# Getting Acquainted with Complex Relationships in FEA

Design engineers have been traditionally somewhat reluctant to use nonlinear analysis. It might be because of its complex problem formulation or long solution time. However, now that nonlinear finite element analysis (FEA) tools such as SIMULIAworks® integrate with SOLIDWORKS® data and workflows, nonlinear analysis may be less intimidating to learn and use.

The Structural Performance Engineer role in SIMULIAworks was developed with SOLIDWORKS users in mind; it is nonlinear static analysis in a more designer-friendly environment. Using a connector, you can quickly transfer models (including the boundary conditions and the materials) within SOLIDWORKS Simulation to SIMULIAworks.

One of the advantages of SIMULIAworks on the 3DEXPERIENCE® platform, especially regarding FEA, is the extra computing power to solve more complex physics—you can run design studies in the cloud, freeing up your local computer for other work.

If you have previously only used linear analysis tools, such as SOLIDWORKS Simulation, I think you’ll be surprised what nonlinear analysis integrated with SOLIDWORKS can bring to the table. Let’s take a quick look at the primary difference between linear and nonlinear analysis.

Predictable and Unpredictable Behavior

In a linear system, the relationship between the force and displacement is generally predictable. When analyzing a simple system, applying a force typically means you get a displacement. When applying double the force, you get double the displacement. So, in the chart below, F in this case is related to X with K being constant. This is a linear approach.

Nonlinear scenarios typically involve more complexity, and the predictable relationship disappears. There are geometric, material, and contact nonlinearities that can result from modeling with complex materials. In the nonlinear example below, the constant (K) is unknown, and you have a curve instead of a straight line. So, you need to understand which curve is related to the material, because otherwise you will not be able to predict and to analyze the materials.

Linear analysis often provides an acceptable approximation of real-life characteristics for many problems that design engineers encounter. But as more challenging problems arise, you may need to consider a nonlinear approach.