# How does FEM software compute inertial forces?

• zoltrix
In summary, a FEM software can apply specific acceleration only such as centrifugal load or linear acceleration/deceleration, or they can handle a general dynamic situation.
zoltrix
TL;DR Summary
FEM for machine design
Hello

I have alwayes seen FEM applications for static structures while each " finite element" of a bar linkage mechanisms should be subjected also to a variable inertial force besides its constant weight
how do FEM softwares compute inertial forces ?

Start with the equation of conservation of momentum. Apply the same steps as in the static case; the result is a system of ordinary differential equations for the evolution of displacement over time.

in principle I know how to take into account also the inertial forces
The point is that , to my knowdlege, all FEM softwares consider only static structures

I was curious so I googled

'non inertial reference frame in ansys'

Some interesting info

zoltrix said:
The point is that , to my knowdlege, all FEM softwares consider only static structures
Exactly what kind of structures and operating conditions do you want to consider ? With a proper level of model simplification and dynamic analysis (supported by almost all FEA programs) it should be possible to account for all such effects. And then there's software meant specifically for multibody dynamics.

zoltrix said:
I have alwayes seen FEM applications for static structures while each " finite element" of a bar linkage mechanisms should be subjected also to a variable inertial force besides its constant weight
how do FEM softwares compute inertial forces ?
The option you are looking for is usually called "inertia relief". It allows to analyse non-inertial bodies by introducing inertial forces.

A.T. said:
The option you are looking for is usually called "inertia relief". It allows to analyse non-inertial bodies by introducing inertial forces.
I'm not sure what the OP is looking for (and thus I asked him for some more details) but it seems that he needs a dynamic analysis or MBD since he mentioned mechanisms. Inertia relief is used to stabilize unconstrained (or not fully constrained) models - it balances applied loads to avoid rigid body motions.

yes I had in mind a dynamic analysis
you can study a mechanism in motion same as it were a static structure provide you add also the inertial forces
a kind of trick
I went through several FEM examples but it seem that they deal only with true static structures
Apparentely there is no mention of the inertial forces even in case of analysis of machines
As I said, each finite element should be subjected also to a local inertial force proportional to its mass and acceleration

Last edited:
zoltrix said:
yes I had in mind a dynamic analysis
you can study a mechanism in motion same as it were a static structure provide you add also the inertial forces
a kind of trick
This is commonly done for rotating structures. Instead of running a transient dynamic analysis, one can apply centrifugal force load (available in most FEA programs) in a static analysis. And there are more loads like this for rotating structures. For example, Abaqus offers also Coriolis forces, rotary acceleration and rotordynamic loads in a fixed reference frame. Of course, gravity load is also available in every FEA software to apply various accelerations (not necessarily only those caused by gravity but also the deceleration of a braking car, for instance) in static analyses.

berkeman
given a body you can distinguish :

- local forces -surface forces and body forces

the body forces are distributed overe the whole volume
in case of a static structure there is one only body force : the weight
in a machine you should add also the inertial forces changing over time and point to point

do you mean that FEM software can apply specific acceleration only such as centrifugal load or linear acceleration/deceleration or can they handle a general dynamic situation

are you familiar with Fusion 360 ?

in other words, take an assembly :

piston-rod-crankshaft

pston is subjected to linear acceleration/ deceleration so FEM analysis is possible
crankshaft is subjected to centrifugal forces again , it is ok
Can a FEM software calculate stress and displacement of the rod ?

With transient analysis using direct implicit time integration, it shouldn't be a problem to solve something like this. Not all FEA programs support such analyses but the standalone ones (like Abaqus or ANSYS) should handle it easily.

berkeman and Lnewqban
Impressive

berkeman

## 1. How does FEM software calculate inertial forces?

FEM software calculates inertial forces by using the mass and acceleration of each element in the finite element model. It uses the equation F=ma, where F is the inertial force, m is the mass, and a is the acceleration. The software then sums up the inertial forces of all elements to get the total inertial force of the structure.

## 2. What is the role of mass in calculating inertial forces in FEM software?

Mass is a crucial factor in calculating inertial forces in FEM software. It represents the amount of matter in an object and is used in the equation F=ma to calculate the inertial force. The mass of each element in the finite element model is used to determine its contribution to the total inertial force of the structure.

## 3. How does FEM software handle the distribution of mass in a structure?

FEM software uses the concept of lumped mass and distributed mass to handle the distribution of mass in a structure. Lumped mass assumes that the entire mass of an element is concentrated at a single point, while distributed mass considers the mass to be distributed throughout the element. The software uses a combination of these approaches to accurately calculate the inertial forces.

## 4. Does FEM software consider the direction of the inertial force?

Yes, FEM software takes into account the direction of the inertial force. The direction is determined by the direction of the acceleration, which is typically in the direction of the applied load. The software uses vector calculations to accurately determine the direction and magnitude of the inertial force for each element in the finite element model.

## 5. How does FEM software handle the effect of rotational motion on inertial forces?

In FEM software, rotational motion is taken into account by using the moment of inertia of each element. The moment of inertia represents the resistance of an object to rotational motion and is used in the equation for calculating the inertial force. The software uses this value to accurately determine the effect of rotational motion on the inertial forces in the structure.

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