Impact of rigid elements in topology optimization

In some cases, using RBE2 elements in your model might introduce extra stiffness, which can adversely affect the topology optimization results.

In the following example, the design objective is to minimize compliance while using a design constraint for weight. The model consists of two discs connected by two small struts. The green meshes indicate the areas to be optimized; the red meshes are omitted from the optimization process (frozen).

External components are represented using RBE elements (which appear orange and brown in these figures). These elements carry the loads and boundary conditions. The master node of the top RBE is fixed, while the master nodes of the three other RBEs are subject to force loading.

If you use RBE2 elements for all four connections, the optimization results include two platters that appear to be completely disconnected. The two small struts disappear. However, in the numerical model, these platters are still mechanically connected because the RBE2 elements provide a fully rigid connection between them, and the optimizer makes full use of that rigid connection.

Such a result might not be satisfactory if you intended to use the RBE elements to replace gearwheels, which, if they can carry some load and transfer it to the rest of the structure, do not provide a good way to maintain the assembly of the two platters. In that case, replacing the two peripheral RBE2s (in brown in the first two figures ) with RBE3 elements enables the optimizer to create more sensible results, as shown below. In this solution, the two connection struts remain part of the optimal design.

You could also replace the other two RBE2 elements with RBE3 elements, although the impact on the results might be less significant.

In general, be sure to exercise particular care when using rigid elements to model connections or external components. If the intent is to create an infinitely rigid connection, to distribute applied loads, and perhaps to create a load path between the components, the RBE2 element might be a reasonable choice. Moreover, in the above example, if you are careful in selecting the connected degrees of freedom, using RBE2 elements might also let the optimizer reach a similar result as with the RBE3 elements.

Conversely, if the intent is to distribute applied loads without adding significant stiffness to the connection along with providing a load path between the components, the RBE3 might be the right choice.

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Impact of rigid elements in topology optimization, Simcenter 3D 2021.1 Series

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