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Design Optimization

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July 16, 2015 By Bruce Jenkins, President, Ora Research
Topology optimization and its seductive biomorphic shapes are what many think of when they hear the
term “optimization” in engineering design. But topology optimization is just one kind of structural
optimization—and that, in turn, is only one of five broad classes of optimization technology available to
engineers today. Equally if not more valuable, depending on the nature of the design problem, are
parameter optimization, multidisciplinary optimization (MDO), multi-objective or Pareto optimization,
and robustness-and-reliability optimization.
Topology optimization. Source: solidThinking.
The power of all these numerical methods is their ability to rationally and rapidly search through design
alternatives for the best possible design(s). Parameters in a design that can be varied to search for a
“best” design are called design variables. Given these variables, design can be structured as a process
of finding the minimum or maximum of some attribute, which is termed the objective function. For a
design to be acceptable, it must also satisfy certain requirements, or design constraints. Optimization
is the process of automatically changing the design variables to identify the minimum or maximum of
the objective function while satisfying the design constraints.
Here’s how these methods work, and what kinds of problems they help engineers solve:
Structural optimization is optimization of a structure’s shape, size, topology, topometry or topography
to satisfy operating limits imposed on the response of the structure, and by further limits on the values
that the structural parameters can assume. Structural optimization methods apply optimization
algorithms to solve structural problems by means of finite element analysis.
Shape optimization means optimizing structural shapes by adjusting the surface shape of a 2D or 3D
solid to minimize volume while satisfying stress and/or displacement constraints (generically termed a
cost functional).
Automotive body-in-white before and after sheet thickness optimization. Source: SIMULIA.
Size optimization consists of modifying size-related properties of structural elements such as shell
thickness, beam cross-sectional properties, spring stiffness and mass to solve the optimization
problem.
Topology optimization denotes optimizing material layout within a given physical design volume, for a
given set of loads and boundary conditions, so that the resulting layout meets prescribed performance
targets. This is often used to identify a conceptual design that best meets specified design
requirements, which is then refined for performance and manufacturability. It frequently yields
biomorphic-appearing shapes best suited to additive manufacturing methods, before being modified
for production by conventional subtractive manufacturing.
Topometry optimization is similar to topology optimization but applied to 2D elements, with the variables
restricted to the element-wise thicknesses.
Topography optimization, like topometry optimization, is applicable only to 2D or shell elements, and
aims at finding the optimum bead pattern in a component.
Parameter optimization, in some respects a more generalized version of structural optimization, is a
procedure for finding values for any parameter(s) in a design—not just structural parameters—that are
optimal in some defined respect, such as minimization of a specified objective function over a defined
data set.
Multidisciplinary optimization (MDO) incorporates all relevant disciplines—structural (linear or
nonlinear, static or dynamic, bulk materials or composites), fluid, thermal, acoustic, NVH, multibody
dynamics, or any combination—simultaneously in an optimization problem. By exploiting interactions
among disciplines, MDO can identify design solutions that are superior to those arrived at by optimizing
each discipline sequentially, with substantially less expenditure of engineering time and labor.
Multi-objective or Pareto optimization is a method for numerically addressing the fact that real-world
optimization problems usually have more than one objective, and these objectives often conflict or
compete with one another. For example, in optimizing a structural design, the desired design will be
both lightweight and rigid. Because these two objectives conflict, a tradeoff must be made: there will
be one design that is lightest, another design that is stiffest, and an infinite number of possible designs
that are some compromise of weight and stiffness. The set of tradeoff designs that cannot be improved
on according to one criterion without harming another criterion is called the Pareto set, and the curve
plotting the Pareto set is called the Pareto frontier. Once the Pareto frontier has been identified, the
action of comparing these various Pareto-optimal solutions with one another in order to choose the
preferred solution is based on exogenous factors (outside the computer model), and is carried out by
human decision-makers.
Robust design optimization. Source: OptiY.
Robustness and reliability optimization are methods for managing the fact that product designs are
nominal, while manufacturing and operating conditions are real-world. Finite geometric tolerances,
variations in material properties, uncertainty in loading conditions, and other variances encountered by
a product either in production or in service can cause it to perform slightly differently from its nominal,
as-designed values. Therefore, robustness and reliability as design objectives beyond the nominal
design are often desirable. Performance of robust and reliable designs is less affected by these
expected variations, and remains at or above specified acceptable levels in all conditions. To evaluate
the robustness and reliability of a design during simulation, its variables and system inputs are made
stochastic by being defined in terms of both mean value and a statistical distribution function. The
resulting system performance characteristics are then measured in terms of a mean value and its
variance.
Here are some of the many optimization software choices available today:
Altair HyperStudy, OptiStruct, solidThinking Inspire
ANSYS Adjoint Solver, Optimetrics
Autodesk Optimization for Inventor
CD-adapco STAR-CCM+ /Enabling Optimate+
Cenaero Minamo
Collier Research HyperSizer
COMSOL Multiphysics Optimization
Concepts NREC TurboOPT II
DATADVANCE MACROS, pSeven
DecisionVis ExplorerDV
Dynamic Design Solutions FEMtools Optimization
Dynardo optiSLang
ESI Group Virtual Performance Solution Optimization
ESTECO modeFRONTIER
Exa PowerFLOW Optimization Solution
FEA-Opt SmartDO
FRIENDSHIP SYSTEMS CAESES/FRIENDSHIP-Framework
FunctionBay RecurDyn/AutoDesign
iChrome Nexus
LIONlab LIONsolver
LSTC LS-OPT
MSC Nastran Design Optimization
NISA Software CSIL NISAOPT
Noesis Solutions Optimus
Optimal Solutions Sculptor
OptiY GmbH OptiY
Phoenix Integration ModelCenter
PIDOTECH PIAnO
PTC Creo BMX (Behavioral Modeling Extension)
Quint OPTISHAPE-TS
RBF Morph
Red Cedar Technology (a CD-adapco company) HEEDS MDO, HEEDS NP
Siemens PLM NX Nastran Optimization, Femap with NX Nastran Optimization, LMS Virtual.Lab
Optimization
Sigma Tech IOSO
SIMULIA Isight, SEE, Tosca
SolidWorks Simulation Structural Optimization
Vanderplaats R&D GENESIS, DOT, BIGDOT, VisualDOC
Virtualpyxis Virtual.PYXIS
Within Technologies (an Autodesk company) Enhance
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