Not Using Design Optimization Yet?

	Bob Williams Product Manager ALGOR, Inc. Pittsburgh, PA

Adding optimization to your standard CAE techniques can give your company a competitive advantage.

This article was published in Machine Design, "How to Make Good Designs Better", May 10, 2007.

Even when using computer-aided engineering (CAE) software, the traditional product-design process often does not go beyond a few cycles of a trial-and-error search for an "adequate" design based on engineering experience. The approved design will likely perform its functional requirements; but, it might not have the most efficient shape or use the least amount of material possible. In other words, it might not be "optimal".

In today's competitive marketplace, adequate designs are no longer good enough. Optimal designs are required not only to ensure desired performance and durability, but also to minimize extraneous material costs, particularly for mass production.

Many CAE software packages come with built-in design optimization tools that make achieving optimal designs practical, fast and easy. Additionally, third-party optimization software (from vendors including Multistat and Vanderplaats Research & Development) can be plugged in to work with your CAE package. If you're not already using optimization, now is the time to start.

Basics of Optimization

Optimization software is a design tool based on the finite element method that generates optimal designs from user-supplied criteria. The ability to optimize a component for a desired performance outcome can mean more time for product innovation and shorter time to market.

In general, design optimization software can be used to automatically optimize three aspects of product designs:

• Size – modify the cross section or thickness of finite elements.
• Shape – consider the coordinates of finite element nodes as design variables. The total number of finite elements does not change.
• Topology – determine the best material distribution over a prescribed design space including removal of unnecessary elements. The result of topology optimization serves as a draft design for the creation of a new finite element model.

Implementation varies with each software package; however, the general procedure for design optimization can be described as follows:

1. Define design variables (the features that you want to change)
    
2. Define the objective function (the goal of the optimization, e.g., minimize volume) and constraints (criteria that must be met, e.g., maximum stress below an upper limit)
    
3. Perform the optimization (run the software, allowing it to automatically analyze the model, compare results to the objective function and constraints, update design variables in order to obtain a more optimal solution and repeat until completion)
    
4. Examine the final model and optimization history (verify the final analysis results and view plots and tables of the objective function, constraints and design variables at each step of the optimization)

Size Optimization of an Airplane Hanger

As an illustration of size design optimization, consider an airplane hanger that has a beam frame with a solid, concave roof. After defining a valid finite element model and performing an initial structural analysis, size design optimization was performed to minimize the volume of the beam frame (the solid roof was not included).

First, the cross-sectional radius for each type of beam in the frame was defined as a design variable. This was done by simply right clicking on the radius field in the cross-section library and choosing the "Set as Design Variable" option.

In ALGOR software, setting design variables for optimization is as easy as right clicking on the desired data field.

Next, for each design variable, lower and upper limits were specified for the allowable range of values.

Then, the objective function and constraints were defined by simply choosing from a menu of available options. The objective function was to minimize the volume of the steel beams. Two constraints were defined to ensure that the maximum von Mises stress and displacement would not exceed user-specified upper limits.

The objective function and constraints for the optimization were conveniently defined using a built-in dialog.

Before the optimization was run, a design variable sensitivity study was performed to pre-determine the effect that changes to each design variable would have on the objective and constraints. This kind of study gives the designer or engineer insight into which design variables would benefit most from optimization. Hence, a design variable sensitivity study is particularly valuable for better understanding complex analyses with many design variables. For the hanger model, the sensitivity study results were displayed in charts that confirmed the objective function (minimize the volume) would significantly change several of the design variables (the beam radii).

After setup was completed, optimization was performed. The software iterated on the solution with values for the beam cross-sectional radii varying between the upper and lower limits. Eight solutions were run until the optimal radii values were determined for the specified objective function and constraints.

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

Size optimization was performed to minimize the volume of the beam frame structure of an airplane hanger. The radii of beam cross sections in the original model (upper left) were defined as design variables (right) and the software automatically produced the optimal design (lower left) with a nearly 73-percent reduction in volume.

The total amount of time spent by the analyst to define the optimization problem, run the software and analyze the results was less than a half-hour. Hence, setting up for and using design optimization isn't necessarily complex or time-consuming. In addition, if the optimized hanger design was mass-produced, the annual savings from reduced material would far exceed the cost of the software.

Benefits of Optimization

Adding optimization to your standard CAE techniques can provide a rational, automated basis for the trial-and-error process of identifying, modifying and analyzing design variables in order to arrive at an optimal design. Thus, you can focus more productively on problem definition, which can encourage a more creative approach to design and give your company a vital competitive advantage.