Figure. Example of a fixed holder (gray) and an optimization part (blue), fastened by two screws (gray).
The parts to be optimized are often fastened to a supporting structure by using
The boundary conditions that would describe these fastening situations accurately are rather sophisticated. Although in usual FEA they can often be drastically simplified without causing too much harm, one can not say the same for topology optimization. Topology optimization removes/redistributes material in accordance to the strain/stress fields and the results usually depend heavily on proper modeling of boundary conditions.
In order to explain the topic in a simple way an example optimization problem will be presented and discussed in the following. Let the task be to optimize the part shown on the figure below, where the optimization region is drawn in blue while the holder and the fastening screws are shown in gray. In this example the optimization part is fastened by screws, but the ideas presented below are in principle also valid for bolts and rivets.
Figure. Example of a fixed holder (gray) and an optimization part (blue), fastened by two screws (gray).
An optimization part typically consists of regions where the material actually should be removed/redistributed and of regions, where for various reasons it should remain unchanged. In our case let the free region be given as shown below.
Figure. The actually free region of the example part.
After adding the remaining fixed regions (gray color), the example part looks like shown in the following figure (the regions close to loading area and fastening boreholes are not free for optimization).
Figure. The example part to be optimized including some fixed regions (gray color).
At this stage it might be tempting to support rigidly the interior of the boreholes and to start optimization. But this would lead to wrong results because the real boundary (support) conditions are substantially different from this assumption.
In order to explain the essentials more clearly, let start by displaying only one half of the optimization part.
Figure. One half of the optimization part.
In order to build a model that would accurately enough reflect the actual boundary conditions, one should start by adding thin layers of contact material (dark gray color) to account for the contact between the screw head and the part as well as between the part and the support. The added contact material layers are shown below.
Figure. The example part with added layers of contact material (dark gray color).
Now it is time to add the screw body (inside the bore holes) which will be later pre-strained for the purpose of FEA.
Figure. The example part with added screw bodies (inside the bore holes; gray color).
Here it is important to note the following:
To finalize the model the last parts to be added are the screw heads and the support. Now, one half of the finalized model looks like
Figure. The final example part with added screw heads and support.
And the complete model is as follows.
Figure. The final example part (complete model).
It might be worth to take a detailed look at the cross-section of the region around the screw.
Figure. A detailed look (cross-section).
Note the following.
A pre-strain field can be assigned to a particular material within the Imported materials dialog.
Figure. The pre-strain can be set within the Imported materials dialog.
Note that a negative pre-strain is required to induce tension stress within the screw body. This can be nicely seen by loading the part only by pre-strain and displaying the stresses.
Figure. Screw part that needs to be pre-strained
The SgnAM stresses look as follows (red color denotes tension; blue color denotes compression).
Figure. SgnAM stresses due to negative pre-strain of the screw.