#### Topic: Different Lagrangian formulation

Hi,

I have two questions:

How can I choose "Semi" Updated Lagrangian Formulation in ATENA? (Table 1.6-1 - Theory Manual)

Does Total Lagrangian Formulation corresponds to Geometrically Linear analysis? (And updated Lagrangian formulation to geometrically nonlinear?)

Thank you,
Kamal

#### Re: Different Lagrangian formulation

Dear kamal2,
as far as I understand, the semi-updated corresponds to linear geometry, the updated to nonlinear, see also ATENA Troubleshooting, 2.1.9 Does the non linear analysis of ATENA consider the geometrical nonlinearity (second order effects, like buckling or necking)?

Is there any specific reason (doubt?) which brings this question?

Regards.

#### Re: Different Lagrangian formulation

Dear dpryl,

I am aware of ATENA Troubleshooting 2.1.9 but that is not what I am exactly asking about. I am trying to understand what does the program do different by activating "geometrical nonlinearity". I have looked at an element and the two approaches (geom. linear vs geom. nonlinear) and the load displacement (or stress-strain) relationship for both are identical.

Also, when I look at Table 1.6-1 ATENA_Theory, there are 3 different option and I am confused which one is which and how to choose each one during an analysis.

Thank you,
Kamal

#### Re: Different Lagrangian formulation

Dear kamal2,
as explained in Troubleshooting, 2.1.9, "linear" means the geometry (deformed shape) is updated once per step, i.e., the shape from the previous step is used throughout all iterations of the next step, and the deformation increments are calculated using small deformation assumptions [from the previous step end as reference state].

"Nonlinear" means the deformed geometry is updated in each iteration.

If there is a specific reason why you are asking about this, maybe it would be easier to explain/understand in that particular context...

Regards.