Thinking Beyond Linear Static FEA
This ALGOR MES of a conveyor belt assembly uses a nonlinear hyperelastic
material model for the belt. This simulation enabled engineers to study the
response of the conveyor belt during tensioning. Linear static stress analysis
could not have accurately represented the nonlinear hyperelastic material
behavior of the belt. 
Michael L. Bussler
President and CEO
ALGOR, Inc.
Pittsburgh, PA
Most realworld engineering problems contain some type of nonlinear effect.
However, linear static FEA has traditionally been the most common type of
engineering analysis because of the perception that nonlinear and dynamic
analyses are timeconsuming and require greater expertise. Although simplified
linear approximations may require less processing time, the resulting solutions
are not always valid. Furthermore, faster computers, refined nonlinear FEA
solvers and more intuitive user interfaces are persuading more engineers and
designers to go beyond linear static FEA.
Engineers should consider going beyond linear static FEA if the answer is
“no” to any of these three questions:
 Does the scenario involve only linear characteristics (no nonlinear
material properties or large deformations)?
 Is the load static (unchanging over time) and can it be accurately
quantified?
 Does the user have a thorough understanding of the implications of any
simplifications resulting from using linear static stress analysis?
Nonlinear FEA analysis enables users to more closely simulate actual
responses observed in the real world. After all, failures are far more common
in dynamic situations. When they occur, nonlinear effects, such as large
deformations, buckling and plastic deformations, typically result.
Understanding how product failures occur is a key step toward preventing them
and designing better products.
Material Nonlinearity
The most obvious reason to move beyond linear static stress analysis is
when you are working with a material that has inherently nonlinear material
properties, such as plastics or rubbers.
In this case, simply select a nonlinear material model and supply the
needed data. For example, if considering a part comprised of a material with a
yield stress, use a material model capable of simulating plasticity. You will
need material properties for both the linear range and for beyond yield, when
the strength of the part has been reduced. Today’s Windowsnative single user
interfaces for FEA make this simple with dialog boxes that prompt you for all
of the needed material data.
Engineers at West Coast Engineering, Ltd. used ALGOR MES to simulate a car
impacting the base of a deadend utility pole. The MES calculated the motion of
the car, buckling that resulted from the impact and stresses at each instant in
time of the event. The results aided the engineers in determining how the impact
stresses were distributed throughout the base plate.

Geometric Nonlinearity
Another reason to consider nonlinear stress analysis is that you expect large or
permanent deformations or are looking at an application such as local or
snapthrough buckling.
Nonlinear stress analyses produce more accurate results than linear static
stress analyses for models where the loading results in concentrated stress
values. Usually, these stress concentrations occur near constraints or around
small geometric features, such as fillets and holes. The increased accuracy is
because linear static stress analyses produce stresses based on the initial
shape of the object, whereas nonlinear analyses determine stresses based on the
object's deformed shape.
Simulating Motion to Eliminate the Need to Approximate Loads
Another reason to move beyond linear static stress analysis is that your design
undergoes some form of motion. An FEAbased simulation method that combines
largescale motion and stress analysis, such as ALGOR’s Mechanical Event
Simulation (MES) software, can incorporate both material and geometric
nonlinearities. This type of simulation software can account for the bending,
twisting, stretching, squashing and inertial effects of an FEA model and show
motion and its results, such as impact, buckling and permanent deformation.
Even if you think that your design won’t be undergoing significant motion, you
should still consider this type of analysis to account for how “static” loads
are applied. The way a force is applied can greatly exaggerate the amount of
stress that a design needs to withstand. For example, a linear static stress
analysis of a table may confirm that it can withstand the pressure of a
fiftypound weight. Indeed, gently placing the fiftypound weight on the table
would probably result in no significant deformation. However, if the weight was
dropped onto the table, a large deformation could occur. The greater the height
from which the weight is dropped, the greater the force on the table at impact.
Engineers at SiWave, Inc. examined the dynamic response of this MEMS optical
switch using ALGOR MES. The simulation was performed to assure that the device
would be in compliance with Telcordia shock loading standards. The MES
calculated motion, stresses and displacements throughout the event, whereas
linear static stress analysis could only have calculated results for one moment
in time.

Sometimes, engineers are able to draw on their experience and engineering
expertise to build products that can withstand estimated or calculated forces.
However, using approximated forces and safety factors often requires more
expertise than simply using software tools to simulate the event as it occurs in
the real world.
MES results are based on physical data, including dynamic or contact forces,
rather than calculated or assumed loads and constraints. Linear static stress
analyses, on the other hand, are only as accurate as their applied loads and
constraints. Methods of obtaining loads such as hand calculations; conducting
physical tests; and overestimating or guessing based on past experiences can be
timeconsuming and prone to error.
Learning About Nonlinear and Combined Motion and Stress Analyses
Fortunately, advances in user interfaces for FEA software have made nonlinear
and motion simulations more accessible to engineers and designers. Some FEA
vendors provide nonlinear and motion capabilities within the same modern
Windowsnative user interface as linear static stress analysis and include full
associativity with leading CAD solid modelers and wizards that help users
perform common tasks. Such an interface often uses standard engineering
terminology and visual process guidance, so that users can focus on the physics
of a part or assembly, rather than having to learn the process and terminology
of a particular nonlinear and/or motion analysis software package.
If you feel that you need more direction on using these types of analyses,
distance learning Web Courses are a good way to learn about the use of this type
of software without leaving your desk. Classroom seminars provide another means
of learning about new analysis techniques and offer the added benefit of
learning alongside other users who bring their own realworld experiences to the
class. For more information about training, see “Planning
for FEA Training” (Machine
Design, May 8, 2003, p. 4850).
No matter how you approach learning about nonlinear and motion simulation,
remember that the three primary reasons to move beyond linear static FEA are
material nonlinearity, the potential for geometric nonlinearity and
consideration of motion. By simulating actual engineering problems including any
nonlinear effects that may occur, engineers can more accurately predict
realworld behavior, test fewer physical prototypes, speed up time to market and
make better, safer products at a lower cost. 