Bennett Wallander

Ansys Inc.

Canonsburg, Pa.

Optimization technology has been used to calculate dimensions of beams, braces, and sections that best limit the deflection on a structure. The general shape of the structure, however, is often just a guess. In the worst case, some portions might carry little or no load. More recent numerical techniques can optimize part shape for given loads and an allowable volume. This later technology, called topological optimization, complements previous optimization methods. The topological version determines a general part shape or where beams and braces should be placed. This introduction to the newer technology shows its capability and where it fits in a design department.

Topological optimization is a conceptual design technique that provides insight to a mechanical component’s best design. It maximizes the stiffness of a structural load-path for a given performance requirement.

The question is, how and in what shape should the component mass be configured to optimize the structural performance? Topological technology uses a modified finite-element technique to simulate a component volume and loads to find structural supports for the stiffest load path. The method exposes both what a conceptual component might look like and where material can be removed from an existing design, thus saving a company up-front conceptual design time and material.

Topological optimization is a little like playing the parlor game in which players remove blocks from a tower one by one until the tower falls. Now imagine putting a cup of coffee atop the stack of blocks. Design requirements would be to keep the coffee from spilling while removing as many blocks as possible. The cup provides the load and the table provides the support. The question is, how many pieces do you remove and from where?

Optimization technology answers these questions by using a finite-element mesh to create the blocks. A stress solver then calculates the maximum stress distribution through the blocks. Where there is minimal or no stress, the software removes blocks.

A conceptual representation of the part geometry completes the process. The display is only a general shape, a rough idea of what the part should look like, and needs design details and dimensioning before manufacturing.

The difference between topological optimization and parametric optimization is the later assumes design features such as holes, ribs, or reinforcements are in approximate optimized locations so it performs numerous stress analyses by manipulating the dimensions of each feature. Should a user request the least weight for a structure, the parametric technology provides precise dimensions for the part features.

The problem with using parametric optimization alone is that it might optimize irrelevant features such as a length or width to reduce material, when what the part really needs is a hole in the middle. Parametric optimization cannot make a bad design better. The advantage comes from using the technologies together.

Using a topological optimizer takes only a few steps. Users first read a volume for the solid part. The software prompts users for how much material to remove and what unit system to work in. One program provides a slider bar calibrated to remove up to 50% of a part’s material for a single evaluation.

Next, users select a material, usually from a pull-down menu. Material properties are required to calculate the structural load path through the part. Then users define the part’s performance environment. That is, define loads on the part and how they are supported.

The optimizer then begins reshaping the topology of the initial solid volume. A solution monitor provides a window to watch material come off. Simple models take only a few minutes for each iteration. Because topological optimization is an iterative process, the solution monitor may display numerous conceptual possibilities for the part’s shape. Users can stop the process at any time once they have an idea of how to modify their design and that often occurs by the second iteration.

When completed, users see a conceptual color-coded display of where material can be removed from the part. Areas in one color can be removed, while areas in another may have marginal significance to the part’s performance.

Because a few programs work on solid models, users can rotate the part and animate the material removal through advanced graphic capabilities. The resulting conceptual geometry’s smoothness is based upon the finite-element-mesh density. The finer the mesh, the smoother the resulting geometry. Solid-modeling software can then modify the design. After producing an optimized solid shape, users may turn to FEA to calculate stresses, deformations, and factors of safety for the design.