Let’s talk today about an interesting topic, Transient analysis!

Most people start FEA simulation with linear static analysis, because it is the most simple type of analysis available, but the “static” hypothesis is not always valid and in some cases, there is no choice but to go for a transient study!

If you have not so much experience in FEA, going directly to transient analysis might be daunting, because **there is a lot of additional knowledge required!**

As usual, let’s get there step by step…

## What is the different between static and transient analysis?

Static and transient both refer to the consideration of time in the physical equations.

In a “static” analysis, we basically ignore the impact of time and consider that our simulation results do not depend on time.

In general, this is because:

- We apply the loads “very slowly” (no dynamic effect during application)
- The loads once applied do not change in time (No time dependency of the load amplitude or direction)
- The system studied interests us when it is at equilibrium.

When any of those is not true, for example, the load has a value which changes with time, then we have to go for a dynamic transient analysis.

(I am talking more in depth about static analysis in the free course, check it out if you are interested to know the details)

In a “transient” analysis, we remove some of the hypothesis we made to be able to perform a “static” analysis so that the solution is now able to reflect the time dimension.

It may seem like a “small change”, but actually, this is a big change. Once we consider time, the basic mechanical equations change to take in account the time dependent phenomena such as damping and inertia.

**Here’s a simple example:**

Imagine a person weighting 100 kg sitting on a fragile chair:

If this person sits very slowly and then remain immobile, the chair may hold.

But, if this person jump backward on the chair **brutally**, the chair will probably break.

This is all due to the **added contribution of inertia and its dynamic effect! **

## What is the transient state of a system?

Now that you understand that doing a transient analysis means simply that we want to study time, let’s talk briefly about transient VS steady state.

Imagine that all systems have 2 main states, a transient and a steady state.

The transient state is basically the state the system is in when it starts until it reaches equilibrium.

Once the system reaches equilibrium, it starts working steadily along time and many of its behaviors become stable and constant and that’s what we call the “steady state” of the system.

It’s difficult to understand without giving a concrete example

A simple example I like is to think about the hot and cold water coming out of your shower in the morning.

When you turn the tap the first time and the water starts flowing, it is generally cold, then you turn the tap in the right direction to control the temperature of the flow.

If you have a good shower installation and the response time of the system is fast, you might get instant hot water (I hope you do!!)

What happens to me very often however is that the temperature takes a significant time to reach the ideal “equilibrium” steady state temperature.

It is first very hot, then cold, then midly hot, then not so cold, then it start to be closer and closer to body temperature! (That’s when it feels the best ;-) )

When you are interested to study the transient state, you basically say:

*Okay, I want to fix what happens between the opening of the tap and the perfect temperature because it don’t know why the the system takes so long to reach ideal temperature!*

In reality, most systems are in constant transient state as they receive some influence from the external environment around them.

Some systems are very stable, so small disturbance of the environment around won’t disturb much and the system goes back to equilibrium very quickly.

Other systems are notoriously unstable… and some of them even by design. Think about Nuclear Fission. A single neutronic impulse is what starts the atomic explosion (or think about explosives!)

So I tend to think about steady state as a simplification of the reality which is sometimes relevant… and sometimes not!

## What will change in my FEA simulation if I perform a transient analysis?

**First**, you have now to consider the contribution of mass, inertia and damping into your system.

A Static system doesn’t need to have a mass because the acceleration is null in the equation and this term disappears in the equations bring the mass with him.

Note that you still need the mass information (and thus the density property in your material) if you have a gravity body load applied to your system!

In a transient system, make sure the mass of your model is correct and that the damping model chosen is correct as well.

**Second change** is that your load will probably have a dependency to time now so you will probably have to define a forcing function with a certain time distribution to be assigned to your load.

**Third change** is that your system being transient dynamic, you will have to use a different solver to get results!

A static solver just solves everything at once by simply inverting the stiffness matrix.

**A dynamic solver is much more complex** as it requires to integrate time and thus requires an incremental procedure to go through the time solve.

There are 2 main methods to integrate time, the **implicit method** and the **explicit method**.

This is pretty complex stuff so I won’t enter in the details here, but if you are interested, watch carefully this webinar I did last year which explains the difference between explicit and implicit.

In short, you will have to look at your analysis as a succession of time steps, rather than a simple matrix inversion.

For implicit, time steps can be large, but your analysis my diverge because the error is too large (Think about how the Euler time integration method works all you’ll understand why). | For explicit, time steps have to be very small otherwise system becomes unstable. Thus the scope is limited to very fast systems. But the good news is that if your time step and mesh are small enough, system becomes unconditionally stable and thus you don’t get as much convergence problem like you might get with implicit. |

Conclusion is… You will have to be very careful about the time step you choose and make sure it is small enough

**Fourth change** will come with the post-processing of time-domain results which will from now on…depend on time!

## Can my model be transient and nonlinear at the same time?

Yes, of course!

Nonlinearity and Transient Behavior are different concepts.

You can have both a nonlinear model that you also need to study in a transient condition!

A classic example is a drop test or a car crash. Both have violent deformation in a very short time which requires a nonlinear transient calculation!

If you are interested by nonlinear, check those articles that are available on the blog:

- How to define a nonlinear material in FEA?
- 5 simple tips that will simplify your life in nonlinear FEA analysis

## How to get started with transient analysis?

The best way is always to start to get your model working with a static analysis if allowed by your FEA software (even if this may be wrong)

In FEA, the best way to go is always to start with something simple!

This will allow you to troubleshoot basic modeling mistakes such as:

- Wrong geometry
- Meshing not working/ not good enough
- And Many other more specific problems linked to the specific FEA software you are using…

Once you get that working, add the dynamic aspect to your simulation and try to change the model so that it can calculate.

In particular:

- Review material properties, density, damping, etc…
- Check your forcing time function
- Think about the eventual time dependency of your material
- Chose wisely the solver and the integration method
- Have a strategy to post-process efficiently the (many) time domain results

That’s all for today! I hope this is insightful for you if you are starting your path towards a “Transient” simulation Journey!

*Let’s hope this knowledge will become steady in your mind and not just transiently enter from one ear and leave from the other ;-) *

Joke apart, let me know in the comments if you have questions, I am always happy to read those comments and to provide some direction.

Stay safe!

**Cyprien “getting your steady FEA knowledge” Rusu — FEAforall**

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