What is a Rigid Body Mode?

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Recently when I asked my subscribers for a blog post topic, I received a ton of awesome suggestions, thank you to all of those who took the time to send me those. So picking one out those many great suggestions, in this post we will discuss the term “Rigid Body Mode”. Ready? Let’s go…

So what exactly is a rigid body mode?

Normally, when you hear someone say rigid body mode, the first thing that comes to mind is Modal or Normal Modes analysis. It is true that a rigid body mode is in fact commonly encountered in such analyses. However, there are other analysis types where this term is also used. For example, in a linear static or a non linear static analysis. Surprised? Don’t be, let us look at the definition of a rigid body mode.

Definition of a Rigid body Mode:

A rigid body mode is defined as the free translation or rotation of a body without undergoing any significant internal deformation.

For a free free normal modes analysis where there are no loads or constraints, there will be 6 rigid body modes, three translational (TX, TY, TZ) and three rotational (RX, RY, RZ). This means the body will not undergo any internal deformation but will be able to move or rotate freely. These first 6 modes will have zero or close to zero modal frequency. If any part of this rigid body is constrained in any way, the corresponding rigid body mode will go away. So now let us talk about using this to our advantage in a linear static or nonlinear static analysis.

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Rigid Body Mode in a static analysis:

So we now know what a rigid body mode is in terms of a normal modes analysis. But what the heck is it doing in a linear static analysis? It is actually quite simple. A rigid body mode in a linear static analysis is basically a ‘mechanism’ that exhibits a rigid body mode.

What in the world is a mechanism you ask?

A mechanism is any part of the model that is a joint, or a link or a load path where two elements are connected together at a common node. If there is a lack of constraint or stiffness in a particular direction and there is some kind of applied loading in that direction, then the system will either move or rotate in that direction unrestrained which results in a fatal error when you run the analysis. This behavior is termed as a ‘mechanism’, similar to mechanisms in machines.

So how can one manage to create unwanted mechanisms in a static analysis?

The answer actually lies in the question. A static analysis is based on the satisfactory convergence of equations of equilibrium. The applied load throughout the load path must be balanced by the total reaction at the end of the load path thus resulting in a static equilibrium.

There are tolerances and parameters in the FEA solver that will abort the analysis if these convergence parameters are exceeded due to modeling issues. So what kind of modeling issues could produce such mechanisms in a static analysis? The following list includes some common modeling issues:

  • Lack of adequate constraints
  • Too much load relative to stiffness
  • Too little stiffness
  • Coincident nodes that are disconnected
  • Bad elements
  • Young’s modulus that is missing a few zeros
  • Huge differences in stiffness from one member to the next
  • Improperly defined RBE elements
  • And incompatible nodal DOFs at connected elements, among other possible modeling errors

In a static analysis the usual suspects are either lack of constraints, coincident nodes that are supposed to be merged, or material issues. And this results in an uncontrolled motion of that part of the model resulting in the failure of the analysis. In other words, your model may have a rigid body mode in terms of a mechanism that is free to move or rotate.

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Example: Just for arguments sake, imagine a door panel (doors are usually not included in the cabin interiors models) that is modeled with hinges on one side and a latch on the other side. If the latch side is unconstrained and there is a pressure load on the door, the very nature of the hinge results in a free rotation about the vertical axis of the hinge, this is a rigid body mode or a mechanism. See the figure below.

Mechanism Example
Mechanism Example

One of the best ways to capture issues like these in the structure models is to run a simple normal modes analysis using the same static model. Same constraints but no loads. If there is noting else wrong with the model and it runs, then look at the first few modes, animate the mode shapes. The mechanism will stand out as a sore thumb, indicating clearly where the problem is so you can go in and fix it.

While a rigid body mode may be bad in some situations, there are definitely ways we can use it to our advantage. That's it folks.

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Surya Batchu
Surya Batchu

Surya Batchu is the founder of Stress Ebook LLC. A senior stress engineer specializing in aerospace stress analysis and finite element analysis, Surya has close to a decade and a half of real world industry experience. He shares his expertise with you on this blog and the website via paid courses, so you can benefit from it and get ahead in your own career.