CIV-E1060 Engineering Computation and Simulation

CIV-E1060 Engineering Computation and Simulation Autumn 2017, period II, 5 credits (MSc) Department of Civil Engineering School of Engineering Aalto University Jarkko Niiranen Assistant Professor, Academy Research Fellow First lecture: 12 14, Tuesday, October 31, 2017

CIV-E1060 Engineering Computation and Simulation Topic Lecturer Assistants Numerical methods for fundamental problems in structural mechanics, structural engineering and building physics: Jarkko Niiranen, assistant professor Sergei Khakalo, doctoral student Summer Shahzad, post-doctoral researcher Viacheslav Balobanov and Tuan Nguyen, doctoral students Lectures Tuesdays 12 14 and Thursdays 14 16 in R2 Exercises (A) Fridays 10 12 in R5 or (B) Fridays 12 14 in R9; (A) Mondays 12 14 in A046a or (B) Mondays 14 16 in R266 or (C) Mondays 16 18 in A046 Web site Material https://mycourses.aalto.fi/course/view.php?id=16859 Lectures slides and assignments (as pdfs in MyCourses); Text book by A. Öchsner and M. Merkel: One-Dimensional Finite Elements (2013); Text book by T.J.R Hughes: The Finite Element Method (2000) CIV-E1060 / 2017 / Jarkko Niiranen 2

CIV-E1060 Engineering Computation and Simulation Attendance and grading I. Attendance for Lectures or Theoretical Exercise Sessions is not compulsory. II. Attendance for Computer Exercise Sessions is compulsory for collecting points. 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 are December 12, 2017, and February 15, 2018. Work load The nominal distribution of the total 133 hours (5 credits) is divided as follows: 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-E1060 / 2017 / Jarkko Niiranen 3

CIV-E1060 Engineering Computation and Simulation 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 / 2017 / Jarkko Niiranen 4

Motivation Computation in Engineering 6

Motivation Computation in Engineering 7

Motivation for difficult disciplines What is common to these activites? CIV-E1060 / 2017 / Jarkko Niiranen 8

Motivation for difficult disciplines What is common to these activites? Talent? CIV-E1060 / 2017 / Jarkko Niiranen 9

Motivation for difficult disciplines What is common to these activites? 10 000 h? CIV-E1060 / 2017 / Jarkko Niiranen 10

Motivation for difficult disciplines What is common to these activites? Talent + 10 000 h? CIV-E1060 / 2017 / Jarkko Niiranen 11

Motivation for difficult disciplines Building systematically on your knowledge and skills for reaching the top! You have talent, you just need to spend some hours train! - Recall your You are here! BSc studies! - Recollect your youth! - Reminisce your childhood! chemistry physics mechanics BSc mathematics programming product design chemistry physics High school mathematics languages biology physics Secondary school mathematics languages history physics Primary school mathematics mother language english CIV-E1060 / 2017 / Jarkko Niiranen 12

Motivation for difficult disciplines What is not common to these activites? Consequencies of incompetence! CIV-E1060 / 2017 / Jarkko Niiranen 13

Motivation for difficult disciplines Consequencies of incompetence! CIV-E1060 / 2017 / Jarkko Niiranen 14

Commercial finite element software examples Commercial analysis software usually provide a simulation environment facilitating all the steps in the ling process: (1) defining the geometry, material data, loadings and boundary conditions; (2) choosing elements, meshing and solving the problem; (3) visualizing and postprocessing 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 structural engineering FEM software: Scia http://www.scia-online.com/ Lusas http://www.lusas.com/ A fairly long list of FEM software in Wikipedia: http://en.wikipedia.org/wiki/list_of_finite_element_software_packages 15

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

1 Modelling principles and boundary value problems in engineering sciences 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 problems References Lecture notes: chapter 1 Text book: chapters 1.1 2 18

1.0 Questioning the computational analysis How well do the computational techniques of different engineering fields simulate the real life? 19

1.1 Modeling and computation in engineering design and analysis step 0 Physical engineering problem with design criteria solution u P =? Customer needs! Dimensions! Laws and regulations! Time slot! Technology available! Price range!... How long? How thick? Which material? How many? Which joints? How to construct?... How to get answers? 20

1.1 Modeling and computation in engineering design and analysis step 1 4D nonlinear all inclusive theory Physical engineering problem with design criteria General physicomathematical solution u P =? solution u 4D =? + Idealization error up u 4D 23

1.1 Modeling and computation in engineering design and analysis 4D nonlinear theory step 2 3D linear elasticity theory Kinetics Constitutive s Kinematics Physical engineering problem with design criteria General physicomathematical Simplified physicomathematical σ b σ Eε ε u & BCs solution u P =? solution u 4D =? + Idealization error solution u 3D =? + Modeling error u 4D u 3D 3D LINEAR ISOTROPIC TIME-INDEPENDENT 25

1.1 Modeling and computation in engineering design and analysis 3D linear theory Physical engineering problem with design criteria General physicomathematical Simplified physicomathematical solution u P =? solution u 4D =? + Idealization error solution u 3D =? + Modeling error step 3 1D axially loaded elastic rod 0 E( x), A( x), b( x) L N times simplified physico-mathematical N L x, u( x) N' b, E u' N( x) solution u =... + N x Modeling error A( x) ( x) u " 3D "u 1D, LINEAR, ISOTROPIC, TIME- INDEPENDENT Hand calculations work! 26

1.1 Modeling and computation in engineering design and analysis 4D nonlinear all inclusive theory step 2 Physical engineering problem with design criteria General physicomathematical Numerical method solution u P =? solution u 4D =? + Idealization error solution u h =... + Discretization error u4d u h u h ( x, t) numerical_method(4d theory; x, t) 27

1.1 Modeling and computation in engineering design and analysis 4D nonlinear all inclusive theory Physical engineering problem with design criteria General physicomathematical solution u P =? solution u 4D =? + Idealization error step 2 Numerical method Reliable & Efficient Applicable Stable Accurate Cheap solution u h =... + Discretization error u4d u h u h ( x, t) numerical_method(4d theory; x, t) 28

1.1 Modeling and computation in engineering design and analysis 4D nonlinear all inclusive theory Physical engineering problem with design criteria General physicomathematical solution u P =? solution u 4D =? + Idealization error step 2 Numerical method Neither a black box nor Inapplicable Unstable Inaccurate Expensive solution u h =... + Discretization error u4d u h u h ( x, t) numerical_method(4d theory; x, t) 29

1.1 Modeling and computation in engineering design and analysis step 3 3D linear B&B theory Physical engineering problem with design criteria General physicomathematical Simplified physicomathematical Numerical method solution u P =? solution u 4D =? + Idealization error solution u 3D =? + Modeling error solution u h =... + Discretization error u3d u h u h ( x) numerical_method(3d theory; x) 30

1.1 Modeling and computation in engineering design and analysis Changes to the methods: verification step 4 Physical engineering problem with design criteria General physicomathematical Simplified physicomathematical Numerical method Observations and conclusions solution u P =? solution u 4D =? + Idealization error solution u 3D =? + Modeling error solution u h =... + Discretization error u3d u h + Human errors 31

1.1 Modeling and computation in engineering design and analysis Changes to the s: validation Changes to the methods: verification step 4 Physical engineering problem with design criteria General physicomathematical Simplified physicomathematical Numerical method Observations and conclusions solution u P =? solution u 4D =? + Idealization error solution u 3D =? + Modeling error solution u h =... + Discretization error u3d u h + Human errors 32

1.1 Modeling and computation in engineering design and analysis Changes to the problem and design Changes to the s: validation Changes to the methods: verification step 4 Physical engineering problem with design criteria General physicomathematical Simplified physicomathematical Numerical method Observations and conclusions solution u P =? solution u 4D =? + Idealization error solution u 3D =? + Modeling error solution u h =... + Discretization error u3d u h + Human errors 33

1.1 Modeling and computation in engineering design and analysis Changes to the problem and design Changes to the s: validation Changes to the methods: verification step 5 Physical engineering problem with design criteria General physicomathematical Simplified physicomathematical Numerical method Observations and conclusions Acceptance solution u P =? solution u 4D =? + Idealization error solution u 3D =? + Modeling error solution u h =... + Discretization error u3d u h + Human errors 34

1.1 Modeling and computation in engineering design and analysis Break exercise 1 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). u P " " u h... 35

1.2 Boundary and initial value problems in engineering sciences step 1 Physical engineering problem with design criteria General physicalmathematical solution u P =? solution u 4D =? + Idealization error up u 4D F L z B General physico-mathematical. A vertical profile (pipe or tube) mast OB is supported by a balland-socket joint O and cables BC and BD. A force F is acting on the the mast at point B. x a C O a D c y Problem. Determine the displacements and stresses in the mast for given length L, cross-sectional area A, density ρ, and Young s modulus E, distances a and c, as well as force F. 36

1.2 Boundary and initial value problems in engineering sciences Physical engineering problem with design criteria solution u P =? details in exercises General physicomathematical solution u 4D =? + Idealization error x step 2 3D linear elasticity F z B L a O a C D c y Simplified physicomathematical F B = F z + T Cz + T Dz b = Ag F A = O z equilibrium eq. constitutive eq. kinematics solution u 3D =? + Modeling error u 4D u 3D Under reasonable assumptions: σ b σ Eε ε u & BCs 37

1.2 Boundary and initial value problems in engineering sciences σ b σ Eε ε u Physical engineering problem with design criteria General physicomathematical solution u P =? solution u 4D =? + Idealization error 3D linear theory Simplified physicomathematical solution u 3D =? + Modeling error details in exercises step 2N 1D axially loaded elastic rod 0 E( x), A( x), b( x) L N times simplified physico-mathematical N L x, u( x) N' b, E u' N( x) solution u =... + N x Modeling error A( x) ( x) u " 3D "u Assumptions: symmetry, pointwise joints and actions etc. 38

1.2 Boundary and initial value problems in engineering sciences σ b σ Eε ε u Physical engineering problem with design criteria General physicomathematical solution u P =? solution u 4D =? + Idealization error 3D linear theory Simplified physicomathematical solution u 3D =? + Modeling error step 2N u(0) AEu' N( L) u '( x) 0 N L b( x) details in exercises N times simplified physico-mathematical u( x) solution u =... + N x Modeling error x x L d s u N AE 1 0 L AE 0 0 s bdr ds 39

1.2 Boundary and initial value problems in engineering sciences σ b σ Eε ε u Physical engineering problem with design criteria General physicomathematical solution u P =? solution u 4D =? + Idealization error 3D linear theory Simplified physicomathematical solution u 3D =? + Modeling error step 2N N times simplified physico-mathematical solution u =... + N x Modeling error step 3 L 0 uˆ h ' AEu h 'dx uˆ h ( L) N L L 0 uˆ h bdx, Numerical method u h (0) u 0 solution u h =... + Discretization error u u h 40

1.2 Boundary and initial value problems in engineering sciences Axially loaded linearly elastic bar problem (in a displacement form): (1) EAu' (2a) u(0) u (2b) ( EAu')( L) '( x) b( x), N L 0 0 x L differential equation essential BC natural BC Other 1D problems of the same form: Problem I variable Data Load II variable Axially loaded bar displacement EA extensional force force Torsionally loaded bar angle GJ torsional moment torque Seepage in soils head (pressure) k infiltration velocity Heat diffusion temperature k heat generation heat Electrostatics electric potential ε charge density electric flux 41

1.2 Boundary and initial value problems in engineering sciences Axially loaded linearly elastic bar problem (in a displacement form): (1) EAu' (2b) ( EAu')( L) '( x) b( x), (2a) u(0) u N L 0 0 x L differential equation essential BC natural BC 1D generalization. Axially, torsionally and transversally loaded beam (uncoupled): extension : (1) (2) torsion : (3) (4) bending : (5) u(0) EAu' GJ' EIw'' u (6) w(0) '( x) 0 '( x) (0), 0 ' '( x) w, 0, b( x), 0 x L ( EAu')( L) r( x), 0 x L ( GJ')( L) q( x), 0 x L w'(0), 0 N T L L ( EIw'')( L) This one is of a different form! M L, ( EIw'')'( L) Q L 42

1.2 Boundary and initial value problems in engineering sciences 1D modification and 2D generalization. Heat diffusion: (1) (2a) (2b) T (1) (2a) (2b) EAu' '( x) b( x), 0 x L kt ' u(0) ( EAu')( L) N u T q q x y T x, q, q x y y ( k( x, y) T ( x, y)) f ( x, y), L 0 T ( x, q( x, y) T 0 y) n ( x, q 0 y), ( x, y), q q x y ( x, ( x, y) y) ( x, '( x) T (0) ( kt ')( L) T y) T q q f ( x), L 0 u u 0 T T 0 0 EA, b q 0 T n x k, f q L N L 43

1.X Continuum mechanics in civil engineering Building blocks of boundary value problems in civil engineering The continuum mechanics concepts for defining deformation and motion are (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. 1D elasticity N' 2D/3D elasticity σ σ Eε ε u 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. b, N E u' b A, & & BCs BCs CIV-E1060 / 2017 / Jarkko Niiranen 44

1.X Continuum mechanics in civil engineering Matter (or material) is composed of particles from electrons and atoms up to molecules which can be, under certain assumptions, led as a continuum, however. Idealizations of physics and chemistry are further simplified or homogenized by the theory of continuum mechanics. CIV-E1060 / 2017 / Jarkko Niiranen 45

1.X Continuum mechanics in civil engineering 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 generalized continuum etc. often applied to capture microstructural effects of granular materials, for instance. CIV-E1060 / 2017 / Jarkko Niiranen 46

1.X Continuum mechanics in civil engineering 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. 47

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