Non-Linear Finite Element Analysis (FEA)

Duration:	1.5 days
Delivery:	E-learning Onsite Classroom
Language:	English
Level:	Advanced
Availability:	Worldwide
Tutor(s):	Tony Abbey
	Request Full Details

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.

Interested?

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.

Find out more

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.
NGECo11	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.