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 Technical       Publications

 

Home

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Services

FEM Applications

Trainings

Technical Publications

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Contacts

 

Claudio Gianini

Computational
Structural Engineering

Automatic calculation of mechanical structures
Introduction to Part I:  Rory Byrne
Introduction to Part II:  Luca Marmorini

CG CAE Sagl - Balerna, Switzerland

 

Disponibile anche in Italiano

 

INDEX

CHAPTER 1
Modeling of structures by Finite Elements

1.1 Introduction

1.2 Modeling with 2D elements
1.2.1 Plane stress
1.2.2 Plane strain
1.2.3 Axisymmetric stress
1.3 Modelling with 3D elements
1.4 Modeling with shell elements
1.5
Considerations about connections between parts
1.5.1 Welded connections
1.5.2 Rivet connections
1.5.3 Screw connections
1.5.4 Bonded connections
1.6 One-dimensional elements
1.7 Zero-dimensional elements
1.8 Non structural elements
1.9 Membrane elements
1.10 General comments
1.10.1 Overviews
1.10.2 One-dimensional elements

CHAPTER 1 (Continued)
1.10.3 2D and shell elements
1.10.4 3D elements
1.10.5 Non structural elements
1.11 Conclusions

CHAPTER 2
Modeling of boundary conditions
2.1 Introduction
2.2 Constraint conditions
2.3
Load conditions
2.3.1 Point loads
2.3.2 Distributed loads
2.3.3 Thermal loads
2.3.4 Inertial loads
2.3.5 Volume forces
2.4 Symmetry and antisymmetry
2.4.1 Geometric and load symmetries
2.4.2 Geometric symmetries and load antisymmetries
2.4.3 Modal analysis
2.4.4 Conclusions

CHAPTER 3
Interpreting the results
3.1 Introduction
3.2 Averaged and un-averaged contours
3.3 The reference system
3.4 Shell elements
3.4.1 Top, Bottom e Middle
3.4.2 Intersections among elements located on different planes
3.4.3 Discontinuous joints
3.4.4 Continuous joints
3.5 Solid elements
3.5.1 Discontinuous joints
3.5.2 Continuous joints
3.6 One-dimensional elements
3.7 Non-structural elements
3.8 Reaction forces
3.9 Graphics post-processing considerations
3.9.1 Overview
3.9.2 The flow lines
3.9.3 The funnel effect
3.9.4 Strain energy
3.9.5 Gauss points and nodes

CHAPTER 4
Natural frequencies and mode shapes
4.1 Introduction
4.2 The dynamic problem
4.3 Free-free modal analysis
4.4 Constrained modal analysis
4.5 The importance of discretization
4.6 Effective modal mass and modal participation factor
4.7 Load stiffening
4.8 Conclusions

CHAPTER 5
Instability of elastic equilibrium
5.1 Introduction
5.2 Linear buckling
5.3 The FEM approach
5.4 Some practical examples
5.4.1 Cylinder under external pressure
5.4.2 Cantilevr beam
5.4.3 Thin-walled cylinder subjected to compressive axial loading
5.4.4 Thin-walled cylinder undergoing pure torsion
5.5 Notes on instability in nonlinear domain

CHAPTER 6
Errors in Finite Element calculation
6.1 Introduction
6.2 User errors

CHAPTER 6 (Continued)
6.3 Discretization errors
6.3.1 Introduction
6.3.2 Mesh density
6.3.2.1 A borderline case 6.3.2.2 A practical case

6.3.3 Element type
6.3.3.1 Beam A 6.3.3.2 Beam B 6.3.3.3 Hexahedra versus tetrahedra 6.3.3.4 Quadrangles versus triangles 6.3.3.5 C-section beam
6.3.3.6 Large-curvature beam 6.3.3.7 The skinning technique
6.3.4 Conclusions
6.4 Modeling errors
6.4.1 "Distraction" errors
6.4.2 Conceptual errors
6.4.2.1 Beam modeled exclusively with brick
elements
6.4.2.2 Beam modeled with brick/shell - Solution I 6.4.2.3 Beam modeled with brick/shell - Solution II 6.4.2.4 Beam modeled with brick/shell - Solution III 6.4.2.5 Beam modeled with brick/shell - Wrong solution 6.4.2.6 Brick/beam interface 6.4.2.7 Interface between other element types 6.5 Numerical errors
6.5.1 The condition number for the stiffness matrix
6.5.2 Eigenvalues and eigenvectors of the stiffness matrix
6.5.3 Perfectly square plane element
6.5.4 Slightly distorted plane element
6.5.5 Highly distorted element
6.5.6 Unacceptably distorted element
6.6 Pre-processing errors

CHAPTER 7
Advanced modeling techniques
7.1 Introduction
7.2 Substructuring
7.2.1 Superelements
7.2.2 A practical example
7.3 Submodeling
7.3.1 A practical example
7.4 The simulation of press fit couplings
7.4.1 Shaft - Flywheel
7.4.2 Wheel - Axle
7.4.3 Gearmotor support
7.4.4 Cage-pin couplig
7.5 Preload in bolted connections
7.6 Conclusions

CHAPTER 8
Linear elastic calculation of composite materials
8.1 Introduction
8.1.1 Historical background
8.2 Element types to be used
8.3 Short and non-oriented fiber composites
8.4 Long and oriented fiber composites
8.4.1 Materials
8.4.2 Stacking of sheets
8.4.3 Orientation of sheets
8.4.4 Orientation of the element normal
8.4.5 The draping
8.5 An example of laminate without core
8.5.1 Bar with symmetrical stacking sequence
8.5.2 Bar with non-symmetrical stacking sequence
 

CHAPTER 8 (Continued)
8.5.3 Bar with symmetrical stacking and increase of unidirectional sheets
8.5.4 Bar with symmetrical stacking and ifferently oriented sheets
8.5.5 Symmetrically stacked bar subjected to bending - Case 1
8.5.6 Symmetrically stacked bar subjected to bending - Case 2
8.6 Sandwich panels
8.7 The 3D layered elements
8.8 The 3D continuum shell elements
8.9 "Zone based" and "ply based" methods
8.9.1 Introduction
8.9.2 Zone based method
8.9.3 Ply based method
8.9.4 Zone based vs ply based
8.10 More about 3D elements
8.11 3D Composites
8.12 Joining systems
8.13 Notes on metal matrix composites
8.14 Final considerations

CHAPTER 9
Finite element model validation methods
9.1 Introduction
9.2 Numerical validation
9.2.1 Applied loads and reaction forces
9.2.2 Index "EPSILON
9.2.3 Index "MAXRATIO"
9.2.4 Rigid mode check index
9.2.5 Controllo sulla strain energy
9.2.6 Considerations about check indices
9.2.7 Visual checks
9.3 Experimental validation
9.3.1 Load application without stress measurement
9.3.2 Load application with strain gauge measurements
9.3.3 Photoelasticity

CHAPTER 10
Strength assessments
10.1 Introduction
10.2 Static assessment for homogeneous and isotropic materials

CHAPTER 10 (Continued)
10.2.1 Continuous structure parts

10.2.2 Connection systems 10.2.2.1 Introduction 10.2.2.2 Screws 10.2.2.3 Rivets 10.2.2.4 Holes and eyelets 10.2.2.5 Welding
10.3 Fatigue assessment for homogeneous and isotropic materials
10.3.1 Continuous structure parts
10.3.1.1 Classic Method 10.3.1.2 The Gough-Pollard criterion 10.3.1.3 The UIC (Union International des Chemins de Fer) method 10.3.1.4 The Von Mises criterion 10.3.1.5 The b2 coefficient (surface finishing) 10.3.1.6 The b3 coefficient (dimensional effect) 10.3.1.7 Notching coefficients Kt and Kf 10.3.1.8 A practical example 10.3.1.9 Miner's rule
10.3.2 Connection systems
10.4 Failure criteria for composite materials
10.4.1 The maximum stress criterion
10.4.2 The Tsai-Hill criterion
10.4.3 The Tsai-Wu criterion
10.4.4 Interlaminar shear
10.4.5 Considerations

CHAPTER 10 (Continued)
10.4.6 Connection systems
10.4.6.1
Introduction
10.4.6.2
Bonding
10.4.6.3
Insert pull-out
10.5 Fatigue assessment for composite materials
10.6 Assessments beyond the elastic limit
10.7 Conclusions

CHAPTER 11
Geometric nonlinearity
11.1 Introduction
11.2 Geometric nonlinearity
11.3 Considerations
11.4 Post-buckling
11.4.1 Beam in compression
11.4.2 Planar frame

CHAPTER 11 (continued)
11.4.3 Modeling geometric imperfections
11.4.4 Conclusions

CHAPTER 12
Contact nonlinearity
12.1 Introduction
12.2 GAP elements
12.2.1 Sphere on infinitely rigid plane
12.2.2 The finite element model
12.3 Contact surfaces
12.3.1 Sphere on deformable plane
12.3.2 The finite element model
12.3.3 Gearmotor support (Chapter 7)
12.3.4 Cage - pin coupling (Chapter 7)
12.3.5 Self-contact
12.4 Some suggestions
12.5 Conclusions

CHAPTER 13
Material nonlinearity
13.1 Introduction
13.2 Beam in bending at elastic limit
13.3 Beam in bending beyond the elastic limit
13.4 Beam in torsion beyond the elastic limit
13.5 Industry practice
13.5.1 Drive shafts for racing car
13.5.2 Spacer for flange connection
13.6 True stresses and true strains
13.6.1 Flanged pipe (Chapter 7)
13.7 Elastomeric materials
13.7.1 Introduction
13.7.2  Uniaxial tensile-compression test
13.7.3  Study of an O-Ring
13.8 Conclusions

CHAPTER 14
Dynamic analyses
14.1 Introduction
14.2 Frequency response
14.2.1  Structural damping
14.2.2  Solution techniques
14.2.3  Direct integration
14.2.4  Modal superposition
14.2.5  Comparison between the two methods
14.2.6  Modal superposition with an insufficient number of modes
14.2.7  Conclusions

14.3 Transient dynamic analysis

14.3.1  Direct integration
14.3.2  Modal superposition
14.3.3  Comparison with the static case
14.3.4  Material nonlinearity
14.3.5  Conclusions
14.4 Spectrum analysis
14.5 Random vibration analysis
14.6 Explicit methods
14.6.1  Introduction
14.6.2  Comparison with the implicit method
14.6.3  Some considerations about the explicit approach
14.6.4  Conclusions
i

CHAPTER 15
Structural optimization
15.1 Introduction
15.1.1 Size optimization
15.1.2 Shape optimization
15.1.3 Topological optimization
15.2 A case study
15.3 Conclusions

CHAPTER 16
Damage simulation
16.1 Introduction
16.2 Damage in ductile materials
16.3 Damage in composite materials
16.4 Damage in bonding

CHAPTER 17
Examples of advanced calculations
17.1 Introduction
17.2 Modeling of ball bearings
17.2.1 Introduction
17.2.2 The wheel group
17.2.3 The FE model of the bearing
17.2.4 Validation of the calculation model
17.2.5 Wheel group optimization
17.2.6 Conclusions

CHAPTER 17 (Continued)
17.3 Modeling of wheel rim and tire
17.3.1 Introduction
17.3.2 The finite element model
17.4 Bolted connections
17.4.1 Introduction
17.4.2 The preload
17.4.3 Preload + symmetrical orthogonal external load
17.4.4 Preload + nonsymmetrical orthogonal external load
17.4.5 Preload + external tangential load
17.4.6 Conclusions
17.5 T-bracket (Chapters 3 and 10)
17.5.1 Introduction
17.5.2 Without preload
17.5.3 With preload
17.5.4 Conclusions
17.6 The calculation of lugs
17.6.1 Introduction
17.6.2 Classical calculation
17.6.3 Finite element calculation
17.7 Conclusions

CHAPTER 18
State of the art and future developments
18.1 Introduction
18.1.1 When to use traditional methods
18.1.2 When to use numerical methods
18.1.3 When to use a "hybrid" method
18.1.4 The principle of the least necessary mass
18.1.5 Conclusions
18.2 Classical FE methods
18.3 Multibody methods and FE
18.4 Multiphysics methods
18.5 The process simulation
18.6 CAE in CAD
18.7 Conclusions

APPENDIX A
Notes on structural calculations in the linear elastic domain
A.1 Introduction
A.2 The stress-strain relationship
A.3 The strain-displacement equations
A.4 The indefinite equilibrium equations
A.5 The plane stress state
A.6 The plane strain state
A.7 The axisymmetric stress state

APPENDIX B
The stiffness matrix for the plane stress 3-node element
B.1 Introduction
B.2 Finite Elements

APPENDIX B (Continued)
B.3 Shape functions for the plane stress triangular element
B.4 The stiffness matrix for the CST element
B.5 A practical example

APPENDIX C
The numerical solution of linear algebraic equation systems
C.1 Introduction
C.2 The system of equations
C.3 Direct methods
C.4 Iterative methods
C.5 Comparison between direct and iterative methods
C.6 Conclusions

Editorials

Un chilo di acciaio o poco pi - Claudio Gianini - Analisi&Calcolo n 103 - Marzo/Aprile 20

La certificazione di strutture realizzatre in materiale composito - Claudio Gianini - Analisi&Calcolo n 79 - Marzo/Aprile 2017

La pre-processazione, fase indispensabile per qualunque modello di calcolo numerico - Claudio Gianini - Analisi&Calcolo n 78 - Gennaio/Febbario 2017

Modernit e tradizione - Claudio Gianini - Analisi&Calcolo n 76 - Settembre/Ottobre 2016

Progettazione strutturale e porgettazione funzionale - Claudio Gianini - Analisi&Calcolo n 62 - Maggio/Giugno 2014

 

Articles

ITER TF COIL DOUBLE PANCAKE ASSEMBLY: LASER WELDING NUMERICAL SIMULATION - F. Lucca, E. Briani, C.Gianini, C. Jong, J. Knaster, A. Marin - 26th Symposium on Fusion Technology

LIMIT ANALYSIS OF NARROW SUPPORT ELEMENTS IN W7-X CONSIDERING THE SERRATION EFFECT OF THE STRESS-STRAIN RELATION AT 4K - E. Briani, C.Gianini, F. Lucca, A. Marin, J.H.H. Fillinger, V. Bykov - 26th Symposium on Fusion Technology

Formula One Car Wheel Bearings: an FE Approach - C. Gianini

I materiali compositi in modelli a elementi finiti di tipo solido - Claudio Gianini - Analisi&Calcolo n 61 - Marzo/Aprile 2014

Modelli FEM di cuscinetti a sfere - Claudio Gianini - PROGETTARE n 284 Dicembre 2004

Gli errori di modellazione nel calcolo di strutture mediante il FEM (Parte IV) - Claudio Gianini - IL PROGETTISTA INDUSTRIALE n 2 Febbraio 2003

Gli errori di modellazione nel calcolo di strutture mediante il FEM (Parte III) - Claudio Gianini - IL PROGETTISTA INDUSTRIALE n 10 Novembre 2002

Gli errori di modellazione nel calcolo di strutture mediante il FEM (Parte II) - Claudio Gianini - IL PROGETTISTA INDUSTRIALE n 9 Ottobre 2002

Gli errori di modellazione nel calcolo di strutture mediante il FEM (Parte I) - Claudio Gianini - IL PROGETTISTA INDUSTRIALE n 8 Settembre 2002

Lo stato di sforzo assialsimmetrico nel calcolo di strutture mediante il FEM - Claudio Gianini - PROGETTARE n 249 - Ottobre 2001

Il calcolo dell'instabilit nelle analisi strutturali con il FEM - Claudio Gianini - IL PROGETTISTA INDUSTRIALE n 7- Luglio 2001

La non linearit del materiale nelle analisi strutturali con il FEM - Claudio Gianini -  IL PROGETTISTA INDUSTRIALE n 1- Gennaio 2001

La non linearit di contatto nelle analisi strutturali con il FEM - Claudio Gianini -  IL PROGETTISTA INDUSTRIALE n 7 - Luglio 2000

Determinazione della matrice di rigidezza - Claudio Gianini - PROGETTARE n 232 - Marzo 2000

L'ottimizzazione strutturale con il FEM - Claudio Gianini -  PROGETTARE n 228 - Novembre 1999

Il calcolo non lineare nelle analisi strutturali con il FEM - Claudio Gianini -  IL PROGETTISTA INDUSTRIALE n 8 - Ottobre 1999

Il precarico dei bulloni nell'analisi di strutture con il FEM - Claudio Gianini -  PROGETTARE n 219 - Gennaio 1999

Importanza della forma degli elementi nel calcolo con il FEM - Claudio Gianini - PROGETTARE n 217 - Novembre 1998

L'interfaccia tra elementi diversi in un'analisi con il FEM - Claudio Gianini - IL PROGETTISTA INDUSTRIALE n 9 - Novembre 1998

Le tecniche di soluzione dei sistemi lineari in un'analisi strutturale a elementi finiti - Claudio Gianini - IL PROGETTISTA INDUSTRIALE n 6 - Luglio 1998

Simmetria e antisimmetria nel calcolo di strutture mediante FEM - Claudio Gianini - IL PROGETTISTA INDUSTRIALE n 3 - Marzo 1998

Quando il FEM non risponde alle aspettative (II parte) - Claudio Gianini - PROGETTARE n 209 - Febbraio 1998

Quando il FEM non risponde alle aspettative (I parte) - Claudio Gianini - PROGETTARE n 207 - Dicembre 1997

Il "submodelling" nel calcolo di strutture mediante il FEM - Claudio Gianini - IL PROGETTISTA INDUSTRIALE n 7 - Settembre 1997

Il "substructuring" nel calcolo di strutture mediante FEM - Claudio Gianini - IL PROGETTISTA INDUSTRIALE n 5 - Maggio 1997

Progetto e calcolo di strutture saldate - Claudio Gianini - PROGETTARE n 201- Maggio 1997

Accoppiamenti forzati calcolati con il FEM - Claudio Gianini - PROGETTARE n 200 - Aprile 1997

Stati tensionali valutati con il FEM - Claudio Gianini - PROGETTARE n 194 - Ottobre 1996

Quando il FEM un valido strumento - Claudio Gianini - PROGETTARE n 188 - Marzo 1996

Ottimizzazione del progetto di strutture - Claudio Gianini - PROGETTARE n 176 - Febbraio 1995