Let’s first introduce the topic of linear and nonlinear analyses.
So for example for every pound of force you put in, you get 1 inch of displacement
So the relationship between how much force causes a set amount of displacement changes and that is why it is called nonlinear.
AutoPIPE’s nonlinear analysis engine uses two methods to handle piping models. The tangent stiffness strategy and the secant stiffness strategy which are both used by FEA programs like ANSYS & ABAQUS.
The tangent stiffness strategy handles all the supports with their gaps. The secant stiffness strategy handles friction.
The total load approach (like most pipe stress software uses) doesn’t understand boundary conditions and how the bearing force can change with the direction of the pipe movement which can possibly double the stress and load range.
For example the magnitude of the friction force as the pipe returns to ambient conditions after an operating condition will be the same magnitude but in the reverse direction and this could possibly double the stress and load range.
It is preferable to perform an incremental analysis (as is done in AutoPIPE) “to ensure no extreme load is overlooked.”
The incremental analysis approach is also the preferred approach of which follows the ASME code philosophy, discussed later
In 2009 ASME published the book Pipe Stress Engineering by L.C. Peng & Alvin Peng which stated that the analysis method used by many pipe stress software packages was incorrect and that the only valid method was used by programs like AutoPIPE.
This book mentions that there are 3 approaches to handling nonlinear analysis:General straight forward approach that many general purpose FEA programs use
The authors only recommend the “operating condition” method like AutoPIPE’s because it “meets the code philosophy and requirements” where the other two methods “have flaws”. See link here for complete details
In a nonlinear analysis, the sequence of the loads is important
The following is the default load sequencing in AutoPIPE
Let’s take a look at the thermal case as it hits the support. This figure shows the pipe movement from the gravity case to the thermal case. As we can see the pipe moves 0.2” in the negative Z direction and hits the support.
Now we will take a look at the seismic case. This figure shows the pipe movement from the gravity case to the seismic case. As we can see the pipe moves 0.306” in the positive Z direction.
And now we will look at the correct load sequencing load case which shows the pipe starting with gravity, (click) applies thermal case which hits the support gap, (click) then with the earthquake load moves to its final position which is 0.106” in the positive Z direction.
Non-linear Load Sequencing Explained