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

Practical Introduction to Non-Linear Finite Element Analysis (FEA)

Duration:	2 days
Delivery:	Onsite Classroom Public Classroom
Language:	English
Level:	Mid-level
Availability:	Worldwide
Tutor(s):	Adib Becker Gino Duffett
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Upgrade your non-linear knowledge with the experts.

This non-linear Finite Element course is intended for delegates interested in learning how finite elements are used to analyse advanced non-linear problems, difficulties encountered in modelling real-life applications and guidelines for using non-linear finite element technology.

The objectives of this Finite Element course are:

To provide delegates with an introduction to the fundamental theory of non-linear Finite Element analysis.
To highlight the possible difficulties that may be encountered in using Finite Element software to analyse non-linear problems.

Course Program

Brief Overview of Linear Finite Element analysis

A brief overview of linear Finite Element formulation, numerical algorithms, etc. to provide a foundation for the non-linear formulation.

General Introduction to Non-linear problems

Classifications of non-linear problems, Comparison of linear and non-linear finite element analysis, Non-linear algorithms and procedures, Difficulties in modelling non-linear problems.

Plasticity

Basic plasticity theory, Uniaxial and multi-axial plasticity, Work hardening and cycle loading, finite element treatment of plasticity, Solution strategy and accuracy, Discussion of typical practical plasticity applications.

Creep and Visco-elasticity

Basic theory of creep, uniaxial and multiaxial creep therory, time and strain hardening, Explicit and implicit time integrations, Discussion of typical practical creep applications.

Contact Problems

Basic theory of contact mechanics, classification of contact configurations, Hertzian and non-Hertzian contact problems, finite element contact algorithms, Penalty methods and Lagrange multipliers, Difficulties in modelling contact problems, Tips and guidelines, Discussion of practical contact problems.

Geometric Non-linearity

Basic theory of geometric non-linearity, GNL stress-strain definitions, finite element algorithms for geometric non-linearities, buckling problems, Arc-length and line-search methods, Solution strategy and accuracy, Discussion of typical GNL problems.

Brief introduction to other advanced Finite Element Applications

A brief overview of fracture mechanics, fatigue analysis, thermo-mechnical problems, viscoelastic materials (polymers, plastics, rubbers), explicit finite element codes

Who Should Attend?

Engineers and scientists who want to gain an understanding of the fundamental theory of non-linear Finite Element Analysis, solution accuracy, difficulties and application to practical problems.

As this is an advanced Finite Element course, a pre-requisite for this course is a reasonable knowledge of linear Finite Element theory and applications. However, no prior knowledge of non-linear Finite Element theory is required.

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.

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PSE Competencies addressed by this training course

ID	Competence Statement
Plasticity
PLASkn1	For a beam under pure bending sketch the developing stress distribution from first yield, to collapse.
PLASkn2	For a simple steel thick cylinder or sphere under internal pressure, state the location of first yield.
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.
PLASco3	Discuss the role of the Hydrostatic and Deviatoric Stress Components in yield criteria for isotropic, polycrystalline solids.
PLASco7	Explain the phenomenon of Shakedown and define the term Shakedown Load.
PLASco8	Contrast the terms Ratchetting and Low Cycle Fatigue.
PLASco11	Explain how plastic effects in a Finite Element system are commonly handled as a series of incremental iterative linear analyses
PLASco12	Explain, in general terms, the function of the Mises Flow Rule or Prandtl - Reuss Equations, used in a finite element solver.
PLASco13	Outline how the cumulative and incremental displacements, total strains, elastic strains, elastic stresses and plastic strains are related.
PLASco14	Illustrate typical examples of Local Plastic Deformation and Gross Plastic Deformation.
PLASco16	Explain the significance of a Hysteresis Loop in a load/deflection test.
PLASco23	Describe the Bauschinger Effect.
PLASco27	Explain the process of Stress Redistribution.
PLASco28	Describe the process and common purpose of Autofrettage.
PLASap4	Use FEA to illustrate Shakedown for a range of components/structures and actions.
PLASap5	Use FEA to determine the presence of ratchetting for a range of components and actions.
PLASap7	Using standard material data, derive a true stress vs true strain curve to be used for nonlinear analysis.
PLASsy2	Plan a series of simple benchmarks in support of a more complex plasticity analysis.
PLASsy4	Prepare an analysis specification for a nonlinear material analysis, including modelling strategy, highlighting any assumptions relating to geometry, loads, etc.
PLASev1	Select appropriate solution schemes for non-linear material problems.
PLASev4	Assess the significance of simplifying geometry, material models, mass, loads or boundary conditions, on a non linear material analysis.
Creep and Time Dependency
CTDkn2	State the Time Hardening and Strain Hardening Laws, based on Norton s Power Law, for primary creep.
CTDkn3	State how typical creep laws depend on temperature.
CTDkn4	List the range of creep and time-dependent constitutive models available in any finite element used.
CTDkn5	Identify the extent to which your application software allows modification of creep solution parameters.
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.
CTDco4	Explain the term Stress Redistribution in a structure subject to creep under load.
CTDco9	Contrast the creep solution procedure with the procedure commonly employed for plasticity.
CTDco10	Discuss the complexities arising from a multiaxial stress state and illustrate how these are normally handled.
CTDco11	Discuss the advantage and validity of using a stiffness matrix that doesn t vary during the creep solution.
CTDco14	Explain why it is important to carefully consider the output required from a finite element system for this type of analysis.
CTDco17	Contrast Explicit and Implicit Creep Integration.
CTDco19	Describe why a creep analysis is necessary for relevant components in your organisation or sector.
CTDap1	Define creep constitutive data as appropriate.
CTDap2	Use FEA to obtain creep solutions for a range of typical components.
CTDsy3	Prepare an analysis specification for a time dependent analysis, including modelling strategy, highlighting any assumptions relating to geometry, loads, boundary...
CTDev3	Assess the significance of simplifying geometry, material models, mass, loads or boundary conditions, on a time dependent analysis.
CTDev4	Select appropriate solution schemes for time dependent problems.
Nonlinear Geometric Effects and Contact
NGECkn1	Identify the contact facilities available in a finite element system, including friction models.
NGECkn2	Identify the algorithm used to follow highly non-linear equilibrium paths in a finite element system.
NGECkn3	List common categories of geometric non-linearity and contact.
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.
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.
NGECap2	Conduct large displacement analyses.
NGECap3	Carry out large strain analyses.
NGECap4	Use an analysis system to carry out contact analyses.
NGECap6	Carry out analyses with load following.
NGECan1	Analyse the results from geometrically nonlinear analyses (including contact) and determine whether they satisfy inherent assumptions.
NGECsy1	Plan a series of simple benchmarks in support of a more complex nonlinear analysis.
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
Buckling and Instability
BINco3	Explain why theoretical Buckling Loads (including those calculated using FEA) often vary significantly from test values.
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.
BINco13	Explain the meaning of Stable Buckling and provide examples.
BINco14	Explain the meaning of Unstable Buckling and provide examples.
BINco18	Explain when geometric non-linear analysis should be used in a buckling analyses.
BINsy3	Plan a series of simple benchmarks in support of a more complex instability analysis.
BINsy4	Plan modelling strategies for buckling and instability problems.
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.

Practical Introduction to Non-Linear Analysis