f. Advanced Nonlinear Analysis - Linear vs. Non-Linear analysis in AutoPIPE

Let’s first introduce the topic of linear and nonlinear analyses.

Linear analysis definition

Pipe properties are constant
Deflections are small
Elastic deformation (pipe goes back to original shape)

So for example for every pound of force you put in, you get 1 inch of displacement

Nonlinear analysis definition

Pipe properties change over time
Large deflections
Plastic deformation can occur (pipe is permanently deformed)

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.

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

Algebraic subtraction which our competitor’s like caesar use
Operating condition approach which AutoPIPE uses

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

Why is Load Sequencing so Important?

In a nonlinear analysis, the sequence of the loads is important

The principle of superposition does not apply in a nonlinear analysis, therefore, the starting point for a load case is important

The following is the default load sequencing in AutoPIPE

Gravity (GR) is analyzed with no initial state
Thermal load cases are analyzed with GR as the initial load case
Pressure load cases are analyzed with the corresponding thermal load case as the initial load case
Occasional load cases are analyzed with GR as the initial load case

Load Sequencing – Example 1 Results

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.