CIV-E4010 Finite Element Methods in Civil Engineering

Transcription

1 CIV-E4010 Finite Element Methods in Civil Engineering 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

2 CIV-E4010 Finite Element Methods in Civil Engineering Topic Lecturers Assistants Lectures Exercises Web site Material Finite element methods for fundamental problems in structural mechanics, structural engineering and building physics: theory, applications and software tools Jarkko Niiranen, Assistant Professor, Academy Research Fellow; Antti Niemi, Senior Research Fellow (visiting for weeks 5 and 6) Sergei Khakalo and Viacheslav Balobanov, Doctoral Students Tuesdays and Thursdays in R2 Fridays in R5 (advice for theoretical assignments) Mondays in R266 (advice/return for computer assignments) 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 / 2017 / Jarkko Niiranen 2

3 CIV-E4010 Finite Element Methods in Civil Engineering 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: 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 3

4 Commercial finite element software examples 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 Adina Abaqus Ansys Some common structural engineering FEM software: Scia Lusas RFEM Robot CIV-E4010 / 2017 / Jarkko Niiranen 4

5 CIV-E4010 Finite Element Methods in Civil Engineering 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 / 2017 / Jarkko Niiranen 5

6 CIV-E4010 Finite Element Methods in Civil Engineering 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 Research activities are going on at our department in many topics of the course! CIV-E4010 / 2017 / Jarkko Niiranen 6

7 1 Role of modern finite element techniques in engineering analysis Let us start with some simulation examples: Cutting process Shell folding Stamping Bar vibrations in fluid Sail ship mast Fastener joints Hemming Comsol release 5.2:

8 1 Role of modern finite element techniques in engineering analysis 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 CIV-E4010 / 2017 / Jarkko Niiranen 8

9 A GLIMPSE TO THE PREVIOUS COURSES

10 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 10

11 1 Modelling principles and boundary value problems in engineering sciences Let us start with some simulation examples: Cutting process Shell folding Stamping Bar vibrations in fluid Sail ship mast Fastener joints Hemming Comsol release 5.2:

12 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 model problems References Lecture notes: chapter 1 Text book: chapters

13 1.0 Questioning the computational analysis How well do the computational techniques of different engineering fields simulate the real life? 13

14 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? 14

15 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? Formulate the problem 15

16 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? Formulate the problem and solve it! 16

17 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 model solution u P =? solution u 4D =? + Idealization error up u 4D 17

18 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 model solution u P =? solution u 4D =? + Idealization error up u 4D NONLINEAR ANISOTROPIC TIME-DEPENDENT MULTI-PHYSICAL 18

19 1.1 Modeling and computation in engineering design and analysis 4D nonlinear theory step 2 3D linear elasticity theory Kinetics Constitutive models Kinematics Physical engineering problem with design criteria General physicomathematical model Simplified physicomathematical model 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 19

20 1.1 Modeling and computation in engineering design and analysis 3D linear theory Physical engineering problem with design criteria General physicomathematical model Simplified physicomathematical model 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 model 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! 20

21 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 model 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) 21

22 1.1 Modeling and computation in engineering design and analysis 4D nonlinear all inclusive theory Physical engineering problem with design criteria General physicomathematical model 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) 22

23 1.1 Modeling and computation in engineering design and analysis 4D nonlinear all inclusive theory Physical engineering problem with design criteria General physicomathematical model 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) 23

24 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 model Simplified physicomathematical model 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) 24

25 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 model Simplified physicomathematical model 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 25

26 1.1 Modeling and computation in engineering design and analysis Changes to the models: validation Changes to the methods: verification step 4 Physical engineering problem with design criteria General physicomathematical model Simplified physicomathematical model 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 26

27 1.1 Modeling and computation in engineering design and analysis Changes to the problem and design Changes to the models: validation Changes to the methods: verification step 4 Physical engineering problem with design criteria General physicomathematical model Simplified physicomathematical model 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 27

28 1.1 Modeling and computation in engineering design and analysis Changes to the problem and design Changes to the models: validation Changes to the methods: verification step 5 Physical engineering problem with design criteria General physicomathematical model Simplified physicomathematical model 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 28

29 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... 29

30 1.2 Motivation for computational structural engineering CIV-E4010 / 2017 / Jarkko Niiranen 30

31 1.2 Motivation for computational structural engineering CIV-E4010 / 2017 / Jarkko Niiranen 31

32 1.2 Motivation for computational structural engineering What is common to these activites? CIV-E4010 / 2017 / Jarkko Niiranen 32

33 1.2 Motivation for computational structural engineering What is common to these activites? Talent? CIV-E4010 / 2017 / Jarkko Niiranen 33

34 1.2 Motivation for computational structural engineering What is common to these activites? h? CIV-E4010 / 2017 / Jarkko Niiranen 34

35 1.2 Motivation for computational structural engineering What is common to these activites? Talent h? CIV-E4010 / 2017 / Jarkko Niiranen 35

36 1.2 Motivation for computational structural engineering Building systematically on your knowledge and skills for reaching the top! You have talent, you just need to 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-E4010 / 2017 / Jarkko Niiranen 36

37 1.2 Motivation for computational structural engineering What is not common to these activites? Consequencies of incompetence! CIV-E4010 / 2017 / Jarkko Niiranen 37

38 1.2 Motivation for computational structural engineering Consequencies of incompetence! CIV-E4010 / 2017 / Jarkko Niiranen 38

39 1.X Continuum mechanics in civil engineering 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 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 39

40 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, modelled as a continuum, however. Idealizations of physics and chemistry are further simplified or homogenized by the theory of continuum mechanics. 40

41 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 Cosserat continuum, higher-order strain gradient continua etc. (often applied to capture microstructural effects of granular materials, for instance). 41

42 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. 42

43 QUESTIONS? ANSWERS LECTURE BREAK!