## When do I need to perform Nonlinear Static Analysis ?.

This is mostly asked question by many students and in the CAE job interview, Nonlinear terms itself is a big topic to learn not only from a software point of view but majorly from understanding the change in the behavior (stiffness changes & physic of problem) during loading and unloading process. I saw many young FEA engineers get stuck while performing nonlinear analysis such as solution is not converging, solution taking too much time, disk space is less, contact abrupt changes, displacement converging but moments does not or wise versa, and many bisections in the converged model. There is a way to overcome these issues first, you should take a big breath, be relaxed guys you are working on a nonlinear simulation, you need to be patient and remember you have chosen a zigzag path (nonlinear), not a straight line (linear) So it takes more time, it takes more energy and juice of your FEA knowledge. Only adding nonlinear material properties or adding nonlinear contact in your model doesn’t mean that it will solve as, like linear simulation, you not only need to think from various nonlinear software setting points of view such as adding load step increments, choosing the right solver setting, choosing the right combination of formulation for contact setting (Augmented Lagrangian, Stiffness matrix updating setting and many more) but also the model behavior point of view.

So, my dear friends, it is not easy as linear analysis but also not too difficult to perform nonlinear analysis, the thing is you should know the concepts behind how-to and when to perform, So today we will discuss this topic. in the coming days, we will go in deep into this topic.

Before we going to understand the nonlinear analysis requirements let’s understand the first difference between linear analysis and nonlinear analysis. If your interviewer asks you what is the difference between the linear and nonlinear analysis then below is a very simple answer for you.

The term “stiffness” defines the fundamental difference between linear and nonlinear analysis.

Remember stiffness matrix is a hero in your nonlinear analysis. If you understand how this hero (stiffness ) works in nonlinear analysis then you understand the entire movie. Stiffness is the heart of your nonlinear analysis.

Adding into your interview answer: Stiffness defines the fundamental difference between linear and nonlinear analysis. In linear analysis, stiffness is constant, which means displacement varies linearly with applied load, and changes in the geometry due to displacement are assumed to be small and hence can be ignored in the other hand in the nonlinear analysis stiffness varies as a function of applied load, it means displacement very non – linearly with applied load and changes in the geometry due to displacement is assumed to be large and hence cannot be ignored. There are three types of Non-linearity, if the stiffness of geometry gets changes (because of shape, size & nature of the load, An I beam has different stiffness from a channel beam.) during the deformation process, it comes under geometric nonlinearity, if the stiffness of material properties get changes or material reaches its failure limit( using nonlinear materials such as Elasto-plastic, Hyperelastic and Creep material model, An iron beam is less stiff than the same size steel beam.) during the deformation process, it comes under material nonlinearity. If the stiffness of mating contact surface or out of contact with each other get changes (because of contact behavior such as Friction contact and Frictionless contact) or change in the boundary conditions such as elastic support come under contact nonlinearity.

Let’s understand more here in other ways and will come to the main point when to perform the nonlinear analysis:

When the structure response (deformation, stress, and strain) is linearly proportional to the magnitude of the load (force, pressure, moment, torque, temperature, etc.) then the analysis of such structure is known as linear analysis. When the load-to-response relationship is not linearly proportional, then the analysis falls under nonlinear analysis. Understand with an example: when a compact structure made of stiff metal is subjected to a load relatively lower in magnitude as compared to the strength of the material, the deformation is the structure will be linearly proportional to the load and the structure is known to have subject to linear static deformation. But most of the time either material behavior is not linear in the operating conditions or the geometry of the structure itself keeps it from responding linearly. Due to the cost or weight advantage of nonmetals (polymers, woods, composites, etc.) over metals, nonmetals are replacing metals for a variety of applications that have nonlinear load-to-response characteristics, even under mild loading conditions. Also, the structure is optimized to make most of its strength, pushing the load level so close to the strength of the material that it starts behaving non-linearly. In order to accurately predicts the strength of the structure in these circumstances, It is necessary to perform a nonlinear analysis. In short: The stiffness matrix relating to the load and response is assumed to be constant for static analysis: however, all the real word structures behave nonlinearity. The stiffness matrix consists of geometric parameters like length, cross-sectional area and moments of inertia of section, etc., and material properties like elastic modulus, rigidity modulus, etc, The static analysis assumes that these parameters do not change when the structure is loaded: On the other hand, static analysis takes into account the changes in these parameters as the load is applied to the structure. These changes are accommodated into the analysis by rebuilding the stiffness matrix using a deformed structure configuration and uploaded properly after each incremental load application.

A linear structure can sustain any load whatsoever and undergo any displacement magnitude.

1. There are no critical (limit, bifurcation, turning, or failure) points.

2. Solutions for various load cases may be superimposed.

3. Removing all loads returns the structure to the reference state.

4. Simple direct solution of the structural stiffness relationship without the need for costly load incrementation and iterative schemes.

Reasons for Nonlinear FEA:

1. Strength analysis – how much load can the structure support before global failure occurs.

2. Stability analysis – finding critical points (limit points and bifurcation points) closest to the operational range.

3. Service configuration analysis – finding the ‘operational’ equilibrium configuration of certain slender structures when the fabrication and service configurations are quite different (e.g. cable and inflatable structures).

4. Reserve strength analysis – finding the load-carrying capacity beyond critical points to assess safety under abnormal conditions.

5. Progressive failure analysis – a combined strength and stability analysis in which progressive deterioration (e.g. cracking) is considered.

6. Establish the causes of a structural failure.

7. Safety and serviceability assessment of existing infrastructure whose integrity may be in doubt due to:

• Visible damage (cracking, etc)
• Health–monitoring
• Concern over corrosion or general aging.

• A shift towards high-performance materials and more efficient utilization of structural components.

• Direct use of NonlinearFEA in design for both ultimate load and serviceability limit states.

1.Learn first how the software works on a simple model before you use a nonlinear feature that you haven’t used. Also how your structural component will behave.

2.Try to understand the software’s supporting documentation, its output, and warnings.

3.Know apriori what you are looking for, Prepare a list of questions which your analysis you think should be able to answer. Design the analysis such as model material model, and boundary conditions in order to answer the question you have in mind.

4.Keep the final model as simple as possible. A linear analysis done apriori can provide a lot of information such as where the high stress in the model where the initial contact may occur, and what level of load will introduce plasticity in the model. Are the physical phenomena to a reasonable level of accuracy.

5.Verify the results of the nonlinear FEA Solution, Before you start the analysis, you should have a rough idea of the results through studies, experience, and benchmarks. When the result seems unreasonable that is they are too much different from what you expect, then try to understand the WHY part of it.

6.Try to look into the assumptions made with respect to the structural component, its geometry behavior wrt large strain (On/off), look into different material models if the earlier model is unable to give you the results you expect (sometimes software only make some models compatible with commonly used elements and in this case, you might look into a possibility of changing the element formulations).

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