civ-e4010 finite element methods in civil engineering · j. n. reddy: an introduction to the finite...
TRANSCRIPT
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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
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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
Finite Element Methods in Civil Engineering
CIV-E4010 / 2017 / Jarkko Niiranen
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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
Finite Element Methods in Civil Engineering
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%
CIV-E4010 / 2017 / Jarkko Niiranen
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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
CIV-E4010 / 2017 / Jarkko Niiranen
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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
Finite Element Methods in Civil Engineering
CIV-E4010 / 2017 / Jarkko Niiranen
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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
Finite Element Methods in Civil Engineering
CIV-E4010 / 2017 / Jarkko Niiranen
Research activities
are going on at our
department in many
topics of the course!
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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
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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
CIV-E4010 / 2017 / Jarkko Niiranen
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A GLIMPSE TO
THE PREVIOUS COURSES…
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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
CIV-E1060 / 2016 / Jarkko Niiranen
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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
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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
CIV-E1060 / 2016 / Jarkko Niiranen
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1.0 Questioning the computational analysis
13
How well do the computational techniques − of
different engineering fields − simulate the real life?
CIV-E1060 / 2016 / Jarkko Niiranen
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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 = ?
CIV-E1060 / 2016 / Jarkko Niiranen
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step 0
How long?
How thick?
Which material?
How many?
Which joints?
How to construct?
...
How to get answers?
Formulate the problem
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 = ?
CIV-E1060 / 2016 / Jarkko Niiranen
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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!
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 = ?
CIV-E1060 / 2016 / Jarkko Niiranen
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17
Physical engineering problem with
design criteria
General physico-mathematical model
step 1
4DP uu
+ Idealization error
solution uP = ?
1.1 Modeling and computation
in engineering design and analysis
4D nonlinear
”all inclusive” theory
solution u4D = ?
CIV-E1060 / 2016 / Jarkko Niiranen
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Physical engineering problem with
design criteria
General physico-mathematical model
step 1
4DP uu
+ Idealization error
solution uP = ?
1.1 Modeling and computation
in engineering design and analysis
NONLINEAR
ANISOTROPIC
TIME-DEPENDENT
MULTI-PHYSICAL
4D nonlinear
”all inclusive” theory
solution u4D = ?
CIV-E1060 / 2016 / Jarkko Niiranen
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step 2
Physical engineering problem with
design criteria
General physico-mathematical model
Simplified physico-mathematical model
3D4D uu
+ Modeling error
+ Idealization error
solution uP = ?
uε
Eεσ
bσ
BCs&
3D linear elasticity theory
Kinetics
Constitutive models
Kinematics
4D nonlinear theory
1.1 Modeling and computation
in engineering design and analysis
solution u4D = ?
solution u3D = ?
3D
LINEAR
ISOTROPIC
TIME-INDEPENDENT
CIV-E1060 / 2016 / Jarkko Niiranen
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1D axially loaded elastic rod
'
)()()(,'
u
E
xxAxNbN
step 3
Physical engineering problem with
design criteria
General physico-mathematical model
Simplified physico-mathematical model
u""3D u
solution u = ...
+ N x Modeling error
+ Idealization error
solution uP = ?
N times simplifiedphysico-mathematical
model
1D, LINEAR, ISOTROPIC, TIME-
INDEPENDENT
… Hand calculations work!
3D linear theory
1.1 Modeling and computation
in engineering design and analysis
solution u3D = ?
+ Modeling error
solution u4D = ?
)(),(),( xbxAxE
)(, xux
LN
L0
CIV-E1060 / 2016 / Jarkko Niiranen
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Numerical method
Physical engineering problem with
design criteria
General physico-mathematical model
huu D4
+ Idealization error
solution uP = ?
+ Discretization error
solution uh = ...step 2
1.1 Modeling and computation
in engineering design and analysis
4D nonlinear
”all inclusive” theory
solution u4D = ?
),; theory4D(methodnumerical_),( txtxh u
CIV-E1060 / 2016 / Jarkko Niiranen
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Numerical method
Physical engineering problem with
design criteria
General physico-mathematical model
huu 4D
+ Idealization error
solution uP = ?
+ Discretization error
solution uh = ...step 2
1.1 Modeling and computation
in engineering design and analysis
),; theory4D(methodnumerical_),( txtxh u
solution u4D = ?
Reliable & Efficient
Applicable
Stable
Accurate
Cheap
4D nonlinear
”all inclusive” theory
CIV-E1060 / 2016 / Jarkko Niiranen
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Numerical method
Physical engineering problem with
design criteria
General physico-mathematical model
huu 4D
+ Idealization error
solution uP = ?
+ Discretization error
solution uh = ...step 2
1.1 Modeling and computation
in engineering design and analysis
solution u4D = ?
Neither a black box nor
Inapplicable
Unstable
Inaccurate
Expensive
),; theory4D(methodnumerical_),( txtxh u
4D nonlinear
”all inclusive” theory
CIV-E1060 / 2016 / Jarkko Niiranen
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Numerical methodstep 3
Physical engineering problem with
design criteria
General physico-mathematical model
Simplified physico-mathematical model
); theory3D(methodnumerical_)( xxh u
+ Idealization error
solution uP = ?
solution uh = ...
1.1 Modeling and computation
in engineering design and analysis
solution u3D = ?
+ Modeling error
3D linear
”B&B” theory
solution u4D = ?
huu D3
+ Discretization error
CIV-E1060 / 2016 / Jarkko Niiranen
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Numerical method
huu 3D
Physical engineering problem with
design criteria
General physico-mathematical model
Simplified physico-mathematical model
+ Idealization error
solution uP = ?
+ Discretization error
solution uh = ...
1.1 Modeling and computation
in engineering design and analysis
solution u3D = ?
+ Modeling error
Observations andconclusions step 4
Changes
to the methods:
verification
+ Human errors
solution u4D = ?
CIV-E1060 / 2016 / Jarkko Niiranen
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Numerical method
huu D3
Physical engineering problem with
design criteria
General physico-mathematical model
Simplified physico-mathematical model
+ Idealization error
solution uP = ?
+ Discretization error
1.1 Modeling and computation
in engineering design and analysis
solution u3D = ?
+ Modeling error
Observations andconclusions step 4
Changes
to the models:
validation
Changes
to the methods:
verification
+ Human errors
solution u4D = ?
solution uh = ...
CIV-E1060 / 2016 / Jarkko Niiranen
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Numerical method
huu 3D
Physical engineering problem with
design criteria
General physico-mathematical model
Simplified physico-mathematical model
+ Idealization error
solution uP = ?
+ Discretization error
1.1 Modeling and computation
in engineering design and analysis
solution u3D = ?
+ Modeling error
Observations andconclusions step 4
Changes
to the models:
validation
Changes
to the problem
and design
Changes
to the methods:
verification
+ Human errors
solution u4D = ?
solution uh = ...
CIV-E1060 / 2016 / Jarkko Niiranen
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Numerical method
huu D3
Physical engineering problem with
design criteria
General physico-mathematical model
Simplified physico-mathematical model
+ Idealization error
solution uP = ?
+ Discretization error
1.1 Modeling and computation
in engineering design and analysis
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 = ...
CIV-E1060 / 2016 / Jarkko Niiranen
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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).
CIV-E1060 / 2016 / Jarkko Niiranen
1.1 Modeling and computation
in engineering design and analysis
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1.2 Motivation for computational structural
engineering
CIV-E4010 / 2017 / Jarkko Niiranen
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1.2 Motivation for computational structural
engineering
CIV-E4010 / 2017 / Jarkko Niiranen
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1.2 Motivation for computational structural
engineering
What is common to these activites?
CIV-E4010 / 2017 / Jarkko Niiranen
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1.2 Motivation for computational structural
engineering
Talent?
What is common to these activites?
CIV-E4010 / 2017 / Jarkko Niiranen
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1.2 Motivation for computational structural
engineering
10 000 h?
What is common to these activites?
CIV-E4010 / 2017 / Jarkko Niiranen
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What is common to these activites?
1.2 Motivation for computational structural
engineering
Talent + 10 000 h?
CIV-E4010 / 2017 / Jarkko Niiranen
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1.2 Motivation for computational structural
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!
CIV-E4010 / 2017 / Jarkko Niiranen
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What is not common to these activites?
1.2 Motivation for computational structural
engineering
Consequencies of incompetence!
CIV-E4010 / 2017 / Jarkko Niiranen
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1.2 Motivation for computational structural
engineering
Consequencies of
incompetence!
CIV-E4010 / 2017 / Jarkko Niiranen
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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
CIV-E1060 / 2016 / Jarkko Niiranen
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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.
1.X Continuum mechanics in
civil engineering
CIV-E1060 / 2016 / Jarkko Niiranen
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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).
1.X Continuum mechanics in
civil engineering
CIV-E1060 / 2016 / Jarkko Niiranen
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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.
1.X Continuum mechanics in
civil engineering
CIV-E1060 / 2016 / Jarkko Niiranen
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QUESTIONS?
ANSWERS”
LECTURE BREAK!