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- Finite Element Procedures For The Numerical Analysis Of Steel And Aluminium Structures

Title: | Finite Element Procedures For The Numerical Analysis Of Steel And Aluminium Structures |

Provider: | MZA Research - Numerical Consulting Ltd |

Duration: | 21 Hours (3 days) |

Date of Recognition: | October 2022 |

Delivery Method: | In Person Classroom |

Location: | London, UK |

For Full Details, Email: research@mza-structuralengineering.com

Aims

This module is intended to be an intensive 3-day numerical application course aimed at providing the correct sequential procedure to obtain a steel/aluminium structure FE model that is compatible, from a design perspective, with dynamic analyses, under geometric, material and boundary non-linear conditions. The numerical examples presented in the course cover the use of beam, plate and brick elements with most of the examples are taken from real experiences.

The course is suitable for structural engineers mainly in the field of Steel and Aluminium Structures who are interested in learning or optimising their approach to ensure that they have a proper and analytical correct model-assembly-procedure, model debugging approach and a verification-validation understanding of the mechanical problem. Participants should have a reasonable-experienced background in Finite Element Methods and Structural Mechanics. Methods and debugging technics will be outlined with only few mathematical references and are illustrated by practical software implementations.

The course/training programme is not software specific, but it will be held by making use of the Strand7® Nonlinear FE package and the new 3D Experience system Simulia/Abaqus (by Dassault Systèmes). For all participants, an educational licence will be provided upon request.

FEAkn01 | List the various steps in the analysis/simulation process | |||

FEAkn02 | Define the meaning of degree of freedom | |||

FEAkn03 | List the nodal degrees of freedom and the associated force actions for common beam, 2D solid, 2D axisymmetric, 3D solid and shell elements, for the Displacement FEM | |||

FEAkn05 | State the variational principle involved in the formulation of the Displacement Finite Element Method and identify the solution quantity assumed within each element | |||

FEAkn06 | State the variational principle involved in the formulation of the Equilibrium Finite Element Method and identify the solution quantity assumed within each element | |||

FEAkn07 | Name other finite element methods | |||

FEAkn14 | List the possible advantages of applying material properties, loads and boundary conditions to underlying geometry rather than to finite element entities | |||

FEAkn15 | List 2 common solvers for large sets of simultaneous equations | |||

FEAco01 | Describe the sources of error inherent in finite element analysis, in general terms | |||

FEAco02 | Discuss checks that may be used post-solution to check for the presence of inaccuracy | |||

FEAco03 | Explain the term solution residual | |||

FEAco04 | Explain the meaning of convergence, including h and p types | |||

FEAco05 | Discuss the difficulties that can arise in using a CAD model as the basis for carrying out analysis and simulation | |||

FEAco06 | Discuss the need for a consistent set of units in any analysis and illustrate possible pitfalls | |||

FEAco07 | Explain why strains and stresses are generally less accurate than displacements for any given mesh of elements, using the Displacement FEM | |||

FEAco09 | Explain the meaning of the term ill-conditioned when used in the context of a set of solution equations and illustrate physical situations where this might reflect reality | |||

FEAco13 | Explain how the structural stiffness matrix is assembled from the individual element matrices | |||

FEAco17 | Explain the process of Gaussian Quadrature and the terms Reduced Integration, Shear Locking and Mechanisms | |||

FEAco18 | Explain the term Isoparametric Element | |||

FEAco20 | Discuss the terms C0 and C1 Continuity | |||

FEAco25 | Explain the term Bubble Function or Nodeless Variable | |||

FEAco28 | Explain why element distortion generally results in poorer results | |||

FEAco29 | Discuss the term Flying Structure or Insufficiently Constrained Structure | |||

FEAco35 | Discuss the terms Validation and Verification and highlight their importance | |||

FEAco39 | Discuss the Geometric Stiffness Matrix and highlight situations where it becomes important | |||

FEAap01 | Employ an analysis system for the determination of stresses and strains in small displacement, linear elastic problems | |||

FEAap04 | Illustrate the various steps in the Displacement Finite Element Method from assumed displacement polynomial to determination of stresses | |||

FEAap10 | Illustrate various physical situations which will result in a Stress Singularity and explain why it is not appropriate to use finite element results at such locations directly | |||

FEAap12 | Employ a range of post-solution checks to determine the integrity of FEA results | |||

FEAap13 | Conduct validation studies in support of FEA | |||

FEAap14 | Carry out sensitivity studies | |||

FEAan03 | Analyse the results from sensitivity studies and draw conclusions from trends | |||

FEAsy01 | Prepare an analysis specification, including modelling strategy, highlighting any assumptions relating to geometry, loads, boundary conditions and material properties | |||

FEAsy02 | Develop an analysis strategy that enables the relative significance of individual model parameters and their interactions to be evaluated | |||

FEAsy04 | Prepare quality assurance procedures for finite element analysis activities within an organisation | |||

FEAsy06 | Contribute to the development of a competency process that supports staff technical development | |||

FEAsy08 | Prepare a validation plan in support of a FEA study | |||

FEAev02 | Assess the significance of neglecting any feature or detail in any idealisation | |||

FEAev03 | Assess the significance of simplifying geometry, material models, loads or boundary conditions | |||

SIMMkn06 | State simulation V&V principles | |||

SIMMco06 | Explain the terms Verification and Validation | |||

SIMMco07 | Explain the term solution verification | |||

SIMMco08 | Explain the term code verification | |||

SIMMap03 | Conduct validation studies in support of simulation | |||

SIMMap04 | Perform basic model checks | |||

SIMMsy07 | Prepare a validation plan in support of a FEA study | |||

NGECkn01 | Identify the common structural and thermal contact facilities available in a finite element system, eg friction models and constraint enforcement methods | |||

NGECkn02 | Identify the algorithms commonly used to follow non-linear equilibrium paths in a finite element system | |||

NGECkn04 | Identify the extent to which your application software allows modification of geometric non-linear solution parameters and their potential effect on the solution | |||

NGECco01 | Discuss the terms Geometric Strengthening and Geometric Weakening | |||

NGECco02 | Explain why the sequence of load application (ie load A followed by B cf. B then A) can give rise to very different end results and identify examples | |||

NGECco03 | Explain how large displacement effects can be handled as a series of linear analyses | |||

NGECco04 | Outline how large displacements, plasticity and instability can affect the failure mode and load of a structure | |||

NGECco05 | Discuss the term Load Following | |||

NGECco06 | Discuss the concept of Mesh Pre-Distortion | |||

NGECco07 | Contrast the terms Large Displacement and Large Strains | |||

NGECco09 | Discuss the limitations of contact algorithms available in a finite element system | |||

NGECco10 | Discuss the theoretical basis of the contact algorithms available in a finite element system | |||

NGECco11 | Explain the challenges of following a highly non-linear equilibrium path with both load control and displacement control | |||

NGECco12 | Contrast the Newton-Raphson method with the Riks arc-length method | |||

NGECap02 | Conduct large displacement analyses | |||

NGECap03 | Carry out large strain analyses | |||

NGECap04 | Use an analysis system to carry out contact analyses | |||

NGECap05 | Conduct analyses with initial pre-loading, eg bolted assemblies or residual fabrication stresses | |||

NGECan01 | Analyse the results from geometrically nonlinear analyses (including contact) and determine whether they satisfy inherent assumptions | |||

NGECsy01 | Plan a series of simple benchmarks in support of a more complex nonlinear analysis | |||

NGECsy02 | Plan modelling strategies for geometrically nonlinear problems, including contact | |||

NGECev02 | Select appropriate solution schemes for geometrically non-linear problems | |||

BINkn01 | Define the term Slenderness Ratio | |||

BINkn02 | Define the term Radius of Gyration | |||

BINkn03 | Define the Determinant of a matrix | |||

BINco01 | Explain the terms Stable Equilibrium, Neutral Equilibrium and Unstable Equilibrium | |||

BINco02 | Discuss the term Load Proportionality Factor and explain what a negative value indicates | |||

BINco03 | Explain why theoretical Buckling Loads (including those calculated using FEA) often vary significantly from test values | |||

BINco04 | Explain the term Local Buckling and indicate how this can normally be prevented | |||

BINco05 | 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 | |||

BINco06 | Discuss the term Post-Buckling Strength and illustrate this with examples | |||

BINco07 | Explain the term Static Equilibrium as used in structural design codes | |||

BINco08 | Explain why symmetry should be used with caution in buckling analyses | |||

BINco20 | Discuss the terms lateral buckling and flexural-torsional buckling, and provide examples of where this behaviour might arise | |||

BINap01 | Use tables to evaluate Euler buckling loads for common configurations of columns, plates and shells | |||

BINap02 | Conduct eigenvalue buckling analyses | |||

BINap03 | Conduct post-buckling analyses | |||

MESMkn09 | Sketch a general 3D stress element showing all stress components | |||

MESMkn10 | Sketch Mohr Circle for a simple tensile test specimen, illustrating the plane of maximum shear | |||

MESMkn11 | Define Hooke's Law | |||

MESMkn12 | Define Poisson's Ratio | |||

MESMkn13 | Define the relationship between Young's Modulus, Poisson's Ratio and Shear Modulus | |||

MESMkn14 | Sketch the through-thickness shear stress distribution in a rectangular beam subjected to a shearing load | |||

MESMkn18 | List various Failure Hypotheses / Criteria | |||

MESMkn20 | Define Tresca and von Mises Stress for a 3D stress state | |||

MESMkn21 | State the elastic Constitutive Relations in 2D, for a homogeneous, isotropic material | |||

MESMco02 | Explain the terms Uniaxial, Biaxial and Triaxial Stress | |||

MESMco04 | Discuss the terms True Stress and Natural Strain | |||

PLASkn01 | For a beam under pure bending sketch the developing stress distribution from first yield, to collapse | |||

PLASkn07 | Sketch a stress-strain curve for an elastic-perfectly plastic and bi-linear hardening material showing elastic and plastic modulii | |||

PLASkn09 | Identify the extent to which your application software allows modification of nonlinear material solution parameters | |||

PLASco01 | Discuss salient features of the inelastic response of metals | |||

PLASco02 | Explain the terms Isotropic Hardening, Kinematic Hardening and Rate Independency | |||

PLASco03 | Discuss the role of the Hydrostatic and Deviatoric Stress Components in yield criteria for isotropic, polycrystalline solids | |||

PLASco05 | Explain the terms First Yield Load, Ultimate Load and Plastic Instability Load | |||

PLASco10 | Discuss the effects of stress singularities at re-entrant corners on limit load | |||

PLASco13 | Outline how the cumulative and incremental displacements, total strains, elastic strains, elastic stresses and plastic strains are related in the finite element solution algorithm | |||

PLASco14 | Illustrate typical examples of Local Plastic Deformation and Gross Plastic Deformation | |||

PLASco15 | Discuss the term Plastic Hinge | |||

PLASco20 | Discuss why implementation of the Tresca Criterion can cause numerical problems in an FEA solution and explain how you might get round the problem | |||

PLASco23 | Describe the Bauschinger Effect | |||

PLASco25 | Explain why finite element solutions tend to become unstable as the limit load is approached | |||

PLASco27 | Explain the process of Stress Redistribution | |||

PLASco37 | Describe why the incompressible nature of plastic deformation can cause difficulties with analysis | |||

PLASap01 | Define elastic perfectly plastic and bi-linear or multi-linear hardening constitutive data as appropriate | |||

PLASap02 | Use FEA to determine Limit Loads for a range of components | |||

PLASap03 | Use FEA to determine Plastic Collapse Loads for a range of components | |||

PLASsy01 | Specify the use of elastic perfectly plastic and bi-linear or multi-linear hardening constitutive data as appropriate | |||

PLASsy04 | Prepare an analysis specification for a nonlinear material analysis, including modelling strategy, highlighting any assumptions relating to geometry, loads, boundary conditions and material properties | |||

PLASco39 | Describe variations on the Newton-Raphson technique that can be used to find a converged solution when analysing problems involving plasticity and discuss the strengths and weaknesses of these approaches | |||

PLASco40 | Explain how and why plastic behaviour involves the appearance of residual stresses in a structure | |||

DVkn10 | State the typical matrix structure of the discrete differential equation system for linear MDOF systems | |||

DVkn11 | Define the terms free and forced vibration | |||

DVkn12 | State typical values for damping in various engineering structures | |||

DVco01 | Explain the terms Kinematics and Kinetics | |||

DVco04 | Explain the term Conservation of Energy and Conversation of Momentum | |||

DVco06 | Discuss the term Relative Motion | |||

DVco09 | Explain the term Conservative Forces, Potential, and Strain energy | |||

DVco10 | Describe the application of Lagrange's Equation to obtain the differential Equation of Motion | |||

DVco11 | Explain the Principle of Virtual Work | |||

DVco12 | Explain the use of physical, analytical and mathematical models in a structural dynamics modelling process | |||

DVco13 | Discuss the full discrete linear differential Equation of Motion in matrix terms and explain the terms Free Response and No Damping | |||

DVco14 | Explain the derivation of the General Matrix Eigenvalue Problem (characteristic equation) from the Equation of Motion | |||

DVco15 | Explain different physical forms of Dynamic Loading (Excitation) in a Force Response analysis | |||

DVco16 | Explain Harmonic, Periodic, Transient, and Random time response | |||

DVco20 | Discuss the term Natural Frequency in relation to a continuum and a discretized system | |||

DVco21 | Discuss the phenomenon of Resonance | |||

DVco22 | Explain the terms Mode Shape/Eigenvector, Modal Mass, Modal Damping, and Modal Stiffness Factors | |||

DVco25 | Discuss the characteristics of mass and damping matrices | |||

DVco27 | Describe the effect of damping on natural frequencies and resonance | |||

DVco28 | Describe Free Vibration of undamped and damped systems | |||

DVco30 | Discuss the concept of mass and stiffness proportional (Rayleigh) damping | |||

DVco33 | Discuss the steady state and total response of a damped system subjected to harmonic excitation | |||

DVco34 | Describe the terms Intertia force, Damping force and Stiffness force | |||

DVco38 | Discuss various strategies for extraction of eigenvalues and mode shapes, including Lanczos and Subspace Iteration | |||

DVco41 | Discuss the influence of pre-stress on natural frequencies | |||

DVco44 | Explain the terms Implicit Solution and Explicit Solution for the time integration of the equations of motion and the appropriate associated problem classes of dynamic analyses | |||

DVco54 | Discuss various approaches to Seismic Analysis and highlight relevant philosophy and analysis considerations | |||

DVco56 | Explain the term response spectra | |||

DVap02 | Use appropriate damping idealisations and/or measured modal damping when necessary | |||

DVap05 | Employ an analysis system for the determination of natural frequencies and mode shapes | |||

DVap06 | Employ an analysis system for the determination of steady state response and frequency response function for a periodic excitation | |||

DVap10 | Employ an analysis system for the simulation of impact | |||

DVap13 | Illustrate the approximate nature of finite element analysis, through dynamic examples chosen from your industry sector |

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