Watching the sunset with a loved one brings about a feeling of peace and tranquillity. It somehow removes you from the hustle and bustle of daily life and can free your mind to think about the bigger picture. From time to time we all get caught up in the detail of the task we are doing and forget about what’s really important in our lives. Our jobs demand attention to detail and this is particularly true in Finite Element Analysis (FEA). To assume someone is wealthy because they live in a big house is a mistake. They may own the house but they could be scraping by on a state pension. Everyone’s circumstances are different and everyone has their reasons which may not be apparent. Making assumptions is something engineers do on a daily basis and is necessary from a commercial perspective. In FEA we make assumptions about everything from material properties to boundary conditions and that’s OK. The assumptions made in FEA can be checked to see how sensitive they are to slight variations. This is called a ‘sensitivity study’ and will help you to understand the bigger picture and the consequences of your assumptions. The following example demonstrates a basic sensitivity study and shows how assumptions made at boundary conditions affect the results in a steel frame FE Model. Sensitivity Study Example Consider a Square Hollow Section (SHS) steel frame with a machine weighing 1000 kg bolted on top of it on it as shown in figure 1. Figure 1 – Square Hollow Section (SHS) Steel Frame FE Model The FE Model was built using beam elements for the frame and a point mass of 1000 kg to represent the machine’s centre of gravity. The point mass was evenly linked to the horizontal members of the frame. The boundary conditions consist of a point constraint at the base of each leg at floor level. The frame is connected to a concrete floor at the base of each leg. The connections could be completely rigid and have all six degrees of freedom held. However, most connections have some flexibility, especially in the rotational degrees of freedom. For example, a ball joint would have its translation degrees of freedom held and its rotational degrees of freedom free. Since most connections are somewhere between fixed and pinned then two alternative constraints were compared for the purposes of the sensitivity study. One model had fixed constraints i.e. all degrees of freedom held in both translation and rotation. The other model had pinned constraints i.e. only the translation degrees of freedom held and rotational degrees of freedom free. Both the fixed and pinned assumptions are at the extreme opposite ends of the scale. Gravity was applied to the two models and the bending moment was compared in the members as shown in figure 2. Figure 2 – Bending Moment Comparison with Pinned and Fixed Constraints A comparison of bending moments in the members shows that the assumption made as to whether the constraints should be fixed or pinned does not affect the bending moments in the members by very much. In fact, the difference in bending moments was less than 2% and it can be concluded that it doesn’t matter all that much whether you choose fixed or pinned constraints for this particular model. This is reasonable for the simple gravity load but what about dynamic effects from seismic floor shaking or vibrations from the machine? We can now check how sensitive the FE model is for dynamic effects by carrying out a modal analysis. This was done by comparing the first mode frequency using both fixed and pinned constraints as shown in figure 3. Figure 3 – First Mode Frequency Comparison with Pinned and Fixed Constraints When the models were compared using fixed and pinned constraints, it can be seen that there is a substantial difference in the first mode frequency of about 87%. This could be very important if you are interested in the effects of seismic floor shaking or vibrations from the machine. It can be concluded that the model is not very sensitive to the constraint assumptions for the gravity load but for dynamic analysis it is very sensitive. Making an assumption about boundary conditions i.e. pinned or fixed constraints without doing a sensitivity study would probably lead to results that are wrong if you are interested in dynamic effects. “Essentially, all models are wrong, but some are useful”. This article has shown that a ‘one size fits all’ approach to FEA is not always a good idea and the sensitivity study is the key to finding reliable and useful FEA results. Much better than having a guess and hoping for the best!
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May 2023
