How can you choose between linear and nonlinear finite element analysis?

1 Linear FEA

Linear FEA is based on the assumption that the relationship between the applied forces and the resulting displacements, stresses, and strains is linear, meaning that they are proportional and reversible. This means that linear FEA can only handle small deformations, elastic materials, and constant loads. Linear FEA is simpler, faster, and more stable than nonlinear FEA, but it can also be inaccurate or unrealistic for many real-world scenarios that involve large deformations, plasticity, contact, or dynamic loads.

2 Nonlinear FEA

Nonlinear FEA is used when the linear assumption is not valid, and the system exhibits nonlinear behavior, meaning that the forces and displacements are not proportional or reversible. Nonlinear FEA can handle large deformations, plasticity, contact, buckling, creep, fatigue, and dynamic loads, among other phenomena. Nonlinear FEA is more accurate and realistic than linear FEA, but it also requires more computational resources, more complex models, and more careful convergence checks.

3 How to choose

When deciding between linear and nonlinear FEA, consider factors such as the nature of the problem, the level of detail required, the available time and budget, and the desired accuracy and reliability. Generally, use linear FEA if the system is relatively simple, the deformations are small, the material is elastic, and the loads are constant or proportional. On the other hand, opt for nonlinear FEA if the system is complex, the deformations are large, the material is plastic or viscoelastic, the loads are variable or dynamic, or there is contact or buckling. If unsure, start with a linear FEA to compare results with empirical or analytical solutions. If results are reasonable and within acceptable limits, you can keep linear FEA; otherwise switch to nonlinear FEA. Additionally, if you have enough time and resources, perform both linear and nonlinear FEA to validate models and optimize parameters.

4 Tips and tricks

When choosing between linear and nonlinear FEA, you may encounter some challenges. To overcome these, make sure your model is consistent and realistic with the same units and dimensions. Simplify the model as much as you can without neglecting important features. Select an appropriate material model and properties that accurately represent the material behavior, and use the right loads and boundary conditions to match the actual or expected scenario. Monitor the convergence and stability of your solution, and be aware of possible sources of non-convergence such as insufficient mesh refinement or unrealistic parameters. Following these tips and tricks can help you make informed decisions when selecting between linear and nonlinear FEA.

5 Examples and applications

Linear and nonlinear FEA have many applications in structural engineering, from simple to complex scenarios. For instance, Linear FEA can be used to analyze the stress and deflection of a beam under a uniform load, or the natural frequency and mode shape of a plate under free vibration. Nonlinear FEA, on the other hand, can be employed to analyze the plastic deformation and failure of a pipe under a bending load, or the dynamic response and impact of a car crash. Moreover, Linear and nonlinear FEA can be combined to analyze the buckling and post-buckling behavior of a column under a compressive load, or the fatigue and crack propagation of a weld under a cyclic load.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?