Static and dynamic analysis are two important techniques used in finite element analysis (FEA).

When you start out working in design simulation and using finite element analysis software, the terms static and dynamic analysis will start appearing everywhere.

But what is the difference between dynamic analysis and static analysis?

**The difference between dynamic and static analysis is time. Dynamic analysis involves some load or stimulus that changes over time. Typically, these loads happen quickly. In static analysis, the loads are applied so slowly that inertia and time do not have an effect. **

In this article, I want to dig deeper into the concepts of static and dynamic analysis so, as designers, we will know what type of analysis to use and when to apply it.

I will cover:

- What Is A Static Analysis?
- What Is A Dynamic Analysis?
- What Is The Difference Between Static And Dynamic Analysis?
- When Should You Use Dynamic Or Static Analysis?

## What Is Static Analysis?

Systems or bodies that are in a perfect state of equilibrium can be studied using static analysis.

Such a component, body, or system must have zero acceleration (no motion) and no loading that changes with time.

The simplest way to think of static analysis is a simple system where your load is applied and will never change. It is constant and therefore static.

### Examples Of Static Stress Analysis Applications

The most frequent form of finite element structural analysis is static stress analysis. The component or assembly is put through a number of loads and the resulting stress, strain, and deformation are analysed to determine the design’s chances of failure.

Here are some examples of static analysis:

- Bridge design
- Vehicle frames
- Mounting brackets
- Housing design

In the above simulation types, the loads applied are of steady state and constant magnitude.

## What Is Dynamic Analysis?

The three primary types of dynamic analysis needed in product design are:

- Frequency Analysis (Takes place in the frequency domain)
- Transient Analysis (Takes place in the time domain)
- Random Response Analysis (Input fits no simple pattern)

As the name implies, ‘dynamic’ implies that something is changing.

With dynamic analysis, time is a factor, and loads changing with respect to time must be calculated using dynamic analysis.

Inertial loads due to acceleration, for example, must be modelled using dynamic analysis. Alternatively, if the loads are not in the time domain, they can also be in the frequency domain for dynamic analysis.

### Examples Of Dynamic Analysis Applications

If a load is applied to a system, body or component with a vibratory or sinusoidal input, then it is probably dynamic and dynamic analysis should be used.

Similarly, if a load is generated by an impact or a collision, it is dynamic.

Here are some examples of dynamic analysis applications:

- Impact analysis
- Component drop test analysis
- Vibrational analysis (although you should use modal analysis here)
- Buckling analysis

## When Should You Use Dynamic Or Static Analysis?

Static analysis is far less time-consuming and simpler than dynamic analysis, but what type of analysis should you choose for your application?

A vast amount of simulations can be completed using static analysis, even if there are some brief time or frequency influences at the time of load application.

Many engineers will opt for a static solution as it is fast, and the cost involved regarding time and software is much higher for dynamic analysis.

However, if your application involves a time or frequency component, such as an impact test, a dynamic analysis should be used.

It is possible to use what is called the “Static Assumption” which assumes that all loads are gradually applied until they reach a full magnitude.

Using a static load equivalent, it is possible to complete a static analysis (where a dynamic is needed) and increase your load by an additional factor to take into account the dynamic loading.

However, if you use a static analysis where a dynamic is appropriate, even if the initial loads to the system are vibratory or short, you must always check against a dynamic solution.

A static run might be great to debug, check your mesh and model setup, but a dynamic problem should always be solved with a dynamic analysis.

### Static Analysis Summary

- Used to calculate stress, strain, and deformation under constant loads
- Generally faster and simpler than dynamic analysis
- May not be as accurate for problems involving time or frequency

### Dynamic Analysis:

- Used to calculate stress, strain, and deformation under time-varying loads
- More accurate than static analysis for problems involving time or frequency
- May be more complicated and take longer to run

## Final Thoughts

Static and dynamic analysis are two important methods of finite element analysis.

Static analysis is used to calculate the stress, strain, and deformation of a component or assembly under constant loads, while dynamic analysis calculates the stress, strain, and deformation of a component or assembly under time-varying loads.

In most cases, static analysis can be used to solve a problem, but if time or frequency are factors in the load application, a dynamic analysis must be used.

Both static and dynamic analysis have their own strengths and weaknesses, so choosing the right type of analysis depends on the specific problem that needs to be solved.

In general, static analysis is faster and simpler than dynamic analysis, but dynamic analysis is more accurate for problems that involve time or frequency and should always be used for this time of engineering problem.