# AceGen: Solving the dynamic equation in the middle of the time step

Note: This question is about AceFEM and AceGen package for automatic code generation for finite element analysis.

If the question is not specific enough, I will try to refrase it, but I am a fairly new user of AceGen/AceFEM package, so I hope this is not an extremely trivial question.

During non-linear dynamic analysis of a shell structure, I would like to compute the equation of motion at the generalized mid-point configuration as written in the equation bellow.

In order to achive that, I compute the left side of equation at times tn+1-alpha_f and tn+1-alpha_m, but I am not completely sure if I am using the right approach to compute the external load at time tn+1-alpha_f.

The weak form of equations is written using the virtual work, so in the end I get an equation for the residual in a form:

Residual=Jacobin*w/alpha_f*(.....)


When doing the analysis in AceFEM, where the load is time-dependent, I use the same basic iteration loop as is shown in the AceFEM tutorial Example: simultaneous incrementation of time and BC multiplier. The load multiplier is changed using the command SMTNextStep[dt,lambda_f].

In case of alpha_f=1/2, does this ensure that the external load is taken at the middle of the time step?

• This is definitely not a trivial question! Could you please provide more explanation of what are you trying to do, ideally with a very simple example? – Pinti Jun 16 '17 at 7:38
• It is hard for me to formulate a good question, but basicly all of the stated above can be boiled down to: How to implement the mid-point integration scheme for non-linear dynamics in AceGen? – marko Jun 19 '17 at 6:54