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Non-Linear Finite Element Analysis

This training course has been accredited by the NAFEMS Education & Training Working Group

Non-Linear Finite Element Analysis (FEA)


Duration:1.5 days
Onsite Classroom
Tutor(s):Tony Abbey
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Break down your nonlinear problem into clearly defined steps.

Nonlinear behaviour 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, the 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.

Course Program

Part 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

Part 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


Part 3: Buckling analysis in depth

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


Part 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


Part 5: Nonlinear Material analysis in depth

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


Part 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


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.


Get in touch to discuss your next steps with our experienced training team. We can work closely with you to understand your specific requirements, cater for your specific industry sector or analysis type, and produce a truly personalised training solution for your organisation.

All NAFEMS training courses are entirely code independent, meaning they are suitable for users of any software package.

Courses are available to both members and non-members of NAFEMS, although member organisations will enjoy a significant discount on all fees.

NAFEMS course tutors enjoy a world-class reputation in the engineering analysis community, and with decades of experience between them, will deliver tangible benefits to you, your analysis team, and your wider organisation.

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PSE Competencies addressed by this training course

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.
NGECo11Explain 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.