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Introduction FEM FE model Solution Visualization Abaqus
Finite element method - tutorial no. 1
Martin NESLADEK
Faculty of mechanical engineering, CTU in Prague
11th October 2017
1 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Introduction to the tutorials
E-mail:
Room no. 622 (6th floor - Dept. of mechanics, biomechanics andmechatronics)
Consultations:
every Wednesday at 12:30 - 14:00
Tutorials on FEM I. course: Wednesdays in odd weeks 16:00 -17:30 in room no. 405b
Lectures on FEM I. course: every Thursday 12:30 - 14:45 inroom no. 259 (Mr. Novotny)
2 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Introduction to the tutorials
Topics of the tutorials:1 Introduction to practical applications of the FEM - basic
terminology, introduction to ABAQUS software (2 – 3 lessons)
2 Minimum total potential energy principle (2 lessons)
3 Application of the basic principles of the FEM to simple problemson mechanical response of bars and trusses (2 lessons)
3 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Finite element method
FEM is a numerical method for solving the partial differentialequations (and their systems) on an arbitrary domain
By using FEM we are able to solve:
Mechanical response of solids - analysis of stress and strain fieldsof a single part or assemblyHeat transfer - calculation of the temperature fieldFluid flow - analysis of velocity and pressure fieldsFluid-structure interaction. . .
4 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Finite element method
https://commons.wikimedia.org/w/index.php?curid=641911https://insidehpc.com/2016/09/accelerating-finite-
element-analysis/
5 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Finite element method
http://www.tuvnel.com/site2/subpage/software solutions finite element analysis
6 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Finite element method
http://www.machinedesign.com/fea-and-simulation/finite-element-analysis-reveals-clutch-vibrations
7 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Finite element method
We restrict the FEM I. course to the problems of staticmechanical response of solids
8 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Simulation procedure by using a FEM-basedsoftware
9 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Preparation of an FE model
10 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Preparation of an FE model
F1
F2
static response of
a flexible body?dσijdxj
+ fi = 0
εij =12
(duidxj
+dujdxi
)
σij = Cijklεkl
+ boundary cond’s
CAD model discretizationCAD model discretizationCAD model
nodes
discretization
elements
CAD model
nodes
discretization
nodes
elements
boundary
conditions
CAD model
y
x
ux = uy = 0
Fy
FxFx
Fy
11 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Preparation of an FE model
F1
F2
static response of
a flexible body?dσijdxj
+ fi = 0
εij =12
(duidxj
+dujdxi
)
σij = Cijklεkl
+ boundary cond’s
CAD model
discretizationCAD model discretizationCAD model
nodes
discretization
elements
CAD model
nodes
discretization
nodes
elements
boundary
conditions
CAD model
y
x
ux = uy = 0
Fy
FxFx
Fy
11 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Preparation of an FE model
F1
F2
static response of
a flexible body?dσijdxj
+ fi = 0
εij =12
(duidxj
+dujdxi
)
σij = Cijklεkl
+ boundary cond’sCAD model
discretizationCAD model
discretizationCAD model
nodes
discretization
elements
CAD model
nodes
discretization
nodes
elements
boundary
conditions
CAD model
y
x
ux = uy = 0
Fy
FxFx
Fy
11 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Preparation of an FE model
F1
F2
static response of
a flexible body?dσijdxj
+ fi = 0
εij =12
(duidxj
+dujdxi
)
σij = Cijklεkl
+ boundary cond’sCAD model discretizationCAD model
discretizationCAD model
nodes
discretization
elements
CAD model
nodes
discretization
nodes
elements
boundary
conditions
CAD model
y
x
ux = uy = 0
Fy
FxFx
Fy
11 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Preparation of an FE model
F1
F2
static response of
a flexible body?dσijdxj
+ fi = 0
εij =12
(duidxj
+dujdxi
)
σij = Cijklεkl
+ boundary cond’sCAD model discretizationCAD model discretizationCAD model
nodes
discretization
elements
CAD model
nodes
discretization
nodes
elements
boundary
conditions
CAD model
y
x
ux = uy = 0
Fy
FxFx
Fy
11 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Preparation of an FE model
F1
F2
static response of
a flexible body?dσijdxj
+ fi = 0
εij =12
(duidxj
+dujdxi
)
σij = Cijklεkl
+ boundary cond’sCAD model discretizationCAD model discretizationCAD model
nodes
discretization
elements
CAD model
nodes
discretization
nodes
elements
boundary
conditions
CAD model
y
x
ux = uy = 0
Fy
FxFx
Fy
11 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Preparation of an FE model
nodes
elements
boundary
conditions
x
ux = uy = 0
FyFx
Fx
Fy
y
node – represents a material point of thebody; equations of equilibrium of internaland external forces are assembled andsolved in nodes
element – represents a volumetricsubdomain of the body; topology of theelements is given by nodes; many types,regarding the topology, idealization ofgeometry (continuum el., shells, beams,truss) and physical nature of the problem,exist
elements and nodes together form the finiteelement mesh
boundary conditions – the kinematic andexternal load conditions
12 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Preparation of an FE modelTo simulate the material response as real as possible, a propermaterial model is needed:
σ
ε
E = tg(ϕ)
ν = −εyεx
ϕ
13 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Preparation of an FE model
Basic pre-processing procedure:1 Create or import CAD geometry of the analysed parts
2 Define and assign material properties to the parts
3 Define the load cycle time distribution (load steps andincrementation)
4 Create assembly from parts
5 Define constraints between parts, loads and kinematic BCs
6 Build the model mesh
14 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Preparation of an FE model
15 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Preparation of an FE model
16 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Solution
17 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Solution
Solver generates and solves the system of linear algebraicequations Ku = f based on the parameters of the model.K – the global stiffness matrixu – the global vector of nodal displacementsf – the global vector of external equivalent nodal forces
Displacements are solved primarily u = K−1f and the othervariables are derived from them.
18 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Solution
19 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Visualization of analysis results
20 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Visualization of analysis results
21 / 22Finite element method - tutorial no. 1
Introduction FEM FE model Solution Visualization Abaqus
Installation of Abaqus
Installation files can be downloaded from thehttp://studium.fs.cvut.cz website (use the CTU loginand password), then switch to ”software/abaqus”directory
Abaqus 6.14 is preferable to ensure compatibility with theversion installed in the school computer rooms
For further instructions on Abaqus installation refer tohttp://mechanika.fs.cvut.cz/predmety/fem-i/website
22 / 22Finite element method - tutorial no. 1