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.

- 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

- 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

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

- 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

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

- 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

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.

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. |

- 10 Steps to Successful Explicit Dynamic Analysis
- Advanced Computational Fluid Dynamics
- Advanced Dynamic Finite Element Analysis
- Basic Finite Element Analysis
- Computational Fluid Dynamics for Structural Designers and Analysts
- Composite Finite Element Analysis
- Elements of Turbulence Modeling
- Essential Principles of Simulation Data Management
- Fatigue & Fracture Mechanics in Finite Element Analysis
- FEA Day-to-Day
- Introduction au Calcul de Structures, aux Éléments Finis et à la Simulation Numérique
- Introduction to CFD Analysis: Theory and Applications
- Introduction to Dynamics using FEA
- Introduction to Engineering Simulation for Non-Specialists
- Introduction to Practical Computational Fluid Dynamics
- Méthode des Eléments Finis pour le Dimensionnement et la Vérification de Pièces et Structures
- Méthodologies et Bonnes Pratiques de Simulation Numérique
- Non-Linear Finite Element Analysis
- Principes essentiels de la simulation des données et des processus de la simulation numérique
- Practical Modelling of Joints and Connections
- Praktische Anwendung der Finite-Elemente-Methode und Ergebnisinterpretation
- Practical Introduction to Finite Element Analysis
- Practical Introduction to Non-Linear Analysis
- Structural Optimization in Finite Element Analysis
- V&V: Vérification et Validation des simulations pour l'ingénierie
- Verification & Validation in Engineering Simulation
- Verification and Validation in Scientific Computing
- Verification & Validation of Computational Models
- Why Do Engineering Simulation

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