There is so much pressure to get jobs done that most designs are deemed adequate after just a few iterations on an initial model.

Product Manager

Algor, Inc.

Pittsburgh, Pa.

**Edited by Paul Dvorak**

This even holds true when teams use CAE software. The approved designs will probably perform all right, but they might not have the most-efficient shape or use the least amount of material possible. In other words, they might not be optimal.

Adequate designs are no longer good enough. It takes optimal designs for the best performance, enhanced durability, and the lowest material costs, particularly when products are headed for mass production.

Many CAE software packages come with built-in optimization tools that make it practical to find a best design. In addition, third-party software from vendors such as **Multistat **and **Vanderplaats Research & Development **can work with CAE packages that do not have such capabilities. Here's how optimization software works.

In essence, the software uses the finite-element method to generate best designs from user-defined criteria. In general, optimization software finds the best size, shape, or topology.

**Size changes **refer to modifying the cross section or thickness of finite elements.

**Shape changes **treats the coordinates of finite-element nodes as design variables. The total number of finite elements does not change.

**Topology changes **determine a best material distribution over a prescribed design space including the removal of unnecessary elements. The result of topology optimization serves as a draft design for the creation of a new finite-element model.

Menus and selections vary from program to program, but a procedure for design optimization generally takes these four steps:

- Define design variables. These features or dimensions are allowed to change.
- Define the goal (objective function) and constraints. A goal might be a minimum volume, and constraints could be not to exceed a particular stress level or cost.
- Run the software. It analyzes the model, compares results to the goal and constraints, updates design variables for a more optimal solution, and repeats until the goals are met within the constraints.
- Examine the final model and optimization history. Verify that the final-analysis results meet the design objective. To do so, the software provides plots and tables of the goal, constraints, and design variables at each step.

Adding optimization to standard CAE provides a rational, automated basis for the trial-and-error process of identifying, modifying, and analyzing design variables to arrive at the best design. It lets a team focus on problem definition, which can encourage a more creative approach to design.

**MAKE CONTACT Algor Inc., (412) 967-2700, **

**algor.com**

**Multistat Inc., (949) 756-8684,**

**multistat.com**

**Vanderplaats Research & Development, (719) 473-4611,**

**vrand.com****Putting the optimizer to work**To show how the software can be put to work, consider an airplane hanger with a beam frame and a solid, curved roof. After defining a finite-element model and performing initial structural analysis, size-design optimization minimizes the volume of the beam frame. (The solid roof has been omitted.)

First, the user defines the cross-sectional radius for each beam as a design variable. In our software, this is done by simply right clicking on the radius field in the cross-section library and choosing the "Set as Design Variable" option. For each design variable, specify lower and upper limits for an allowable range of values.

Then, define the goal and constraints by choosing from a menu of available options. The goal for the hangar is to minimize the volume, and hence cost, of the steel beams. Two constraints ensure the maximum von Mises stress and displacement do not exceed user-specified upper limits.

Before running the software, run a design-variable-sensitivity study to determine the effect that changes to each design variable would have on the goal and constraints. This study reveals which design variables benefit most from optimization and which will have little effect, and so can be left alone. Sensitivity studies are especially valuable in analyses with many design variables. For the hanger, the sensitivity-study results are displayed in charts that confirm that the volume of the beams will be significantly less after changing several design variables, in this case, the beam radii.

The software worked with values for the beam's cross-sectional radii varying them between upper and lower limits. It ran eight solutions until the best radii values were determined for the goal and constraints.

In the final model, the volume of the beam frame was reduced by almost 73%.

The total amount of time spent by the analyst to define the problem, run the software, and review results was less than 30 min. Hence, setting up and using optimization is neither complex nor time consuming. What's more, if the optimized hanger design is mass produced, annual savings from reduced material would far exceed the cost of the software.