Examples of FE models – Selecting the right level of detail

In preparation of a FE-model one need to be aware of the model detail level, associated advantages as well as disadvantages.

Following is a simple example that walks through modelling of a simple supported IPE200-beam of length 2500mm and subject to uniform pressure of 1MPa (or q=100N/mm).

That is max bending occurs at the center and one can use the Timoshenko closed form hand calculation to give a rough idea of the expected response using the steel properties and table figures from e.g. Maskinståbi, where E is steel stiffness, I is area moment of inertia and W is the section modulus:

A total of five parallel versions of the beams are setup and discussed in the following:

• 1-D beam elements are simply a discretization of wireframe geometry. Each element refers to both material and a definition of the cross section properties in result of cross section table values. Simply and quickly to modify or optimize but can only provide results as centroid deflection and stress recovery at pre-defined locations e.g . the profile corners / outermost flange.
• 2D shell elements represent the actual beam geometry in terms of the midsurfaces of the profile and each element refer to both material and a thickness. It may take an effort to derive midsurfaces if the origin is solid geometry. However, simple to modify the web and flange thickness separately for initial optimization purposes. The shell models provide excellent deflection of the representation (both web and flanges) and the stress recovery enables a strong insight of stress contours and components.
• 2½D solid elements are represented as hexagons but requires simple geometry, basically a 6 sided box-like or some-kind of extrusion, and therefore may require some degree of modelling preparation skills to support this. However, doing this, one can get a 3D through thickness deflections and a complete stress field.
• Complex 3D solid elements are represented with the tetrahedrons and can model virtually any arbitrary geometry but at the expense of significant increase in model size. That is the total number of Degrees Of Freedom for the mathematical representation that can result in reliable stress recovery results. The result however is very accurate and often the preferred in detailed areas subject to fatigue calculations.

NB! Important to mention that four-noded TETs (as well as three-noded triangular shell elements) behave too stiff and use should be avoided in general and in transition areas only.

Results of the simulation

What calculation model should be selected?

The below table lists the different versions of the beam calculation in terms of the mathematical model size (No# of elements, nodes, and DoFs) with the impact on the corresponding computational expenses and finally with the resulting deflection and bending stresses in comparison.

Conclusion

One can clearly see why a shell representation is the preferred for many structures as considered the best compromise of model details to computational expense – but requires some effort in establishment.