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.

Objectives

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.

Code-Dependancy

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.

PSE Competencies addressed by this training course

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