Course in
FEM – ANSYS Classic
Introduction
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
• Presentation
– Anders Schmidt Kristensen
– M.Sc. in Mechanical Eng. from Aalborg
University in 1993
– Ph.D. in Mechanical Eng. from Aalborg
University in 1997
– Consultant for PTC Denmark 1997-1998 –
implementation of Pro/ENGINEER
– 1998 to pt. Associate Prof. at Aalborg
University Esbjerg
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
2
Introduction
• The course is conducted the following
way:
– 20-40 minutes lecture followed by 40-60
minutes exercise (including a break)
– Questions are allowed at any time
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
3
References
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[ANSYS] ANSYS 10.0 Documentation (installed with ANSYS):
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Basic Analysis Procedures
Advanced Analysis Techniques
Modeling and Meshing Guide
Structural Analysis Guide
Thermal Analysis Guide
APDL Programmer’s Guide
ANSYS Tutorials
[Cook] Cook, R. D.; Concepts and applications of finite element
analysis, John Wiley & Sons
[Burnett] Burnett, D. S.; Finite element analysis: From concepts to
application, Addison-Wesley
[Kildegaard] Kildegaard, A.; Elasticitetsteori, Aalborg Universitet
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
4
FEM - ANSYS Classic
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Lecture 1 - Introduction:
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Lecture 2 - Preprocessor:
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Boundary conditions/constraints/supports
Loads
Mesh attributes, meshing
Sections
Lecture 4 – 2D plane models :
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Geometric modeling
Specification of Element type, Real Constants, Material, Mesh
Frame systems
Truss systems
Element tables
Lecture 3 - Loads:
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Introduction to FEM
ANSYS Basics
Analysis phases
Geometric modeling
The first model: Beam model
2D Plane Solid systems
Geometric modeling
Postprocessing
Lecture 5 – Analysis types:
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Analysis types
Modal analysis
Buckling analysis
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
5
FEM - ANSYS Workbench/CAD
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Lecture 6 – 3D Solids:
– 3D solid models
– Booleans
– Meshing issues
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Lecture 7 – 3D Modeling:
– Operate
– Import CAD
– Advanced topics
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Lecture 8 – Analysis types:
– Analysis types
– Postprocessing
– TimeHistProc
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Lecture 9 – Workbench basics:
– Workbench basics
– Geometric modeling
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Lecture 10 – Workbench analysis:
– Workbench analysis types
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
6
Overview
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CAD - Computer Aided Design
– AutoCAD, Bentley MicroStation, CadKey
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CAD - Solid Modeling
– Pro/ENGINEER, Inventor, IDEAS, CATIA, UGS, Solid Works
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FEM/FEA - Finite Element Method/Analysis
– ANSYS, ABAQUS, Algor, Altair, MscNastran, Cosmos
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CAE - Computer Aided Engineering
– Workbench, Design Space, Pro/Mechanica, CosmosWorks,
Inventor/ANSYS
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BEM - Boundary Element Method
Mesh-less systems
CFD - Computational Fluid Dynamics
– ANSYS/Fluent, ANSYS/Flotran, ANSYS/CFX, CF-Design, Altair
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Multi-scale systems
Optimization – sizing, shape and topology
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
7
Introduction to Finite Element Analysis
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What is Finite Element Analysis?
Advantages
Disadvantages
How to avoid pitfalls
History
FEM - Resources
Examples
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
8
What is Finite Element Analysis?
• The FEM is a computer-aided
mathematical technique for obtaining
approximate numerical solutions to the
abstract equations of calculus that predict
the response of physical systems
subjected to external influences – [Burnett]
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
9
What is Finite Element Analysis?
Each point have an
infinite number of
deformation state
variables, i.e. degrees of freedom (dof)
Transformation
Real model
Continuum
Each point have a
finite number of
deformation state
variables (u,v), i.e.
degrees of freedom
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
Analysis model
Discrete
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What is Finite Element Analysis?
• Divide a continuum with
infinitely degrees of
freedom in to finite
elements with a given
number of degrees of
freedom
• An element is geometrical
defined by a number of
nodes in which the
elements are connected.
The directions a node can
move in is termed
degrees of freedom (dof)
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
11
What is Finite Element Analysis?
• Following conditions
must always be satisfied
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Equilibrium conditions
Compatibility conditions
Constitutive conditions
Boundary conditions
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
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What is Finite Element Analysis?
• Most FEA systems are displacement
based, i.e. an approximate displacement
field is established
u(x,y) = a1 + a2 x + a3 y
• Using a deformation based method yield
one unique kinematic determined system
to be determined
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
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What is Finite Element Analysis?
• The deformation method yield the FEM
characteristic system of equations:
Unknown displacement vector
[K]{D} = {R}
Stiffness matrix
Load vector
• This system of equations is solved for {D} by,
e.g. Gaussian elimination
• Note on matrix algebra is found here
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
14
What is Finite Element Analysis?
• Formulation techniques to determine the
stiffness matrix [K]
– Direct method
– Variational methods, i.e. principle of stationary
potential energy
– Weighted Residual methods, e.g. the Galerkin
formulation
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
15
What is Finite Element Analysis?
• The unknown displacements (can be any field
variable, e.g. temperature) {D} = {u1, v1, u2, v2
…}T in the element nodes (nodal values) are
determined from
v3
Unknown displacement vector
u3
[K]{D} = {R}
Stiffness matrix
Load vector
y
Displacement field variables:
In 2D: (u,v)
In 3D: (u,v,w)
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
ndof = 6
v2
v1
u2
u1
Introduction
x
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What is Finite Element Analysis?
• It is assumed that displacements within an
element can be interpolated from known
nodal values
u2
ui=?
u ≈ N1 u1 + N2 u2
u1
u2
ui
u1
x1
xi
x2
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
N1 = (1 – x/L)
N2 = x/L
Introduction
x1
xi
x2
Linear case
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What is Finite Element Analysis?
The element stiffness matrix for a beam element with 2 nodes and
2 dof at each node [Cook], see also note:
ndof = 4
Found by the Direct Method
Unknown displacement vector
ndof x 1
-1
[K]{D} = {R} → {D} = [K] {R}
Known stiffness matrix
ndof x ndof
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
Known load vector
ndof x 1
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Advantages
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Irregular Boundaries
General Loads
Different Materials
Boundary Conditions
Variable Element Size
Easy Modification
Dynamics
Nonlinear Problems (Geometric and/or Material)
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
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Disadvantages
NB: Always document assumptions!
• An approximate solution
• An element dependent solution
– Shape quality of elements affect the solution,
e.g. poorly shaped elements (irregular
shapes) reduce accuracy of the FE solution
– Element density affect the solution, i.e. the
element size should be adjusted to capture
gradients
• Example: plate with a circular hole
• Errors in input data
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
20
Disadvantages
[Cook]
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
21
Disadvantages
[Cook]
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
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How to avoid pitfalls
• Carry out:
– Hand calculations (Navier, Airy,
Timoshenko…)
– Norm based calculations (Euro-Code, EN,
API…)
– Experiments (strain-gauge, accelerometer…)
– Evaluate the kinematic behaviour
(deformations)
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
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History
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A. Hrennikoff [1941] - Lattice of 1D bars
McHenry [1943] - Model 3D solids
R. Courant [1943] - Variational form
Levy [1947, 1953] - Flexibility & Stiffness
M. J. Turner [1953] - FEM computations on a wing
Boeing [1950's] Engineer's at Boeing apply FEM to delta
wings
• Argryis and Kelsey [1954] - Energy Prin. for Matrix
Methods
• Turner, Clough, Martin and Topp [1956] - 2D elements
• R. W. Clough [1960] – Coins the term “Finite Elements”
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
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History
• 1963 - Mathematical validity of method
established - applied to non-structural problems
• 1960's - First general purpose FEA code
developed
• 1970's - Non-linear solvers developed
• 1980's - Graphical pre-/postprocessors are
developed
• 1990's - FEM tools integrated in CAD software
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
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FEM - Resources
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ALGOR
ANSYS
COSMOS/M
STARDYNE/FEMAP
MSC/NASTRAN
SAP90/2000
ADINA
NISA
GT Strudl
ABAQUS
Plaxis
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
• Matlab based:
– CalFem
– FemLab
• CAE products:
– Pro/ENGINEER
• Pro/FEA
• Pro/MECHANICA
– Cosmos/Works
– Inventor/ANSYS
– IDEAS
• Resources
Introduction
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Introduction to ANSYS
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What is ANSYS
Facilities in ANSYS
Interfacing with ANSYS
Common terms
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
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What is ANSYS
• ANSYS finite element analysis software enables
engineers to perform the following tasks:
– Build computer models or transfer CAD models of
structures, products, components, or systems.
– Apply operating loads or other design performance
conditions.
– Study physical responses, such as stress levels,
temperature distributions, or electromagnetic fields.
– Optimize a design early in the development process to
reduce production costs.
– Do prototype testing in environments where it otherwise
would be undesirable or impossible (for example,
biomedical applications).
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
28
Facilities in ANSYS
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Structural Linear
Structural Nonlinear
Structural Contact/Common Boundaries
Structural Dynamic
Structural Buckling
Thermal Analysis
CFD Analysis
Electromagnetic - Low Frequency
Electromagnetics - High Frequency
Field and Coupled-Field Analysis
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
29
Facilities in ANSYS
• Solvers
– Iterative
– Sparse
– Frontal
– Explicit
• Preprocessing
• Postprocessing
• General Features
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
30
Facilities in ANSYS
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ANSYS Commands reference
ANSYS Element reference
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Basic Analysis Procedures
Advanced Analysis Techniques
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Structural Analysis Guide
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ANSYS Tutorials
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
31
Facilities in ANSYS
During an analysis, you may want to modify or delete
commands entered since your last SAVE or RESUME.
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You can access the following file
operations from the session editor
dialog:
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OK: Enters the series of operations
displayed in the window below. You will
use this option to input the command
string after you have modified it.
Save: Saves the command string
displayed in the window below to a
separate file. ANSYS names the file
Jobnam000.cmds, with each
subsequent save operation
incrementing the filename by one digit.
You can use the /INPUT command to
reenter the saved file.
Cancel: Dismisses this window and
returns to your analysis.
Help: Displays the command reference
for the UNDO command.
The Session Editor is available in
interactive (GUI) mode only.
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
32
Facilities in ANSYS
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
33
Interfacing with ANSYS
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Matlab, Excel
CAD – Pro/ENGINEER
IGES
Log-file editing
Application Programming Interface (API)
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
34
Interfacing with ANSYS
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
35
Common terms
Processor
Function
GUI Path
Command
PREP7
Build the model (geometry, materials, etc.)
Main Menu> Preprocessor
/PREP7
SOLUTION
Apply loads and obtain the finite element solution
Main Menu> Solution
/SOLU
POST1
Review results over the entire model at specific time points
Main Menu> General Postproc
/POST1
POST26
Review results at specific points in the model as a function of time
Main Menu> TimeHist Postpro
/POST26
OPT
Improve an initial design
Main Menu> Design Opt
/OPT
PDS
Quantify the effect of scatter and uncertainties associated with input
variables of a finite element analysis on the results of the analysis
Main Menu> Prob Design
/PDS
AUX2
Dump binary files in readable form
Utility Menu> File> List> Binary Fi
les
/AUX2
Utility Menu> List> Files> Binary F
iles
AUX12
Calculate radiation view factors and generate a radiation matrix for a
thermal analysis
Main Menu> Radiation Matrix
/AUX12
AUX15
Translate files from a CAD or FEA program
Utility Menu> File> Import
/AUX15
RUNSTAT
Predict CPU time, wavefront requirements, etc. for an analysis
Main Menu> Run-Time Stats
/RUNST
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
36
Basics
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Launching of ANSYS
Graphical User Interface (GUI)
Menus, dialogs and toolbars
Working area
Preferences
Files used by ANSYS
ANSYS Menus
ANSYS File menu
ANSYS PlotCtrls menu
Units
Undo
Hints
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
37
Analysis phases
• Build the model.
• Apply loads and
obtain the solution.
• Review the results.
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
PREPROCESSOR
SOLUTION
POSTPROCESSOR
Introduction
38
Analysis phases
Element Type – select appropiate element type to model
the structural response/behaviour most accurately.
Real Constants – properties depending on the element
type, e.g. cross-sectional properties, area, area moment
of inertia
Material Props – material properties, e.g. modulus of
elasticity E and Poisson’s ratio n
Sections – cross-section definition
Modeling – define the geometry of the structure - “it is
essential to make some modeling considerations in
this phase”
Meshing – divide the geometry of the structure into
elements – “take care of element distribution/density”
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
39
Analysis phases
Analysis Type – specify the character of the problem
Define Loads – apply loads to the element model
Solve – run the solution process, e.g. for linear static
systems solve (Gaussian elimination) for the unknown
displacements:
The global stiffness
Unknown displacement vector
ndof x 1
-1
matrix [K]:
ndof = total number of
nodes x number
degrees of freedom
per node
[K]{D} = {R} → {D} = [K] {R}
Known global
stiffness matrix
ndof x ndof
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
Known load vector
ndof x 1
40
Geometric modeling
Create – geometrical entities
Operate – perform Boolean operations
Move / Modify – move or modify geometrical entities
Copy – copy geometrical entities
Delete – geometrical entities
Update Geom – update the geometry in relation
to for example buckling analysis
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
41
Modeling - Create
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The hierarchy of modeling entities is as listed
below:
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FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Elements (and Element Loads)
Nodes (and Nodal Loads)
Volumes (and Solid-Model Body Loads)
Areas (and Solid-Model Surface Loads)
Lines (and Solid-Model Line Loads)
Keypoints (and Solid-Model Point Loads)
Introduction
42
Examples - content
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Example0100’s: Link and/or beam models
Example0200’s: Plane 2D models
Example0300’s: Solid 3D models
Example0400’s: Vibration/dynamic models
Example0600’s: Thermal models
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
43
The first model
FEM – ANSYS Classic
Computational Mechanics, AAU, Esbjerg
Introduction
44