Home » When do I need to perform Nonlinear Static Analysis ?.

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- Ajay Singh Sisodiya
- June 11, 2022

**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.

**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.

**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.

**difference between linear analysis and nonlinear analysis.**

**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.

** 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.

**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. **

**(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 exampl****e:** 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**.

**Advantages of linear response:**

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)
- Special loadings not envisaged at the design state
- 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.

**Essential Steps to start with Nonlinear FEA – Fews Advice**

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

**WHY** part of it.

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**Thank you so much for reading!.**

A Product design & development professional FEA Linear and Nonlinear Analyst, Technologist and Professional trainer having more than 11 years of industries working experience. Worked on various automotive, engine and drive train FEA projects in durability domain with many International & National clients. His mission is to minimize the gap between Industry and Mechanical Engineering students by providing quality of skill industries oriented job leading training courses to make them employable ready professionals.

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