What is Non-Linear Analysis?
Non-linear analysis refers to a type of simulation used in engineering and product development that accounts for non-linear behavior in materials, geometry, or boundary conditions. Unlike linear analysis, which assumes that the relationship between loads and responses (such as stress and strain) is directly proportional, non-linear analysis deals with more complex situations where this assumption no longer holds.
This is crucial for accurately predicting the behavior of materials and structures under real-world conditions, where factors like large deformations, material plasticity, or contact between components can lead to non-linear responses.
The role of non-linear analysis in digital engineering
In many cases, linear analysis is enough for early-stage design or for systems operating within certain limits. However, as products become more advanced and are required to perform under increasingly demanding conditions, non-linear analysis becomes essential.
For example, when materials like rubber or steel are pushed beyond their elastic limits, or when components exhibit significant deformation, linear assumptions break down. Non-linear analysis provides a more accurate understanding of how these materials will behave under stress, allowing engineers to optimize designs for performance and safety.
What are the benefits of conducting non-linear analysis?
Enhance accuracy
Provide a more accurate representation of real-world behaviors by accounting for factors such as material plasticity, large deformations, and contact interactions between components. This leads to better predictions of how products will perform under various conditions.
Optimize designs
By simulating complex behaviors that cannot be captured by linear models, non-linear analysis allows engineers to optimize designs for performance, safety, and efficiency. This results in products that are not only more effective but also more cost-efficient over their lifecycle.
Improve process efficiency
Non-linear analysis allows engineers to capture complex, non-linear relationships between variables, which can lead to more efficient processes. By accurately simulating real-world behaviors, engineers can optimize production processes, reduce operational costs, and improve overall efficiency. For example, in process industries, non-linear models can predict behavior beyond the available data range, improving decision-making and reducing downtime.
Ensure safety and resilience
Non-linear analysis is essential for designing structures that need to withstand extreme conditions such as seismic events, impacts, or large deformations. It helps engineers assess how materials and structures respond under various loading scenarios, ensuring that designs are resilient and safe under dynamic or extreme conditions. This is particularly important in industries like aerospace, automotive, and civil engineering where safety is critical.
Mitigate risks
Non-linear analysis enables the prediction of failure modes in materials or structures before they occur in real-world applications. By understanding how a system behaves under stress or deformation, engineers can identify potential weak points and mitigate risks early in the design process. This reduces the likelihood of costly failures during operation or manufacturing.
Reduce costs
Non-linear analysis enables engineers to optimize material usage and reduce waste. This leads to more sustainable designs that minimize resource consumption while maintaining performance standards. Additionally, by preventing over-engineering and avoiding unnecessary safety margins, non-linear analysis helps reduce material costs.
What's the best way to get started with non-linear analysis in your organization?
Getting started with non-linear analysis requires a solid understanding of both the theoretical concepts behind it and the practical tools used to perform simulations. Typically, the process begins with identifying the specific non-linear behaviors that need to be modeled – such as material plasticity or large deformations – and selecting appropriate simulation software capable of handling these complexities. Keep reading to discover our recommended approach to conducting non-linear analysis as a central part of your product development process, or reach out to us for a free consultation today.
The first step is to assess whether your project requires non-linear analysis. This type of analysis is necessary when you expect non-linear behavior in materials, geometry, or boundary conditions.
For example, if your product involves materials that exhibit plasticity or undergo large deformations, or if there are complex interactions between different components, non-linear analysis will provide more accurate insights than linear methods. Typical applications include crash simulations, structural buckling, and predicting material failure.
Accurate material data is fundamental to non-linear analysis. This includes not only elastic properties like Young’s modulus and Poisson’s ratio but also non-linear characteristics such as plasticity and hyperelasticity for materials like rubber.
Depending on the materials used in your project, you may need to include stress-strain curves that extend beyond the elastic limit or use advanced material models like Mooney-Rivlin for polymers. If necessary, conduct material testing or consult established material databases to ensure you have the most accurate data.
The next step is to create a detailed geometric model of your product or structure. The model should accurately represent the real-world system, particularly in areas where large deformations or stress concentrations are expected. This may involve importing CAD models or refining certain geometrical features to better capture non-linear behavior.
Define the boundary conditions and external loads that will act on the system. Boundary conditions might include fixed supports or sliding surfaces, while loads could be forces, pressures, or dynamic impacts.
In non-linear analysis, it’s important to carefully define contact interactions between components if applicable. For example, frictional contact between surfaces can significantly affect how a system behaves under load.
A finite element mesh divides the model into smaller elements for analysis. In areas where high stress gradients or large deformations are expected, it’s important to use a finer mesh to capture these behaviors accurately. A well-refined mesh ensures that the results of your non-linear simulation will be reliable and precise.
Non-linear problems require iterative solvers due to their complexity. At this stage, select an appropriate solver method based on whether you’re applying loads incrementally (load-controlled) or using displacement increments (displacement-controlled), which is common in buckling or failure mode analyses. Ensure that solver settings are optimized for accuracy and efficiency by adjusting parameters such as the number of iterations per step.
Before diving into complex scenarios, run initial simulations with simplified models to validate your setup. This helps identify potential issues with material properties, boundary conditions, or mesh quality early on, allowing you to make adjustments before proceeding with more detailed analyses.
Non-linear simulations often face challenges related to convergence due to their inherent complexity. It’s important to monitor convergence during each iteration by checking error measures against predefined tolerances. If convergence issues arise—such as slow progress or divergence—you may need to reduce step sizes or adjust solver settings for better stability and accuracy.
After reviewing initial results from the simulation, refine your model as needed by adjusting parameters like mesh density in critical areas or fine-tuning material properties based on test data. This iterative process helps improve accuracy and ensures that your model reflects real-world behavior as closely as possible.
Once the simulation is complete, carefully analyze the results by examining factors such as deformations, stress concentrations, and failure points within the model. If contact interactions were part of the analysis, review how forces were distributed across surfaces during loading events. These insights can inform design decisions such as reinforcing weak areas or optimizing material usage.
Use your findings to optimize designs for performance under real-world conditions – whether that means reducing weight while maintaining strength or improving safety margins under extreme loads – and continue refining designs iteratively based on subsequent analyses.
Finally, document all key findings from your non-linear analysis process in detail. Sharing this information with stakeholders ensures transparency and facilitates collaboration across teams involved in product development.
This structured approach to implementing non-linear analysis within your product development workflow helps ensure more accurate simulations and better-informed design decisions that lead to improved product performance under real-world conditions.
Need help with Non-linear analysis?
Johan Kolfors and team are on-hand to provide tailored guidance and support with a deep knowledge of the full Dassault Systèmes portfolio. Reach out for a free consultation today.
Essential software for non-linear analysis
Abaqus
For advanced engineering simulations and comprehensive analyses.
For virtual testing, analyzing, and optimizing product performance.
CATIA Analysis
For advanced engineering analysis and design validation.
SOLIDWORKS Simulation
For evaluating performance and behavior inside the product design environment.
View our extensive range of software solutions