true second mid-point scheme?

Thank you so much

Yours sincerely,
DO XUAN NAM