An Example Optimization

The below example of rapidly maturing a design from concept to near complete design comes from a presentation I created for the Aerospace Corporation in 2007.

Example : multi-constraint optimization of an actuated door 
For a given design space, materials, and fully-reversible pressure loading, create the layout and dimensions of
a door which:

• is at least 15 Hz away from the first 2 harmonics of 50hz
• does not experience gross tension yielding under pressure loading
• Prevents buckling under pressure loading
• Minimizes weight

Optimization steps:

1. Create a model with applied loads and solid material filling the design space
2. Perform topology optimization to find stiffest layout for the design space
3. Using the results of the topology optimization, make a shell model of the door
4. Perform size optimization of thicknesses of shell model to satisfy design constraints while minimizing weight

Step 1
Shell- and hex-mesh the design space, and apply pressure distribution.
Dimensions are roughly 16"x11", with the door covering roughly a quarter wedge of a full cylinder wall

What stiffener pattern might most efficiently stiffen the design space? One of these?  Any of these?  

The best stiffening pattern is seen below.

The small radius of curvature means that the design is naturally stiff down the axis of rotation, so the stiffeners tended to cross the design space in the other direction.  They also increased the connection between the two main support points.  This a typical result of topology optimization, a layout which would have required careful consideration by an experienced analyst.
The geometric results of the topology optimization can be imported into the Hypermesh pre-processor, which then can guide the analyst in laying out a detailed mesh to be used for more detailed optimization.

To perform an optimization in Optistruct, the optimization problem must meet a few requirements:

1. One or more responses, such as weight or maximum stress 
2. Only one objective, based on one or more response, such as minimize weight or minimize maximum stress
3. As many constraints as an analyst desires, such as limiting maximum stress while also limiting the natural frequency of a design

The shell model had responses based on stress, natural frequency, and weight.  The objective was to minimize weight, and the constraints were to limit the stress of the material and the natural frequency of the door.  The shell model was divided into the design regions seen below, each color representing a different design region.

Within six iterations, Optistruct had taken a design which had responses 35% higher than allowed to one which met all design constraints.

The dominant ribs and underlying webs required the thickest dimensions.

A design that meets all design constraints at the first iteration will usually see only improvement in the objective; i.e. a part that already is strong enough will only become lighter.  The alternative is a design which does not meet its design constraints will make its design constraints, hopefully without the addition of too much material.  The quality of the layout from the topology optimization allowed the design to meet its constraints with the addition of only 6% more weight.

The full presentation on the broader utility of the Altair Hyperworks suite can be found here.  Note that later versions of Hypermesh and Optistruct have added new features outside of the limits seen in the linked presentation.