Figure 1: Reinforced concrete mesh

Welcome back to our blog series on FEA.  In the last blog entry, we introduced some of the fundamental concepts in finite element analysis (FEA).  This entry in the blog series focuses on the initial steps in preparing a computer-aided design (CAD) model ready for use in an FEA program.  Since FEA programs are very sensitive to the data they have to work with, it’s important that the CAD models being analyzed are compatible with the analysis methods the FEA program uses.

In order to illustrate my points throughout the blog series, I will introduce a recent FEA consulting project that we completed.

# Modeling Punching Shear in a Concrete Slab

We were recently approached by an academic, who was examining the behavior of a reinforced concrete slab with a concrete column through the center.  This configuration can be problematic in that it can lead to a phenomenon known as punching shear or “punch through.” An insufficiently reinforced concrete slab can fail in shear around a supporting column.  You might recall that pressure is force divided by the area.  A person in tennis shoes and a person in stiletto heels (Figure 2) exert the same force (their weight) on the ground they stand on.  However, the pressure exerted by the stiletto heel is much greater than the flat shoe, since the contact area is so much smaller, and the heels are likely to punch into the ground.

Figure 2: Stilleto heels; fine on concrete, impossible on dirt
christian-louboutin-stilettos-sling-back-platform-pumps-black by Maegan Tintari / CC BY 2.0

This academic was investigating the effectiveness of a Ancon Building Products’ Shearfix system which uses vertical rebar studs set in the concrete during pouring, as shown below in Figure 3.  He had constructed analytical models, and wanted verification that a numerical calculation would give similar results.  We agreed to assist, and will be using our work on this concrete problem as an example for these blogs.

Figure 3: Ancon Shearfix punching shear reinforcement in a concrete slab

As reviewed in the introductory blog of this series, one often needs to clean up or simplify CAD models before we can analyze them in FEA software.  Sometimes this means simplifying a model so that the FEA software can create the mesh and analyze the model faster and more accurately.  In other instances, due to interferences or missing surfaces, the model might not mesh correctly at all, which must be repaired.

## Interferences

In CAD parlance, an interference in a model is an occurrence where two solids or surfaces overlap.  This can happen in a computer, but not in real life.  It is up to the engineer or designer to correct the problems.  If any parts intersect in the same space, the FEA program will not be able to mesh correctly at that point, let alone mathematically analyze the behavior of such a physically impossible situation.

We created a simple example to illustrate the example in Autodesk Inventor™, as shown in the Figure 4 below.  The hole for the bolt is too narrow, and overlaps.  Most CAD programs have an interference check feature, which in this case lights up where the sides of the bolt are inside the block. It is not unusual that overlap or interference is the design intent, as in an interference fit. Nonetheless, one would still need to modify the CAD drawing to generate a mesh in an FEA program.  If one was interested in the stresses due to the interference fit, that must be handled separately.  A meshing program would not be able to mesh this piece correctly with overlapping parts.

Figure 4: Interference in a CAD model

## Complex features

Many parts and assemblies have complex features that don’t actually affect their structural integrity.  In our reinforced concrete problem, for instance, the rebar studs have a raised pattern around their sides to provide a better bond with the concrete, visible in the Figure 5 below.  However, since we simply set the concrete and rebar as bonded in the FEA program, these raised patterns will only significantly increase the complexity of the mesh; better to leave the rebar as smooth cylinders.

Figure 5: Typical steel reinforcement bars (rebar)
Rebar by Shauqee Pauzi /  Freeimages.com

## Symmetry

One of the most important concepts that can improve FEA performance is the use of symmetry.  The concrete problem we were presented involved a square concrete slab 6 meters to a side; with elements small enough to model the behavior across the 30mm-wide rebar studs, a 6m x 6m square would require millions of elements.  However, by taking advantage of the equal loading across the slab and three sets of 2-fold symmetry (horizontally, vertically, and one about the 45° diagonal), we could slice the slab down to one eighth (½3) of the size, as shown in Figure 6.  By setting the correct boundary conditions (discussed in the next blog), the results in our slice would mirror back out to the rest of the slab.  This simple change cut our meshing and analysis time by approximately 88%.

Figure 6: Symmetry planes used in our concrete slab FEA