Interview related to this work
In this post I will go through the methodology to perform topology optimization with Catia (CAD), Abaqus (FEA) and Tosca (Topology Optimization). Topology optimization evolves the geometry to remove unneeded material effectively minimizing weight. This is carried out by automatically scaling individual element’s density and stiffness based on the stress state of the previous simulation. This is an iterative process where material flows to regions to satisfy constraints and minimize the objective function.
The created geometry represents the maximum allowable geometry and would be a heavy stiff head. High stiffness is desirable however weight is not. This will be the basis for the objective function of the optimization. The basic workflow is to create CAD geometry with the maximum allowable footprint. Create a standard FEA simulation. Create a topology optimization setting goals and constraints.
You can download the files created in this article freely below.
Computer Aided Design (CAD) in Catia
To create the geometry the NCAA Men’s Lacrosse rule book was used as a reference. An old lacrosse stick was also used along with my trusty calipers.
2. The top of the head flairs out so an angled line was created on the symmetry plane, splines and a Multi-Section Surface was created shown in green.
3. The bottom of the head was created with another Multi-Section Surface using an Offset Surface from step 2.
4. Up until here everything was created using surfaces in GSD. In this step we turn the surfaces into solids using Thick Surface.
5. A Closed Surface created the bottom of the head. Then an extruded cut was made for the shaft.
6. Mirror was used as the last step in the head creation.
7.The shaft was created by Extruding a Surface, Thickening and then Mirroring.
This Catia part was exported as a STEP file for import into Abaqus. The Catia part and STEP files are provided below.
Finite Element Analysis (FEA) in Abaqus
1. Upon importation in to Abaqus the head geometry was partitioned with the red cut planes. This allowed for a hexahedral mesh in the yellow regions which are much more computationally efficient than tetrahedral meshes. The pink region was a more complex shape which did not warrant the user time to achieve a hexahedral mesh.
2. The cut plane at the top of the head was fixed to provide a load sink. A coupling constraint was added to the bottom of the shaft to a reference point. The shaft was Tied to the head for load transfer. Rotations were fixed and 3 load cases were created for applying force in the orthogonal directions. An initial simulation was used to scale the loads to achieve a similar level of maximum stress in the head. This was done to drive stiffness in each direction similarly. Ideal designs would have more rigorous loading scenarios.
3. Baseline results of stresses plotted on the same scale. The loads were: top, side and front respectively.
The Abaqus CAE and INP files are provided below.
Topology Optimization in Tosca
1. A topology optimization was created in Abaqus/CAE which uses Tosca in the background for the optimization. The optimization minimized strain energy and targeted a 50% mass reduction as a constraint. Geometric restrictions included: a size restriction for a minimum cross-section, symmetry and freezing the faces in red.
2. Here is the optimized geometry after 36 design cycles with a clock time of roughly 5 hours on a modest CAD laptop.
3. Optimized results of stresses plotted on the same scale as previously. The loads were: top, side and front respectively.
Exporting and Importing Tosca Results
1. The optimized geometry was imported into Abaqus by creating an *.inp file. From here additional simulations could be performed on the orphan mesh model.
2. The optimized geometry was also imported into Catia by creating a*.stl file and using Digitized Shape Editor for point cloud manipulation. Quick Surface Reconstruction or Generative Shape Design could then be used to create NURBS geometry for further design work.
The Abaqus INP and STEP files of the optimized geometry are provided below.
The introduction of simulation and optimization can greatly speed development time and improve product performance.
A google search of “men’s lacrosse head” yields many designs which share remarkable similarities to this optimized design. I like to imagine the design space offered by simply changing the inputs such as target weight and ratios of stiffness…. maybe that will be the topic of a future post.
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