## Why displacement formulation always lead to over stiff representation of the structure?

## Why displacement formulation always lead to over stiff representation of the structure?

(OP)

To all,

While doing some reading on FE related matters I came across the statement:

While I am fully aware of the issue of elements such as the 4-nodes tetra (the famous TET4) being too stiff and requiring a fine mesh to be effective/accurate why is the general statement made above ?

I understand from that statement that all displacement-based elements are inherently too stiff: Why is that? Is it in opposition to the

Thanks

Regards

While doing some reading on FE related matters I came across the statement:

*displacement formulation always lead to over stiff representation of the structure*While I am fully aware of the issue of elements such as the 4-nodes tetra (the famous TET4) being too stiff and requiring a fine mesh to be effective/accurate why is the general statement made above ?

I understand from that statement that all displacement-based elements are inherently too stiff: Why is that? Is it in opposition to the

__hybrid formulation__of the element stiffness?Thanks

Regards

## RE: Why displacement formulation always lead to over stiff representation of the structure?

I'm working with Abaqus since many years and I've never heared of that - and this does not only include Abaqus.

## RE: Why displacement formulation always lead to over stiff representation of the structure?

incidentally some "random" web searched produced this link

http://www.twi-global.com/technical-knowledge/faqs/structural-integrity-faqs/faq-what-is-reduced-integration-in-the-context-of-finite-element-analysis/

where the statement is repeated

## RE: Why displacement formulation always lead to over stiff representation of the structure?

another day in paradise, or is paradise one day closer ?

## RE: Why displacement formulation always lead to over stiff representation of the structure?

Imposing a restraint on a structure will never decrease its overall stiffness, and will usually increase its overall stiffness. When you set up an FE model of a structure you discretise it into a set of finite elements. Within each of these finite elements you impose a (mathematical) restraint that its displacement field will be described by a set of parabolic or cubic or quintic or hyperbolic or whatever equations. Left to its own devices, the element's displacement field would prefer to adopt a slightly different displacement field. So this mathematical restraint will "artificially" stiffen the overall structure. If the assumed displacement field is a good approximation to the actual displacement field, the amount of artificial stiffening will be small.

## RE: Why displacement formulation always lead to over stiff representation of the structure?

When we discretize our geometry into some number of elements,that number of elements is always significantly less than the number of atoms/molecules that actually make up the material. As a result, fewer degrees-of-freedom in the model, make for a more stiff model than reality which has more degrees-of-freedom to move.

When we are building FEA models, and performing convergence checks, we are trying to determine the size of the mesh that is small enough to represent the actual system to our desired level of precision.

## RE: Why displacement formulation always lead to over stiff representation of the structure?

That section may point toward volumetric locking, where fully integrated elements might have to many 'constraints' when the incompressibility needs also to be enforced.

## RE: Why displacement formulation always lead to over stiff representation of the structure?

## RE: Why displacement formulation always lead to over stiff representation of the structure?

Brian

www.espcomposites.com