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Non-Linear FEA

What are the most important nonlinear FEA analysis topics?
What practical hints and tips do I need to be able to carry out nonlinear analysis effectively?
What theoretical background do I need to understand the implications of my nonlinear analysis?

Get the answers to these questions and more with this industry-leading, code-independent e-learning course.

Non-Linear FEA

This 6-session, live, online course addresses the important features of non-linear FEA. The course is independent of any specific software – you won’t get bogged down in the details of specific menus and workflows! You will be able to focus on key background and practical hints and tips, covering topics including:

  • Background to non-linear FEA
  • Nonlinear analysis strategy
  • Geometric nonlinearity
  • Material nonlinearity
  • Contact nonlinearity
  • Explicit analysis background

You can either attend the live sessions or take the course on-demand at your leisure.

NAFEMS e-learning gives you the best of both worlds, giving you real, practical knowledge that you can use day-to-day to improve your analyses.


What will you learn?

  • The importance of building a sound nonlinear FEA planning, analysis and review process
  • The background to the various types of nonlinear analysis
  • An understanding of when and how to use nonlinearity
  • An understanding of the risks and strategy needed to successfully tackle nonlinear analysis
  • Limitations of non-linear FEA simulation


Who should attend?

Designers and engineers who are moving into the area of Non-Linear FEA, or need a refresher to brush-up their knowledge. Familiarity with FEA is assumed, but no other background knowledge is required.

Many problems facing designers and engineers are nonlinear in nature. The response of a structure cannot be simply assessed using linear assumptions. Nonlinear behavior can take many forms and can be bewildering to the newcomer.

All physical systems in the real world are inherently nonlinear in nature. One of the most difficult tasks facing an engineer is to decide whether a nonlinear analysis is really needed and, if so, what degree of nonlinearity should be applied. Looking at a bolt heavily loaded in an attachment fitting, it may be that the change in stiffness and load distribution path are critical in evaluating peak stress levels. Perhaps the assembly is in an overload condition and we need to check that plastic growth is stable and there is no ultimate failure – bent but not broken! A flange on a connector arm may be under compressive load, but also sees heavy bending. We need to assess the resistance to buckling with deflection dependent loading paths and possible plastic behavior.

Whatever the nature of the challenge, this objective of this course is to break down the nonlinear problem into clearly defined steps, give an overview of the physics involved and show how to successfully implement practical solutions using Finite Element Analysis.

The course is completely code independent.

  • A full set of notes in PDF format will be available for download. Each session is presented live and is available for review via a streamable recording.
  • Personal passwords are provided to allow you to access e-learning backup material via our special bulletin board. Reading lists, homework submissions, supplementary data are all stored as files on the bulletin board.
  • Interaction via the bulletin board is strongly encouraged to obtain the most from the e-learning class. Typically the board runs for 4 weeks after the last live class sessions, giving you plenty of time to catch up with homework, review and ask questions.

Note: homework is purely voluntary!


Course Process and Details

Students will join the audio portion of the meetings by utilizing the VoIP (i.e. headset connected to the computer via headphone and microphone jacks) or by calling into a standard toll line. If you are interested in additional pricing to call-in using a toll-free line, please send an email to: e-learning @ .

Course Program

This is a six-session online training course, with each session lasting for approximately 2.5/3 hours, depending on homework submissions, questions & discussions.

You can attend the sessions live, and/or by listening to the recordings, which will be made available shortly after the end of each session.

(click to expand) 

Session 1: Overview of non-linear analysis


  • Background to Non-linear
  • Linear versus Non-linear
  • Types of non-linearity
  • Geometric non-linearity
  • Example - oil tank
  • Material Non-linearity
  • Contact non-linearity
  • Session 1 homework


Session 2: Geometric non-linear analysis in depth


  • Review: Homework Session 1
  • Large Displacement or Geometric Nonlinearity
  • Shallow roof example
  • Non-linear convergence strategy
  • Non-linear loading strategy
  • Real world boundary conditions
  • Scope of the Analysis
  • Session 2 Homework


Session 3: Buckling analysis in depth


  • Review: Session 2 Homework
  • Further Buckling
  • Linear Buckling Rod Example
  • Further Nonlinear Buckling


Session 4: Contact analysis in depth


  • Contact surface methods
  • Gap and slideline elements
  • Background to contact technology
  • Penalty and Lagrange methods
  • Modern Contacts
  • Contact types
  • Setting up contacts
  • Contact hints and tips


Session 5: Nonlinear Material analysis in depth


  • Yield and Hardening
  • Examples using Material nonlinearity
  • Viscoelastic material analysis
  • Hyperelastic material analysis
  • Examples using Viscoelasticity and Hyperelasticity


Session 6: Advanced methods


  • Mesh Adaptivity and Element erosion
  • Nonlinear Transient Analysis
  • Implicit versus explicit FE Analysis methods
  • Explicit Background
  • Explicit Examples
  • Overview of Explicit Analysis
  • Lagrangian and Eulerian Elements


PSE Competencies addressed by this training course (click to reveal)


IDCompetence Statement
NGECkn1Identify the contact facilities available in a finite element system, including friction models.
NGECkn2Identify the algorithm used to follow highly nonlinear equilibrium paths in a finite element system.
NGECkn3List common categories of geometric non-linearity and contact.
NGECkn4Identify the extent to which your application software allows modification of geometric nonlinear solution parameters.
NGECco1Discuss the terms Geometric Strengthening and Geometric Weakening.
NGECco2Explain why load sequencing can give rise to different end results and identify relevant examples.
NGECco3Explain how large displacement effects can be handled as a series of linear analyses.
NGECco4Outline how large displacements, plasticity and instability can interact in a collapse scenario.
NGECo5Discuss the term Load Following.
NGECo7Contrast the terms Large Displacement and Large Strains.
NGECo8Discuss the meshing requirements for accurate contact area and contact pressure.
NGECo9Discuss the limitations of contact algorithms available in a finite element system.
NGECo10Discuss the theoretical basis of the contact algorithms available in a finite element system.
NGECollExplain the challenges of following a highly non-linear equilibrium path with both load control and displacement control.
NGECo12Contrast the Newton-Raphson method and the Riks arc-length method.
NGECap1Identify whether a system has automatic re-meshing and implement a re-meshing strategy as appropriate, due to significant distortion of a mesh.
NGECap3Carry out large strain analyses.
NGECap4Use an analysis system to carry out contact analyses.
NGECap5Conduct analyses with pre-stress and pre-strain.
NGECap6Carry out analyses with load following.
NGECan1Analyse the results from geometrically nonlinear analyses (including contact) and determine whether they satisfy inherent assumptions.
NGECan2Compare the results from geometrically nonlinear analyses (including contact) with allowable values and comment on findings.
NGECsy2Plan modelling strategies for geometrically nonlinear problems, including contact.
NGECev1Assess whether Load Following is likely to be required in any analysis.
NGECev2Select appropriate solution schemes for geometrically non-linear problems
NGECev3Assess whether element distortion effects are affecting the quality of solution and take appropriate remedial action where necessary.
PLASkn1For a beam under pure bending sketch the developing stress distribution from first yield, to collapse.
PLASkn7Sketch a stress-strain curve for an elastic-perfectly plastic and bi-linear hardening material showing elastic and plastic modulii.
PLASco1Discuss salient features of the inelastic response of metals.
PLASco2Explain the terms Isotropic Hardening, Kinematic Hardening and Rate Independency.
PLASco4Explain the terms Limit Load and Plastic Collapse Load and explain why the latter is often a misnomer.
PLASco10Discuss the effects of stress singularities at reentrant corners on limit load.
PLASco14Illustrate typical examples of Local Plastic Deformation and Gross Plastic Deformation.
PLASco19Derive the load-displacement relationship for simple two or three-bar structures with elastic-perfectly plastic materials. Repeat the derivation for elastic strain hardening materials.
PLASco23Describe the Bauschinger Effect.
PLASco25Explain why finite element solutions tend to become unstable as the limit load is approached.
PLASco26Discuss approaches employed to improve the finite element prediction of limit load.
PLASco27Explain the process of Stress Redistribution.
PLASco31Discuss the general relationship between finite element mesh and size of plastic zone.
PLASco37Describe why the incompressible nature of plastic deformation can cause difficulties with analysis.
PLASap7Using standard material data, derive a true stress vs true strain curve to be used for nonlinear analysis.
PLASan2Compare the results from nonlinear material analyses of typical pressure components with allowable values and comment on findings.
PLASsy1Specify the use of elastic perfectly plastic and bilinear or multi-linear hardening constitutive data as appropriate.
PLASsy3Plan modelling strategies for nonlinear material problems.
PLASev3Assess the significance of neglecting any feature or detail in any nonlinear material idealisation.
PLASev4Assess the significance of simplifying geometry, material models, mass, loads or boundary
BINkn1Define the term Slenderness Ratio.
BINkn2Define the term Radius of Gyration.
BINkn3Define the Determinant of a matrix.
BINco1Explain the terms Stable Equilibrium, Neutral Equilibrium and Unstable Equilibrium.
BINco2Discuss the term Load Proportionality Factor and explain what a negative value indicates.
BINco3Explain why theoretical Buckling Loads (including those calculated using FEA) often vary significantly from test values.
BINco4Explain the term Local Buckling and indicate how this can normally be prevented.
BINco5Discuss the snap-through buckling of a shallow spherical shell subjected to a lateral load and explain why a linear buckling analysis is not appropriate.
BINco6Discuss the term Post-Buckling Strength and illustrate this with examples.
BINco8Explain why symmetry should be used with caution in buckling analyses.
BINco10Explain the effects of an offset shell mid-surface on buckling.
BINco12Explain what a structural mechanism is.
BINco13Explain the meaning of Stable Buckling and provide examples.
BINco14Explain the meaning of Unstable Buckling and provide examples.
BINco16Describe the theoretical steps in a linear buckling analysis, highlighting the role of the Geometric Stiffness Matrix.
BINco17Outline various methods of extracting eigenvalues, including the Power Method.
BINco18Explain when geometric non-linear analysis should be used in a buckling analyses.
BINco19Explain the phenomenon of mode jumping.
BINco20Discuss the terms lateral buckling and flexural-torsional buckling, and provide examples of where this behaviour might arise.
Binco23Discuss the characteristics of thin-walled structures that could influence buckling behaviour.
BINap1Use tables to evaluate Euler buckling loads for common configurations of columns, plates and shells.
BINap2Conduct eigenvalue buckling analyses.
BINap3Conduct post-buckling analyses.
BINan1Compare FEA results with buckling and instability tests and justify conclusions.
BINan2Analyse the results from buckling and instability analyses of typical pressure components and determine whether they satisfy code requirements.
BINsy1Plan modelling strategies for buckling of stiffened plate/shell structures.
BINsy2Plan modelling strategies for plate/shell structures with an offset in midsurface.
BINsy3Plan a series of simple benchmarks in support of a more complex instability analysis.
BINsy4Plan modelling strategies for buckling and instability problems.
BINsy5Prepare an analysis specification for buckling and instability analyses, including modelling strategy, highlighting any assumptions relating to geometry, loads, boundary conditions and material properties.
BINev1Assess the possibility of local and global buckling from the results of a non-buckling analysis.
BINev2Select appropriate idealisation(s) for a buckling analysis.
BINev3Assess whether a non-linear buckling analysis is necessary.
BINev4Select appropriate solution schemes for buckling problems.
BINev5Assess the significance of neglecting any feature or detail in any buckling idealisation.
CTDkn6State the basic definitions of stress relaxation and creep.
CTDco1Describe and illustrate a standard creep curve for steels, highlighting the steady state regime.
CTDco2Using the standard creep curve, describe the effects of (i) increasing stress level and (ii) removing the stress.
CTDco3Describe different ways of presenting creep data.
CTDco7Explain, in general terms, the creep solution process as typically implemented in finite element systems.
MASco7Describe the following constitutive behaviour for materials relevant to your industry sector: hyperelastic, viscoelastic, viscoplastic.
MASco18Describe the effects of strain rate (if any) on the behaviour of materials used in products within your organisation.



Event Type eLearning
Member Price £397.03 | $502.00 | €469.69
Non-member Price £588.43 | $744.00 | €696.11
Tutor: Tony Abbey


Start Date End Date Location

Session Times


Session Times

Non-Linear FEA

Six-Session Live Online Training Course

2.5/3 hours per session
PDH Credits - 15*

Attend the live sessions, or view the recordings at your convenience

Not Available to Attend this Time?

Would you like us to notify you when the next run of this course is open for enrollment? If so, add yourself to the eLearning Waitlist!

Please click here to view the FAQ section, or if you need to contact NAFEMS about this course.

Engineering Board PDH Credits

*It is your individual responsibility to check whether these e-learning courses satisfy the criteria set-out by your state engineering board. NAFEMS does not guarantee that your individual board will accept these courses for PDH credit, but we believe that the courses comply with regulations in most US states (except Florida, North Carolina, Louisiana, and New York, where providors are required to be pre-approved)

Special Note(s):

Telephony surcharges may apply for attendees who are located outside of North America, South America and Europe. These surcharges are related to individuals who join the audio portion of the web-meeting by calling in to the provided toll/toll-free teleconferencing lines. We have made a VoIP option available so anyone attending the class can join using a headset (headphones) connected to the computer. There is no associated surcharge to utilize the VoIP option, and is actually encouraged to ensure NAFEMS is able to keep the e-Learning course fees as low as possible. Please send an email to the e-Learning coordinator (e-learning @ ) to determine if these surcharges may apply to your specific case.

Just as with a live face-to-face training course, each registration only covers one person. If you plan to register a large group (10+), please send an email to e-learning @ in advance for group discounts.

For NAFEMS cancellation and transfer policy, click here.