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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
Pittsburgh, PA

Most real-world 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 time-consuming 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 Windows-native 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 dead-end 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 snap-through 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 FEA-based simulation method that combines large-scale 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 fifty-pound weight. Indeed, gently placing the fifty-pound 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 time-consuming 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 Windows-native 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 real-world experiences to the class. For more information about training, see “Planning for FEA Training” (Machine Design, May 8, 2003, p. 48-50).

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 real-world behavior, test fewer physical prototypes, speed up time to market and make better, safer products at a lower cost.

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