CIV-E4010 Finite Element Methods in Civil Engineering · J. N. Reddy: An Introduction to the Finite...

Spring 2017, period V, 5 credits (MSc/DSc)

Department of Civil Engineering

School of Engineering

Aalto University

Jarkko Niiranen

Assistant Professor, Academy Research Fellow

First lecture: 12–14, Tuesday, April 11, 2017

CIV-E4010

Finite Element Methods in Civil Engineering

2

Topic Finite element methods for fundamental problems in structural

mechanics, structural engineering and building physics:

theory, applications and software tools

Lecturers Jarkko Niiranen, Assistant Professor, Academy Research Fellow;

Antti Niemi, Senior Research Fellow (visiting for weeks 5 and 6)

Assistants Sergei Khakalo and Viacheslav Balobanov, Doctoral Students

Lectures Tuesdays and Thursdays 12─14 in R2

Exercises Fridays 10─12 in R5 (advice for theoretical assignments)

Mondays 14─16 in R266 (advice/return for computer assignments)

Web site https://mycourses.aalto.fi/course/view.php?id=12996

Material Lectures slides and assignments (2017, as pdfs in MyCourses);

T. J. R Hughes: The Finite Element Method;

F. Hartmann & C. Katz: Structural Analysis with Finite Elements;

A. Öchsner & M. Merkel: One-Dimensional Finite Elements;

J. N. Reddy: An Introduction to the Finite Element Method;

J. N. Reddy: An Introduction to Nonlinear Finite Element Analysis

CIV-E4010


CIV-E4010 / 2017 / Jarkko Niiranen

https://mycourses.aalto.fi/course/view.php?id=12996

3

Attendance and grading

I. Attendance for Lectures or Theoretical Exercise Sessions is not compulsory.

II. Attendance for Computer Exercise Sessions is compulsory for ”in situ” grading.

III. The final grade is built as a combination of examination (50%), home

assignments (25%) and computer/software assignments (25%).

IV. Passing grade 1 can be achieved by about 40% of the total maximum.

V. Examination dates in 2017: on May 26 and in the beginning of September.

Work load

The nominal distribution of the total 133 hours (5 credits) is divided as follows:

CIV-E4010


Contact teaching 38 % Independent studying 62 %

Lectures 18% Reading 18%

Exercise classes 9% Home assignments 18%

Computer classes 9% Computer assignments 18%

Examination 2% Preparation for examination 8%


4

Commercial finite element analysis software usually provide a simulation

environment facilitating all the steps in the modelling process:

(1) defining the geometry, material data, loadings and boundary conditions;

(2) choosing elements, meshing and solving the system equations;

(3) visualizing and post-processing the results.

Some common general purpose or multiphysics FEM software:

Comsol http://www.comsol.com/

http://www.comsol.com/video/thermal-stress-analysis-turbine-stator-blade

https://www.comsol.com/release/5.2a

Adina http://www.adina.com/

Abaqus http://www.simulia.com/products/abaqus_fea.html

Ansys http://www.ansys.com/

Some common structural engineering FEM software:

Scia http://www.scia-online.com/

Lusas http://www.lusas.com/

RFEM https://www.dlubal.com/en/products/rfem-fea-software/what-is-rfem

Robot http://www.autodesk.com/products/robot-structural-analysis/overview

Commercial finite element software −

examples


http://www.comsol.com/

http://www.comsol.com/video/thermal-stress-analysis-turbine-stator-blade


http://www.adina.com/

http://www.simulia.com/products/abaqus_fea.html

http://www.ansys.com/

http://www.scia-online.com/

http://www.lusas.com/

https://www.dlubal.com/en/products/rfem-fea-software/what-is-rfem

http://www.autodesk.com/products/robot-structural-analysis/overview

5

Contents

Week 1

1. Role of modern finite element techniques in engineering analysis

2. Abstract formulation and accuracy of finite element methods

Week 2

3. Finite element methods for Kirchhoff−Love plates

4. Finite element methods for Reissner−Mindlin plates

Week 3

5. Finite element methods for time dependent problems

Week 4

6. Nonlinearities in finite element simulations

Week 5

7. Finite element methods for shells

Week 6

8. Finite element methods for vibrations and buckling

CIV-E4010



6

Contents

Week 1

1. Role of modern finite element techniques in engineering analysis

2. Abstract formulation and accuracy of finite element methods

Week 2

3. Finite element methods for Kirchhoff−Love plates

4. Finite element methods for Reissner−Mindlin plates

Week 3

5. Finite element methods for time dependent problems

Week 4

6. Nonlinearities in finite element simulations

Week 5

7. Finite element methods for shells

Week 6

8. Finite element methods for vibrations and buckling

CIV-E4010



Research activities

are going on at our

department in many

topics of the course!

1 Role of modern finite element techniques

in engineering analysis

Let us start with some simulation examples:

Cutting process http://www.adina.com/newsgH141.shtml

Shell folding http://www.adina.com/newsgH118.shtml

Stamping http://www.adina.com/stamping.shtml

Bar vibrations in fluid http://www.adina.com/newsgH137.shtml

Sail ship mast http://www.adina.com/newsgH146.shtml

Fastener joints http://www.adina.com/newsgH150.shtml

Hemming http://www.adina.com/hemming.shtml

Comsol release 5.2: https://www.comsol.com/release/5.2a

http://www.adina.com/newsgH141.shtml


http://www.adina.com/stamping.shtml




http://www.adina.com/hemming.shtml


8

Contents

1. Modelling and computation in engineering design and analysis

2. Motivation for computational structural engineering

Learning outcome

A. Understanding of the main implications of the approximate nature of

computational methods in engineering design and analysis

B. Recognizing the character of computation and simulation as a discipline

References

Text book 1: Chapters 1.1−2

1 Role of modern finite element techniques

in engineering analysis


A GLIMPSE TO

THE PREVIOUS COURSES…

10

Contents

1. Modelling principles and boundary value problems in engineering sciences

2. Basics of numerical integration and differentiation

3. Basic 1D finite difference and collocation methods

- bars/rods, heat diffusion, seepage, electrostatics

4. Energy methods and basic 1D finite element methods

- bars/rods, beams, heat diffusion, seepage, electrostatics

5. Basic 2D and 3D finite element methods

- heat diffusion, seepage

6. Numerical implementation techniques for finite element methods

7. Finite element methods for Euler−Bernoulli beams

8. Finite element methods for 2D and 3D elasticity

CIV-E1060

Engineering Computation and Simulation


1 Modelling principles and boundary value

problems in engineering sciences

Let us start with some simulation examples:

Cutting process http://www.adina.com/newsgH141.shtml

Shell folding http://www.adina.com/newsgH118.shtml

Stamping http://www.adina.com/stamping.shtml

Bar vibrations in fluid http://www.adina.com/newsgH137.shtml

Sail ship mast http://www.adina.com/newsgH146.shtml

Fastener joints http://www.adina.com/newsgH150.shtml

Hemming http://www.adina.com/hemming.shtml

Comsol release 5.2: https://www.comsol.com/release/5.2a



http://www.adina.com/stamping.shtml




http://www.adina.com/hemming.shtml


12

Contents

1. Modelling and computation in engineering design and analysis

2. Boundary and initial value problems in engineering sciences

Learning outcome

A. Understanding of the main implications of the approximate nature of

computational methods in engineering design and analysis

B. Ability to formulate and solve some basic 1D model problems

References

Lecture notes: chapter 1

Text book: chapters 1.1−2

1 Modelling principles and boundary value

problems in engineering sciences


1.0 Questioning the computational analysis

13

How well do the computational techniques − of

different engineering fields − simulate the real life?


14

step 0

How long?

How thick?

Which material?

How many?

Which joints?

How to construct?

...

How to get answers?

Physical engineering problem with

design criteria

Customer needs!

Dimensions!

Laws and regulations!

Time slot!

Technology available!

Price range!

...

1.1 Modeling and computation

in engineering design and analysis

solution uP = ?


15

step 0

How long?

How thick?

Which material?

How many?

Which joints?

How to construct?

...

How to get answers?

Formulate the problem


design criteria

Customer needs!

Dimensions!


Time slot!


Price range!

...



solution uP = ?


16

step 0

How long?

How thick?

Which material?

How many?

Which joints?

How to construct?

...

How to get answers?

Formulate the problem

− and solve it!


design criteria

Customer needs!

Dimensions!


Time slot!


Price range!

...



solution uP = ?


17


design criteria

General physico-mathematical model

step 1

4DP uu

+ Idealization error

solution uP = ?



4D nonlinear

”all inclusive” theory

solution u4D = ?


18


design criteria


step 1

4DP uu


solution uP = ?



NONLINEAR

ANISOTROPIC

TIME-DEPENDENT

MULTI-PHYSICAL

4D nonlinear


solution u4D = ?


19

step 2


design criteria


Simplified physico-mathematical model

3D4D uu

+ Modeling error


solution uP = ?

uε

Eεσ

bσ

BCs&

3D linear elasticity theory

Kinetics

Constitutive models

Kinematics

4D nonlinear theory



solution u4D = ?

solution u3D = ?

3D

LINEAR

ISOTROPIC

TIME-INDEPENDENT


20

1D axially loaded elastic rod

'

)()()(,'

u

E

xxAxNbN

step 3


design criteria



u""3D u

solution u = ...

+ N x Modeling error


solution uP = ?

N times simplifiedphysico-mathematical

model

1D, LINEAR, ISOTROPIC, TIME-

INDEPENDENT

… Hand calculations work!

3D linear theory



solution u3D = ?

+ Modeling error

solution u4D = ?

)(),(),( xbxAxE

)(, xux

LN

L0


21

Numerical method


design criteria


huu D4


solution uP = ?

+ Discretization error

solution uh = ...step 2



4D nonlinear


solution u4D = ?

),; theory4D(methodnumerical_),( txtxh u


22

Numerical method


design criteria


huu 4D


solution uP = ?






solution u4D = ?

Reliable & Efficient

Applicable

Stable

Accurate

Cheap

4D nonlinear



23

Numerical method


design criteria


huu 4D


solution uP = ?





solution u4D = ?

Neither a black box nor

Inapplicable

Unstable

Inaccurate

Expensive


4D nonlinear



24

Numerical methodstep 3


design criteria



); theory3D(methodnumerical_)( xxh u


solution uP = ?

solution uh = ...



solution u3D = ?

+ Modeling error

3D linear

”B&B” theory

solution u4D = ?

huu D3



25

Numerical method

huu 3D


design criteria




solution uP = ?


solution uh = ...



solution u3D = ?

+ Modeling error

Observations andconclusions step 4

Changes

to the methods:

verification

+ Human errors

solution u4D = ?


26

Numerical method

huu D3


design criteria




solution uP = ?




solution u3D = ?

+ Modeling error


Changes

to the models:

validation

Changes

to the methods:

verification

+ Human errors

solution u4D = ?

solution uh = ...


27

Numerical method

huu 3D


design criteria




solution uP = ?




solution u3D = ?

+ Modeling error


Changes

to the models:

validation

Changes

to the problem

and design

Changes

to the methods:

verification

+ Human errors

solution u4D = ?

solution uh = ...


28

Numerical method

huu D3


design criteria




solution uP = ?




solution u3D = ?

+ Modeling error

Observations andconclusions

Acceptancestep 5

Changes

to the models:

validation

Changes

to the problem

and design

Changes

to the methods:

verification

+ Human errors

solution u4D = ?

solution uh = ...


29

Break exercise 1

...""P huu

Formulate an error estimate for the total error present in a typical

design and analysis process in terms of the error terms described above

(the difference between the physical reality and the final 1D numerical solution).




30

1.2 Motivation for computational structural

engineering


31


engineering


32


engineering

What is common to these activites?


33


engineering

Talent?



34


engineering

10 000 h?



35



engineering

Talent + 10 000 h?


36


engineering

chemistry physics High school mathematics languages

biology physics Secondary school mathematics languages

history physics Primary school mathematics mother language english

chemistry physics mechanics BSc mathematics programming product design

You are here!

Building systematically on

your knowledge and skills

for reaching the top!

- Recall your

BSc studies!

- Recollect

your youth!

- Reminisce

your

childhood!

You have talent,

you just need to train!


37

What is not common to these activites?


engineering

Consequencies of incompetence!


38


engineering

Consequencies of

incompetence!


39

Building blocks of boundary value problems in civil engineering:

Deformation and motion is defined by the continuum mechanics concepts as

(1) Kinematics (displacements and strains)

(2) Kinetics (conservation of linear and angular momentum)

(3) Thermodynamics (I and II laws)

(4) Constitutive equations (stresses vs. strains)

The main mathematical tools are

(i) Vector and tensor algebra and analysis

(ii) Differential, integral and variational calculus

(iii) Partial differential equations

Altogether, physical conservation principles, i.e., the laws of conservation of mass,

momenta and energy as well as constitutive responses of materials or other

observed relations, are covered by a combination of the theoretical tools above.

1.X Continuum mechanics in

civil engineering

uε

Eεσ

bσ

BCs&

elasticity 2D/3D

'

,,' BCs&

elasticity 1D

u

E

ANbN


40

Matter (or material) is composed of particles ─ from

electrons and atoms up to molecules ─ which can be,

under certain assumptions, modelled as a continuum,

however.

Idealizations of physics and chemistry are further

simplified – or homogenized – by the theory of

continuum mechanics.


civil engineering


41

Continuum is a hypothetical tool with specific assumptions and features

─ overlooks particles up to the molecular size (homogenity)

─ scales of interest are large enough (practicality)

─ physical quantities of interest are continuously differentiable (mathematicality)

─ applicaple for all materials (generality)

Within continuum mechanics, a wide spectrum of physical phenomena can be

studied, however.

Many variations, modifications or extensions for the classical continuum theories

exist as well: discontinuum-continuum, pseudo-continuum or Cosserat continuum,

higher-order strain gradient continua etc. (often applied to capture microstructural

effects of granular materials, for instance).


civil engineering


42

Continuum mechanics studies not only the deformation of solids but the

deformation and flow of a continuum covering solids, liquids and gases.

Engineering sciences as structural engineering study particular tailorings of

continuum mechanics: bars, beams, plates and shells within elasticity,

plasticity, viscoelasticity or viscoplasticity, for instance.

Problems formulated in terms of continuum mechanics are transformed by

mathematical tools into the form of computational mechanics: continuum

mechanics and numerical methods with the corresponding computer

implementations – referred as numerical simulation tools.


civil engineering


QUESTIONS?

ANSWERS”

LECTURE BREAK!

CIV-E4010 Finite Element Methods in Civil Engineering · J. N. Reddy: An Introduction to the Finite...

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