Figure. Low-density mesh; approximately 0.57 million elements and 0.32 million DOFs
Large FEA models, containing many millions of finite elements, are frequently encountered in practical topology optimization. Since engineering optimization is always an iterative process, large-scale models may represent a serious obstacle preventing to get a good result within reasonable time. In this respect ProTOp offers two technologies that can be combined to solve large-scale problems very efficiently. These two technologies are
The fundamental idea is to start the optimization process with a FE mesh of low density. As the optimization progresses, material is typically removed, resulting in a reduced volume of the optimized part. As this happens, one can switch to a finer FE mesh, without increasing the problem size to an unmanageable extent.
A step by step procedure how to get the most out of ProTOp is described in the following.
To address large-scale problems and get the most out of ProTOp, one has to engage several FE meshes with various mesh densities. To get such meshes one can either:
Typically, two or three different meshes should be engaged. Note that this does not impose any additional CAD work; the CAD model is prepared as usually, just the mesh generator or the mesh refinement tool have to be run several times - each time with different mesh density requirements.
Let us consider a bracket structure as an illustrative example. Let the two generated FE meshes be as shown on the figures below.
Figure. Low-density mesh; approximately 0.57 million elements and 0.32 million DOFs
Figure. Low-density mesh detail
Figure. High-density mesh; approximately 3.07 million elements and 1.65 million DOFs
Figure. High-density mesh detail
The optimization should be started by using the low-density mesh, which (in the present case) contains less than 1 million tetrahedral finite elements. So, the optimization problem can be solved rather quickly, and the obtained result (for 35% volume part) is shown below.
Figure. Optimization result obtained by the low-density mesh (35% volume part)
For illustration it might be worth to list the approximate performance data (desktop PC, i7 CPU, 4 cores):
The optimization should be started from the result obtained by the low-density mesh. This is achieved by starting a new optimization session with the high-density mesh. But instead of using the normal session start, one should utilize the ProTOp's start-from option and point to the low-density mesh result. In this case the initial (starting) design for the high-density mesh looks like shown below.
Figure. Starting design for the high-density mesh
By running optimization from this starting point, a lot of finite elements will never get activated due to the ProTOp's semi-active element technology. Therefore, the consumed RAM and required CPU time will remain far below the levels that would actually be needed when starting the optimization from a full-material design.
This means that the optimization process will proceed very efficiently until the final design (figure below) is obtained.
Figure. Optimization result obtained by the high-density mesh (30% volume part)
For illustration it might be worth to list the approximate performance data (desktop PC, i7 CPU, 4 cores):
NOTE. By using the proposed technique, the optimal design of a 3-million-elements model has been obtained by utilizing only 3.5 GB of RAM and within less than 20 minutes. If the optimization would be started with the dense mesh from full-material design, the process would require about 12 GB of RAM and dramatically more CPU time.