Hello,

Is the nonlinear analysis algorithm in Caesar II the same as other general FEA softwares by using the Newton-Raphson method with force convergence criteria?

Mostly all posts in this forum just mention nonlinear properties (gap, friction, resting support) but no discussion about the algorithm.

I wouldn't call it Newton-Raphson, but force/restraint convergence is a better description.

That's about the name of the description. Actually, I think you are mentioning convergence criteria only, not about analysis procedure

My question is: is Caesar II process the same as the nonlinear analysis procedures from other FEA software (such as Ansys) which is using the Newton-Raphson method?

What I understand the way Ceasar II processes nonlinear analysis is as follows:

Basically, if the model has no +Y restraints (instead of that, just only Y restraints), no friction, no gaps. Then the software will solve equation F=KX only one time, and no iterations are required

If +Y restraints, friction, and gaps are included in the model. Then the software will solve equation F=KX and check whether the following convergence criteria are met:

Criteria 1: the global stiffness matrix K matches the positions of restraints

Criteria 2: the friction normal load variation within 15%

Criteria 3: the friction angle variation within 15 degree

If the above criteria 1 is not met, the K matrix shall be updated by adding or removing restraint stiffnesses at non-converge restraints. I understand the software has nothing to update in the K matrix if criteria 2 and 3 are not met. However, the software will update F vector if there is a tendency to move greater than the friction force by replacing friction restraints with the force vector. But I'm still confused about what kind of force. Is it only friction force? Or together with the force pulling the pipe to move to be updated?

Also, I understand that, when the K and F are updated, the software will solve again equation F=KX with the initial configuration of the model. There is no update of Displacement increments, no increment of load, and no check of Force convergence like the Newton-Raphson method.

The term "iteration" in Ceasar II can be understood as rerun F=KX from the beginning after resetting the K and F. It's different from the continuous iterations of the Newton-Raphson method.

Is this the way Ceasar doing for nonlinear boundary conditions?

Yes, you are correct.

Hi Richard,

Thank you for replying

Could you also confirm whether the below image matches what I said ?

Can you confirm?

In addition, I see the way Caesar II doing as what I mentioned similar to the method called "Secant stiffness". Am I right?

I'm quite curious behind the sense of CII algorithm for nonlinear analysis.

Looking for response

Yes, your sketch above is how the algorithm works.