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What is Topology Optimization and Why Use It?

May 22, 2017 By: Steven Hale

What can you do when you need a novel approach to improve on an existing design? Or perhaps you’ve been asked to design a brand new part that needs to fit into a limited space, be lightweight, and survive a lengthy life cycle, but you only have a rough idea of what the part should look like. In most cases, parts are designed by improving on an existing design or concept. In such cases, dimensions or other design inputs are typically defined in terms of parameters. In cases where you don’t already have an existing design to work from, you would typically create one or two conceptual designs, define these designs parametrically, and then apply standard optimization methods such as Design of Experiments. These methods have been described in some of our earlier blogs; specifically Opting to Optimize, Two Approaches to Design Optimization During Finite Element Analysis, and How Does my DOE Model Determine How Many Design Points to Generate? An alternate method when you don’t have an existing design to work from is to simply start with a block of material and allow the optimizer to determine both the shape and size of each design feature. This type of optimization is known as topology optimization.

Topology optimization finds the best distribution of material given an optimization goal and a set of constraints. It works by taking a solid block of material in any shape and removes material from it to minimize or maximize an optimization objective such as mass, displacement, or compliance while satisfying a set of constraints such as maximum stress or displacement. For example, the mass of a test rig platform could be optimized to minimize mass while avoiding a detrimental range of natural frequencies. As you can imagine, this type of optimization can result in some very novel and complex shapes. In the past, it was often impractical to manufacture particularly complex shapes because of the limitations of traditional manufacturing methods. However, newer methods such as additive manufacturing have allowed for a proliferation of highly complex designs.

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As another example of topology optimization, the mass of a control arm can be minimized without exceeding specific deflection limits. The envelope defining the allowable dimensional limits of the control arm is shown in Figure 1. All attachment features are shown. In this example, the bottom attachment point is loaded with 33,000 N in both the horizontal and vertical directions.  The top two attachment points are fully constrained. Running topology optimization with the objective of minimizing mass while limiting the maximum horizontal displacement to 10.7 mm and the maximum vertical displacement to 1.2 mm produces the optimized structure shown in Figure 2.

Figure 1: Control Arm – Allowable Dimensional Limits

Figure 2: Control Arm – Optimized Shape and Dimensions

Optimized shapes generated with the help of topology optimization software can be exported as STL files for use with 3D printing software. However, as mentioned previously, these shapes can be quite complex and organic, which can be difficult to manufacture. Some topology optimization software, such as ANSYS Topology Optimization, also allow for manufacturing constraints such as symmetry about a plane, extrusion direction, and max./min. allowable member size. These constraints help prevent the generation of optimized shapes that would be too difficult or costly to manufacture. Also, with some additional effort, tools such as ANSYS SpaceClaim can be used to reverse engineer dimensioned parts from exported STL files. In our earlier example, this process produced the final dimensioned control arm shown in Figure 3. More details about reverse engineering STL geometry in SpaceClaim can be found in our blog Moving Forward with Reverse Engineering and in our e-Learning video Reverse Engineering with SpaceClaim.

While there are other shape optimization tools, topology optimization remains the most general and powerful tool for developing novel shapes and concept designs.  I’d be very interested to hear about any experience you have with topology optimization or how you might be able to use this powerful tool in your work!