introduction fem fe model solution visualization...

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:

martin.nesladek@fs.cvut.cz

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