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- Practical Introduction to Non-Linear Analysis

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.

Who Should Attend ?

This non-linear finite element course is aimed at **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. The course is independent of any finite element software code.

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

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.

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.

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

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.

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.

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

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. |

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