Page 390 - Finite Element Modeling and Simulations with ANSYS Workbench

Design Optimization 375

Plate thickness t

Longitudinal stiffener
thickness t long

Lateral stiffener thickness
t lat

Stiffener height h

FIGURE 11.2
A stiffened panel with clamped edges.

(design variables) . . element model . . Outputs
Inputs . Parametric finite . (responses)

Optimizer: to find
optimum design

FIGURE 11.3
“Black Box” optimization schematic.

be established between the design variables and responses. The optimizer then explores
the mapping of the parametric design space to find the optimal set of design variables that
fulfill the given response criteria.
In the design space exploration, design of experiments are usually used in combination
with response surface modeling to efficiently map out a parametric design space through
simulating a minimum number of design scenarios.

11.4.1 Design of Experiments
Design of experiments (DOE) is a technique originally developed for model fitting with
experimental data. In design optimization, DOE can be used to fit the simulated response
data to mathematical equations. These equations, also referred to as response surface equa-
tions, serve as models (see Figure 11.4) to predict the responses for any combination of
design variable values.
In DOE, each design variable is viewed as one dimension in a design space. In general,
we have an n-dimensional space if there are n design variables. Each design variable has
many possible discrete values or levels. An array can be constructed by considering all the
combinations of design variable levels. In most cases, we cannot afford the response data