Introduction FEM FE model Solution Visualization Abaqus

Finite element method - tutorial no. 1

Martin NESLADEK

Faculty of mechanical engineering, CTU in Prague

11th October 2016

1 / 17Finite 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 10:45 - 12:15

Tutorials to the FEM I. course: Tuesdays in odd weeks 15:00 -16:30 in room no. 405b

Lectures to the FEM I. course: every Wednesday 14:15 - 16:30in room no. 311 (Mr. Novotny)

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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)

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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. . .

We restrict the FEM I. course to problems of the mechanicalresponse of solids

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Introduction FEM FE model Solution Visualization Abaqus

Simulation procedure by using a FEM-basedsoftware

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Introduction FEM FE model Solution Visualization Abaqus

Preparation of an FE model

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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

7 / 17Finite 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

7 / 17Finite 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

7 / 17Finite 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

7 / 17Finite 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

7 / 17Finite 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

7 / 17Finite 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

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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

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Introduction FEM FE model Solution Visualization Abaqus

Preparation of an FE model

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Introduction FEM FE model Solution Visualization Abaqus

Preparation of an FE model

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Introduction FEM FE model Solution Visualization Abaqus

Solution

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Introduction FEM FE model Solution Visualization Abaqus

Solution

Solver generates and solves the system of linear equationsKu = 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.

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Introduction FEM FE model Solution Visualization Abaqus

Solution

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Introduction FEM FE model Solution Visualization Abaqus

Visualization of analysis results

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Introduction FEM FE model Solution Visualization Abaqus

Visaulization of analysis results

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Introduction FEM FE model Solution Visualization Abaqus

Installation of Abaqus

Installation files can be downloaded from thehttp://studium.fs.cvut.cz website (use the same loginas to the other school systems), then switch to”software/abaqus”directory

At first, install the Abaqus documentation

When installing the program, refer to elic.fsid.cvut.cz licenseserver and port no. 1701

Windows 8+ is compatible only with Abaqus 6.13+ versions

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