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Non-Linear FEA

March 9th - April 6th, 2018
07:00 PST / 10:00 EST / 15:00 GMT / 16:00 CET
Five Session Online Training Course - 2.5 hours per session
one session per week


  • 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.

This 5-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

Note: This is a five-week course. Each session represents one 2-hour session per week.

Session 1

  • Background to non-linear analysis
    • Linear versus non-linear
  • Overview of types of non-linearity
    • Geometric non-linearity
    • Buckling
    • Follower forces
    • Material non-linearity
    • Contact non-linearity
  • Example – oil tank
  • Session 1 homework

Session 2

  • Review of homework from session 1
  • Geometric non-linearity
    • Background
    • Theory
    • Shallow Roof example
  • Non-linear strategy
    • Non-linear convergence
    • Non-linear loading
    • Real world boundary conditions
    • Scope of the analysis
  • Session 2 homework

Session 3 

  • Review: Session 2 Homework
  • Further Buckling
    • Background and Theory
    • Linear buckling example
    • Non-linear Buckling
  • Contact surface methods
    • Background
    • Types of contact
    • Contact challenges

Session 4

  • Further Nonlinear Material analysis
    • Background
    • Yield Failure theories
    • Hardening Types
    • Beyond Yield
    • Examples
  • Viscoelasticity
    • Background
    • Examples
  • Hyperelastic material analysis
    • Background
    • Examples

    Session 5 

    • Mesh adaptivity and element erosion
    • Nonlinear transient analysis
    • Implicit versus explicit analysis
      • Explicit background
      • Explicit rod example
      • Explicit cylinder example
      • Overview of Explicit analysis
      • Lagrangian and Eulerian methods


    PSE Competencies addressed by this training course 

    ID Competence Statement
    NGECkn1 Identify the contact facilities available in a finite element system, including friction models.
    NGECkn2 Identify the algorithm used to follow highly nonlinear equilibrium paths in a finite element system.
    NGECkn3 List common categories of geometric non-linearity and contact.
    NGECkn4 Identify the extent to which your application software allows modification of geometric nonlinear solution parameters.
    NGECco1 Discuss the terms Geometric Strengthening and Geometric Weakening.
    NGECco2 Explain why load sequencing can give rise to different end results and identify relevant examples.
    NGECco3 Explain how large displacement effects can be handled as a series of linear analyses.
    NGECco4 Outline how large displacements, plasticity and instability can interact in a collapse scenario.
    NGECo5 Discuss the term Load Following.
    NGECo7 Contrast the terms Large Displacement and Large Strains.
    NGECo8 Discuss the meshing requirements for accurate contact area and contact pressure.
    NGECo9 Discuss the limitations of contact algorithms available in a finite element system.
    NGECo10 Discuss the theoretical basis of the contact algorithms available in a finite element system.
    NGEColl Explain the challenges of following a highly non-linear equilibrium path with both load control and displacement control.
    NGECo12 Contrast the Newton-Raphson method and the Riks arc-length method.
    NGECap1 Identify whether a system has automatic re-meshing and implement a re-meshing strategy as appropriate, due to significant distortion of a mesh.
    NGECap3 Carry out large strain analyses.
    NGECap4 Use an analysis system to carry out contact analyses.
    NGECap5 Conduct analyses with pre-stress and pre-strain.
    NGECap6 Carry out analyses with load following.
    NGECan1 Analyse the results from geometrically nonlinear analyses (including contact) and determine whether they satisfy inherent assumptions.
    NGECan2 Compare the results from geometrically nonlinear analyses (including contact) with allowable values and comment on findings.
    NGECsy2 Plan modelling strategies for geometrically nonlinear problems, including contact.
    NGECev1 Assess whether Load Following is likely to be required in any analysis.
    NGECev2 Select appropriate solution schemes for geometrically non-linear problems
    NGECev3 Assess whether element distortion effects are affecting the quality of solution and take appropriate remedial action where necessary.
    PLASkn1 For a beam under pure bending sketch the developing stress distribution from first yield, to collapse.
    PLASkn7 Sketch a stress-strain curve for an elastic-perfectly plastic and bi-linear hardening material showing elastic and plastic modulii.
    PLASco1 Discuss salient features of the inelastic response of metals.
    PLASco2 Explain the terms Isotropic Hardening, Kinematic Hardening and Rate Independency.
    PLASco4 Explain the terms Limit Load and Plastic Collapse Load and explain why the latter is often a misnomer.
    PLASco10 Discuss the effects of stress singularities at reentrant corners on limit load.
    PLASco14 Illustrate typical examples of Local Plastic Deformation and Gross Plastic Deformation.
    PLASco19 Derive the load-displacement relationship for simple two or three-bar structures with elastic-perfectly plastic materials. Repeat the derivation for elastic strain hardening materials.
    PLASco23 Describe the Bauschinger Effect.
    PLASco25 Explain why finite element solutions tend to become unstable as the limit load is approached.
    PLASco26 Discuss approaches employed to improve the finite element prediction of limit load.
    PLASco27 Explain the process of Stress Redistribution.
    PLASco31 Discuss the general relationship between finite element mesh and size of plastic zone.
    PLASco37 Describe why the incompressible nature of plastic deformation can cause difficulties with analysis.
    PLASap7 Using standard material data, derive a true stress vs true strain curve to be used for nonlinear analysis.
    PLASan2 Compare the results from nonlinear material analyses of typical pressure components with allowable values and comment on findings.
    PLASsy1 Specify the use of elastic perfectly plastic and bilinear or multi-linear hardening constitutive data as appropriate.
    PLASsy3 Plan modelling strategies for nonlinear material problems.
    PLASev3 Assess the significance of neglecting any feature or detail in any nonlinear material idealisation.
    PLASev4 Assess the significance of simplifying geometry, material models, mass, loads or boundary
    BINkn1 Define the term Slenderness Ratio.
    BINkn2 Define the term Radius of Gyration.
    BINkn3 Define the Determinant of a matrix.
    BINco1 Explain the terms Stable Equilibrium, Neutral Equilibrium and Unstable Equilibrium.
    BINco2 Discuss the term Load Proportionality Factor and explain what a negative value indicates.
    BINco3 Explain why theoretical Buckling Loads (including those calculated using FEA) often vary significantly from test values.
    BINco4 Explain the term Local Buckling and indicate how this can normally be prevented.
    BINco5 Discuss the snap-through buckling of a shallow spherical shell subjected to a lateral load and explain why a linear buckling analysis is not appropriate.
    BINco6 Discuss the term Post-Buckling Strength and illustrate this with examples.
    BINco8 Explain why symmetry should be used with caution in buckling analyses.
    BINco10 Explain the effects of an offset shell mid-surface on buckling.
    BINco12 Explain what a structural mechanism is.
    BINco13 Explain the meaning of Stable Buckling and provide examples.
    BINco14 Explain the meaning of Unstable Buckling and provide examples.
    BINco16 Describe the theoretical steps in a linear buckling analysis, highlighting the role of the Geometric Stiffness Matrix.
    BINco17 Outline various methods of extracting eigenvalues, including the Power Method.
    BINco18 Explain when geometric non-linear analysis should be used in a buckling analyses.
    BINco19 Explain the phenomenon of mode jumping.
    BINco20 Discuss the terms lateral buckling and flexural-torsional buckling, and provide examples of where this behaviour might arise.
    Binco23 Discuss the characteristics of thin-walled structures that could influence buckling behaviour.
    BINap1 Use tables to evaluate Euler buckling loads for common configurations of columns, plates and shells.
    BINap2 Conduct eigenvalue buckling analyses.
    BINap3 Conduct post-buckling analyses.
    BINan1 Compare FEA results with buckling and instability tests and justify conclusions.
    BINan2 Analyse the results from buckling and instability analyses of typical pressure components and determine whether they satisfy code requirements.
    BINsy1 Plan modelling strategies for buckling of stiffened plate/shell structures.
    BINsy2 Plan modelling strategies for plate/shell structures with an offset in midsurface.
    BINsy3 Plan a series of simple benchmarks in support of a more complex instability analysis.
    BINsy4 Plan modelling strategies for buckling and instability problems.
    BINsy5 Prepare an analysis specification for buckling and instability analyses, including modelling strategy, highlighting any assumptions relating to geometry, loads, boundary conditions and material properties.
    BINev1 Assess the possibility of local and global buckling from the results of a non-buckling analysis.
    BINev2 Select appropriate idealisation(s) for a buckling analysis.
    BINev3 Assess whether a non-linear buckling analysis is necessary.
    BINev4 Select appropriate solution schemes for buckling problems.
    BINev5 Assess the significance of neglecting any feature or detail in any buckling idealisation.
    CTDkn6 State the basic definitions of stress relaxation and creep.
    CTDco1 Describe and illustrate a standard creep curve for steels, highlighting the steady state regime.
    CTDco2 Using the standard creep curve, describe the effects of (i) increasing stress level and (ii) removing the stress.
    CTDco3 Describe different ways of presenting creep data.
    CTDco7 Explain, in general terms, the creep solution process as typically implemented in finite element systems.
    MASco7 Describe the following constitutive behaviour for materials relevant to your industry sector: hyperelastic, viscoelastic, viscoplastic.
    MASco18 Describe the effects of strain rate (if any) on the behaviour of materials used in products within your organisation.

    Purchasing Details

    Members Price
    £269 | $346 | €296

    Non-Members Price
    £403 | $518 | €443
    Order Ref: el-230
    Event Type: Course
    Location: e-Learning Online
    Date: March 9, 2018

    Course Tutor:

    Read Tony's bio on the NAFEMS Tutors Page

    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!

    Session 1:
    Friday. March 9th

    Session 2:
    Friday, March 16th

    Session 3:
    Friday March 23rd

    Session 4:
    Friday, March 30th

    Session 5:
    Friday, April 6th

    NoteOnce you register for the course using the "order" button (look up), you will receive your invoice, and the day before the course starts, an email invite to the class discussion board. Please note that no 'physical' goods will be mailed to you.

    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