Plates and Shells: Theory and Computation. Dr. Mostafa Ranjbar

Size: px
Start display at page:

Download "Plates and Shells: Theory and Computation. Dr. Mostafa Ranjbar"

Transcription

1 Plates and Shells: Theory and Computation Dr. Mostafa Ranjbar

2 Outline -1-! This part of the module consists of seven lectures and will focus on finite elements for beams, plates and shells. More specifically, we will consider! Review of elasticity equations in strong and weak form! Beam models and their finite element discretisation! Euler-Bernoulli beam! Timoshenko beam! Plate models and their finite element discretisation! Shells as an assembly of plate and membrane finite elements! Introduction to geometrically exact shell finite elements! Dynamics Page 2

3 Outline -2-! There will be opportunities to gain hands-on experience with the implementation of finite elements using MATLAB! One hour lab session on implementation of beam finite elements (will be not marked)! Coursework on implementation of plate finite elements and dynamics Page 3

4 Why Learn Plate and Shell FEs?! Beam, plate and shell FE are available in almost all finite element software packages! The intelligent use of this software and correct interpretation of output requires basic understanding of the underlying theories! FEM is able to solve problems on geometrically complicated domains! Analytic methods introduced in the first part of the module are only suitable for computing plates and shells with regular geometries, like disks, cylinders, spheres etc.! Many shell structures consist of free form surfaces and/or have a complex topology! Computational methods are the only tool for designing such shell structures! FEM is able to solve problems involving large deformations, non-linear material models and/or dynamics! FEM is very cost effective and fast compared to experimentation Page 4

5 Literature! JN Reddy, An introduction to the finite element method, McGraw-Hill (2006)! TJR Hughes, The finite element method, linear static and dynamic finite element analysis, Prentice-Hall (1987)! K-J Bathe, Finite element procedures, Prentice Hall (1996)! J Fish, T Belytschko, A first course on finite elements, John Wiley & Sons (2007)! 3D7 - Finite element methods - handouts Page 5

6 Examples of Shell Structures -1! Civil engineering Masonry shell structure (Eladio Dieste)! Mechanical engineering and aeronautics Ship hull (sheet metal and frame) Page 6 Concrete roof structure (Pier Luigi Nervi) Fuselage (sheet metal and frame)

7 Examples of Shell Structures -2! Consumer products! Nature Crusteceans Page 7 Ficus elastica leaf Red blood cells

8 Representative Finite Element Computations Wrinkling of an inflated party balloon Virtual crash test (BMW) Sheet metal stamping (Abaqus) buckling of carbon nanotubes Page 8

9 Shell-Fluid Coupled Airbag Inflation m 0.49 m 0.74 m 0.86 m m m Shell mesh: elements Fluid mesh: 48x48x62 cells Page 9

10 Shell-Fluid Coupled Airbag Inflation -2- Page 10

11 Detonation Driven Fracture -1Fractured tubes (Al 6061-T6)! Modeling and simulation challenges!! Page 11 Ductile mixed mode fracture Fluid-shell interaction

12 Detonation Driven Fracture -2- Page 12

13 Roadmap for the Derivation of FEM! As introduced in 3D7, there are two distinct ingredients that are combined to arrive at the discrete system of FE equations! The weak form! A mesh and the corresponding shape functions! In the derivation of the weak form for beams, plates and shells the following approach will be pursued 1) Assume how a beam, plate or shell deforms across its thickness 2) Introduce the assumed deformations into the weak form of three-dimensional elasticity 3) Integrate the resulting three-dimensional elasticity equations along the thickness direction analytically Page 13

14 Elasticity Theory -1-! Consider a body in its undeformed (reference) configuration! The body deforms due to loading and the material points move by a displacement! Kinematic equations; defined based on displacements of an infinitesimal volume element)! Axial strains Page 14

15 Elasticity Theory -2-! Shear components! Stresses! Normal stress components! Shear stress component! Shear stresses are symmetric Page 15

16 Elasticity Theory -3-! Equilibrium equations (determined from equilibrium of an infinitesimal volume element)! Equilibrium in x-direction! Equilibrium in y-direction! Equilibrium in z-direction! are the components of the external loading vector (e.g., gravity) Page 16

17 Elasticity Theory -4-! Hooke s law (linear elastic material equations)! With the material constants Young s modulus and Poisson s ratio Page 17

18 Index Notation -1-! The notation used on the previous slides is rather clumsy and leads to very long expressions! Matrices and vectors can also be expressed in index notation, e.g.! Summation convention: a repeated index implies summation over 1,2,3, e.g.! A comma denotes differentiation Page 18

19 Index Notation -2-! Kronecker delta! Examples: Page 19

20 Elasticity Theory in Index Notation -1-! Kinematic equations! Note that these are six equations! Equilibrium equations! Note that these are three equations! Linear elastic material equations! Inverse relationship! Instead of the Young s modulus and Poisson s ratio the Lame constants can be used Page 20

21 Weak Form of Equilibrium Equations -1-! The equilibrium, kinematic and material equations can be combined into three coupled second order partial differential equations! Next the equilibrium equations in weak form are considered in preparation for finite elements! In structural analysis the weak form is also known as the principle of virtual displacements! To simplify the derivations we assume that the boundaries of the domain are fixed (built-in, zero displacements)! The weak form is constructed by multiplying the equilibrium equations with test functions v i which are zero at fixed boundaries but otherwise arbitrary Page 21

22 Weak Form of Equilibrium Equations -1-! Further make use of integration by parts! Aside: divergence theorem! Consider a vector field and its divergence! The divergence theorem states! Using the divergence theorem equation (1) reduces to! which leads to the principle of virtual displacements Page 22

23 Weak Form of Equilibrium Equations -2-! The integral on the left hand side is the internal virtual work performed by the internal stresses due to virtual displacements! The integral on the right hand side is the external virtual work performed by the external forces due to virtual displacements! Note that the material equations have not been used in the preceding derivation. Hence, the principle of virtual work is independent of material (valid for elastic, plastic, )! The internal virtual work can also be written with virtual strains so that the principle of virtual work reads! Try to prove Page 23

Finite Element Method in Geotechnical Engineering

Finite Element Method in Geotechnical Engineering Finite Element Method in Geotechnical Engineering Short Course on + Dynamics Boulder, Colorado January 5-8, 2004 Stein Sture Professor of Civil Engineering University of Colorado at Boulder Contents Steps

More information

Esben Byskov. Elementary Continuum. Mechanics for Everyone. With Applications to Structural Mechanics. Springer

Esben Byskov. Elementary Continuum. Mechanics for Everyone. With Applications to Structural Mechanics. Springer Esben Byskov Elementary Continuum Mechanics for Everyone With Applications to Structural Mechanics Springer Contents Preface v Contents ix Introduction What Is Continuum Mechanics? "I Need Continuum Mechanics

More information

A HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS

A HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS A HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS A. Kroker, W. Becker TU Darmstadt, Department of Mechanical Engineering, Chair of Structural Mechanics Hochschulstr. 1, D-64289 Darmstadt, Germany kroker@mechanik.tu-darmstadt.de,

More information

Recommended teaching texts Theory:

Recommended teaching texts Theory: Recommended teaching texts Theory: M. Sochor: Strength of materials II Czech Technical University Prague, 2006. In Czech: Ondráček, Vrbka, Janíček, Burša: Mechanika těles, Pružnost a pevnost II. CERM,

More information

202 Index. failure, 26 field equation, 122 force, 1

202 Index. failure, 26 field equation, 122 force, 1 Index acceleration, 12, 161 admissible function, 155 admissible stress, 32 Airy's stress function, 122, 124 d'alembert's principle, 165, 167, 177 amplitude, 171 analogy, 76 anisotropic material, 20 aperiodic

More information

Mechanics of Inflatable Fabric Beams

Mechanics of Inflatable Fabric Beams Copyright c 2008 ICCES ICCES, vol.5, no.2, pp.93-98 Mechanics of Inflatable Fabric Beams C. Wielgosz 1,J.C.Thomas 1,A.LeVan 1 Summary In this paper we present a summary of the behaviour of inflatable fabric

More information

MEG 741 Energy and Variational Methods in Mechanics I

MEG 741 Energy and Variational Methods in Mechanics I MEG 741 Energy and Variational Methods in Mechanics I Brendan J. O Toole, Ph.D. Associate Professor of Mechanical Engineering Howard R. Hughes College of Engineering University of Nevada Las Vegas TBE

More information

Lecture 15 Strain and stress in beams

Lecture 15 Strain and stress in beams Spring, 2019 ME 323 Mechanics of Materials Lecture 15 Strain and stress in beams Reading assignment: 6.1 6.2 News: Instructor: Prof. Marcial Gonzalez Last modified: 1/6/19 9:42:38 PM Beam theory (@ ME

More information

Using MATLAB and. Abaqus. Finite Element Analysis. Introduction to. Amar Khennane. Taylor & Francis Croup. Taylor & Francis Croup,

Using MATLAB and. Abaqus. Finite Element Analysis. Introduction to. Amar Khennane. Taylor & Francis Croup. Taylor & Francis Croup, Introduction to Finite Element Analysis Using MATLAB and Abaqus Amar Khennane Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Croup, an informa business

More information

Introduction to Aerospace Engineering

Introduction to Aerospace Engineering Introduction to Aerospace Engineering Lecture slides Challenge the future 1 Aircraft & spacecraft loads Translating loads to stresses Faculty of Aerospace Engineering 29-11-2011 Delft University of Technology

More information

CE-570 Advanced Structural Mechanics - Arun Prakash

CE-570 Advanced Structural Mechanics - Arun Prakash Ch1-Intro Page 1 CE-570 Advanced Structural Mechanics - Arun Prakash The BIG Picture What is Mechanics? Mechanics is study of how things work: how anything works, how the world works! People ask: "Do you

More information

3D Elasticity Theory

3D Elasticity Theory 3D lasticity Theory Many structural analysis problems are analysed using the theory of elasticity in which Hooke s law is used to enforce proportionality between stress and strain at any deformation level.

More information

Stress analysis of a stepped bar

Stress analysis of a stepped bar Stress analysis of a stepped bar Problem Find the stresses induced in the axially loaded stepped bar shown in Figure. The bar has cross-sectional areas of A ) and A ) over the lengths l ) and l ), respectively.

More information

MITOCW MITRES2_002S10nonlinear_lec15_300k-mp4

MITOCW MITRES2_002S10nonlinear_lec15_300k-mp4 MITOCW MITRES2_002S10nonlinear_lec15_300k-mp4 The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources

More information

Mechanical Properties of Materials

Mechanical Properties of Materials Mechanical Properties of Materials Strains Material Model Stresses Learning objectives Understand the qualitative and quantitative description of mechanical properties of materials. Learn the logic of

More information

INTERMEDIATE MECHANICS OF DEFORMABLE BODIES (58:150/51:151/53:140) Fall 2003

INTERMEDIATE MECHANICS OF DEFORMABLE BODIES (58:150/51:151/53:140) Fall 2003 INTERMEDIATE MECHANICS OF DEFORMABLE BODIES (58:150/51:151/53:140) Fall 2003 Instructor: Lecture: Office Hours: Sharif Rahman, 2140 SC, 335-5679, rahman@engineering.uiowa.edu WF, 3:30 4:45 pm at 3315 SC

More information

Continuum mechanics of beam-like structures using one-dimensional finite element based on Serendipity Lagrange cross-sectional discretisation, Mayank Patni, Prof. Paul Weaver, Dr Alberto Pirrera Bristol

More information

Chapter 5 Structural Elements: The truss & beam elements

Chapter 5 Structural Elements: The truss & beam elements Institute of Structural Engineering Page 1 Chapter 5 Structural Elements: The truss & beam elements Institute of Structural Engineering Page 2 Chapter Goals Learn how to formulate the Finite Element Equations

More information

DEVELOPMENT OF A CONTINUUM PLASTICITY MODEL FOR THE COMMERCIAL FINITE ELEMENT CODE ABAQUS

DEVELOPMENT OF A CONTINUUM PLASTICITY MODEL FOR THE COMMERCIAL FINITE ELEMENT CODE ABAQUS DEVELOPMENT OF A CONTINUUM PLASTICITY MODEL FOR THE COMMERCIAL FINITE ELEMENT CODE ABAQUS Mohsen Safaei, Wim De Waele Ghent University, Laboratory Soete, Belgium Abstract The present work relates to the

More information

Unit 18 Other Issues In Buckling/Structural Instability

Unit 18 Other Issues In Buckling/Structural Instability Unit 18 Other Issues In Buckling/Structural Instability Readings: Rivello Timoshenko Jones 14.3, 14.5, 14.6, 14.7 (read these at least, others at your leisure ) Ch. 15, Ch. 16 Theory of Elastic Stability

More information

Jeff Brown Hope College, Department of Engineering, 27 Graves Pl., Holland, Michigan, USA UNESCO EOLSS

Jeff Brown Hope College, Department of Engineering, 27 Graves Pl., Holland, Michigan, USA UNESCO EOLSS MECHANICS OF MATERIALS Jeff Brown Hope College, Department of Engineering, 27 Graves Pl., Holland, Michigan, USA Keywords: Solid mechanics, stress, strain, yield strength Contents 1. Introduction 2. Stress

More information

MATERIAL PROPERTIES. Material Properties Must Be Evaluated By Laboratory or Field Tests 1.1 INTRODUCTION 1.2 ANISOTROPIC MATERIALS

MATERIAL PROPERTIES. Material Properties Must Be Evaluated By Laboratory or Field Tests 1.1 INTRODUCTION 1.2 ANISOTROPIC MATERIALS . MARIAL PROPRIS Material Properties Must Be valuated By Laboratory or Field ests. INRODUCION he fundamental equations of structural mechanics can be placed in three categories[]. First, the stress-strain

More information

Finite Element Method

Finite Element Method Finite Element Method Finite Element Method (ENGC 6321) Syllabus Objectives Understand the basic theory of the FEM Know the behaviour and usage of each type of elements covered in this course one dimensional

More information

The Finite Element Method for the Analysis of Non-Linear and Dynamic Systems. Prof. Dr. Eleni Chatzi Lecture 1-20 September, 2017

The Finite Element Method for the Analysis of Non-Linear and Dynamic Systems. Prof. Dr. Eleni Chatzi Lecture 1-20 September, 2017 The Finite Element Method for the Analysis of Non-Linear and Dynamic Systems Prof. Dr. Eleni Chatzi Lecture 1-20 September, 2017 Institute of Structural Engineering Method of Finite Elements II 1 Course

More information

Lecture 8. Stress Strain in Multi-dimension

Lecture 8. Stress Strain in Multi-dimension Lecture 8. Stress Strain in Multi-dimension Module. General Field Equations General Field Equations [] Equilibrium Equations in Elastic bodies xx x y z yx zx f x 0, etc [2] Kinematics xx u x x,etc. [3]

More information

Numerical Prediction of the Cracks Effect on the Square Origami Tube

Numerical Prediction of the Cracks Effect on the Square Origami Tube Master's Degree Thesis ISRN: BTH-AMT-EX--2013/D14--SE Numerical Prediction of the Cracks Effect on the Square Origami Tube Tianchen Feng Department of Mechanical Engineering Blekinge Institute of Technology

More information

UNCONVENTIONAL FINITE ELEMENT MODELS FOR NONLINEAR ANALYSIS OF BEAMS AND PLATES

UNCONVENTIONAL FINITE ELEMENT MODELS FOR NONLINEAR ANALYSIS OF BEAMS AND PLATES UNCONVENTIONAL FINITE ELEMENT MODELS FOR NONLINEAR ANALYSIS OF BEAMS AND PLATES A Thesis by WOORAM KIM Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the

More information

SIMPLIFIED MODELING OF THIN-WALLED TUBES WITH OCTAGONAL CROSS SECTION AXIAL CRUSHING. Authors and Correspondance: Abstract:

SIMPLIFIED MODELING OF THIN-WALLED TUBES WITH OCTAGONAL CROSS SECTION AXIAL CRUSHING. Authors and Correspondance: Abstract: SIMPLIFIED MODELING OF THIN-WALLED TUBES WITH OCTAGONAL CROSS SECTION AXIAL CRUSHING Authors and Correspondance: Yucheng Liu, Michael L. Day Department of Mechanical Engineering University of Louisville

More information

Aircraft Structures Kirchhoff-Love Plates

Aircraft Structures Kirchhoff-Love Plates University of Liège erospace & Mechanical Engineering ircraft Structures Kirchhoff-Love Plates Ludovic Noels Computational & Multiscale Mechanics of Materials CM3 http://www.ltas-cm3.ulg.ac.be/ Chemin

More information

ELASTOPLASTIC STEEL BEAM BENDING ANALYSIS BY USING ABAQUS

ELASTOPLASTIC STEEL BEAM BENDING ANALYSIS BY USING ABAQUS 11 ELASTOPLASTIC STEEL BEAM BENDING ANALYSIS BY USING ABAQUS Biswajit Jena * * Corresponding author: biswa.tech88@gmail.com Abstract: In recent years tremendous efforts have been made in development of

More information

Static & Dynamic. Analysis of Structures. Edward L.Wilson. University of California, Berkeley. Fourth Edition. Professor Emeritus of Civil Engineering

Static & Dynamic. Analysis of Structures. Edward L.Wilson. University of California, Berkeley. Fourth Edition. Professor Emeritus of Civil Engineering Static & Dynamic Analysis of Structures A Physical Approach With Emphasis on Earthquake Engineering Edward LWilson Professor Emeritus of Civil Engineering University of California, Berkeley Fourth Edition

More information

Exact and Numerical Solution of Pure Torsional Shaft

Exact and Numerical Solution of Pure Torsional Shaft Australian Journal of Basic and Applied Sciences, 4(8): 3043-3052, 2010 ISSN 1991-8178 Exact and Numerical Solution of Pure Torsional Shaft 1 Irsyadi Yani, 2 M.A Hannan, 1 Hassan Basri, and 2 E. Scavino

More information

ERM - Elasticity and Strength of Materials

ERM - Elasticity and Strength of Materials Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: 2018 205 - ESEIAAT - Terrassa School of Industrial, Aerospace and Audiovisual Engineering 712 - EM - Department of Mechanical Engineering

More information

Toward a novel approach for damage identification and health monitoring of bridge structures

Toward a novel approach for damage identification and health monitoring of bridge structures Toward a novel approach for damage identification and health monitoring of bridge structures Paolo Martino Calvi 1, Paolo Venini 1 1 Department of Structural Mechanics, University of Pavia, Italy E-mail:

More information

Lecture #10: Anisotropic plasticity Crashworthiness Basics of shell elements

Lecture #10: Anisotropic plasticity Crashworthiness Basics of shell elements Lecture #10: 151-0735: Dynamic behavior of materials and structures Anisotropic plasticity Crashworthiness Basics of shell elements by Dirk Mohr ETH Zurich, Department of Mechanical and Process Engineering,

More information

Analytical Strip Method for Thin Isotropic Cylindrical Shells

Analytical Strip Method for Thin Isotropic Cylindrical Shells IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) e-issn: 2278-1684,p-ISSN: 2320-334X, Volume 14, Issue 4 Ver. III (Jul. Aug. 2017), PP 24-38 www.iosrjournals.org Analytical Strip Method for

More information

Large Thermal Deflections of a Simple Supported Beam with Temperature-Dependent Physical Properties

Large Thermal Deflections of a Simple Supported Beam with Temperature-Dependent Physical Properties Large Thermal Deflections of a Simple Supported Beam with Temperature-Dependent Physical Properties DR. ŞEREF DOĞUŞCAN AKBAŞ Civil Engineer, Şehit Muhtar Mah. Öğüt Sok. No:2/37, 34435 Beyoğlu- Istanbul,

More information

Chapter 3. Load and Stress Analysis. Lecture Slides

Chapter 3. Load and Stress Analysis. Lecture Slides Lecture Slides Chapter 3 Load and Stress Analysis 2015 by McGraw Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner.

More information

Chapter 3 Variational Formulation & the Galerkin Method

Chapter 3 Variational Formulation & the Galerkin Method Institute of Structural Engineering Page 1 Chapter 3 Variational Formulation & the Galerkin Method Institute of Structural Engineering Page 2 Today s Lecture Contents: Introduction Differential formulation

More information

Large deflection analysis of planar solids based on the Finite Particle Method

Large deflection analysis of planar solids based on the Finite Particle Method yuying@uiuc.edu 10 th US National Congress on Computational Mechanics Large deflection analysis of planar solids based on the Finite Particle Method 1, 2 Presenter: Ying Yu Advisors: Prof. Glaucio H. Paulino

More information

Effect of Specimen Dimensions on Flexural Modulus in a 3-Point Bending Test

Effect of Specimen Dimensions on Flexural Modulus in a 3-Point Bending Test Effect of Specimen Dimensions on Flexural Modulus in a 3-Point Bending Test M. Praveen Kumar 1 and V. Balakrishna Murthy 2* 1 Mechanical Engineering Department, P.V.P. Siddhartha Institute of Technology,

More information

Longitudinal buckling of slender pressurised tubes

Longitudinal buckling of slender pressurised tubes Fluid Structure Interaction VII 133 Longitudinal buckling of slender pressurised tubes S. Syngellakis Wesse Institute of Technology, UK Abstract This paper is concerned with Euler buckling of long slender

More information

Accepted Manuscript. R.C. Batra, J. Xiao S (12) Reference: COST Composite Structures. To appear in:

Accepted Manuscript. R.C. Batra, J. Xiao S (12) Reference: COST Composite Structures. To appear in: Accepted Manuscript Finite deformations of curved laminated St. Venant-Kirchhoff beam using layerwise third order shear and normal deformable beam theory (TSNDT) R.C. Batra, J. Xiao PII: S0263-8223(12)00486-2

More information

Basic Energy Principles in Stiffness Analysis

Basic Energy Principles in Stiffness Analysis Basic Energy Principles in Stiffness Analysis Stress-Strain Relations The application of any theory requires knowledge of the physical properties of the material(s) comprising the structure. We are limiting

More information

If you take CT5143 instead of CT4143 then write this at the first of your answer sheets and skip problem 4 and 6.

If you take CT5143 instead of CT4143 then write this at the first of your answer sheets and skip problem 4 and 6. Delft University of Technology Faculty of Civil Engineering and Geosciences Structural Mechanics Section Write your name and study number at the top right-hand of your work. Exam CT4143 Shell Analysis

More information

Measurement of deformation. Measurement of elastic force. Constitutive law. Finite element method

Measurement of deformation. Measurement of elastic force. Constitutive law. Finite element method Deformable Bodies Deformation x p(x) Given a rest shape x and its deformed configuration p(x), how large is the internal restoring force f(p)? To answer this question, we need a way to measure deformation

More information

EE C245 ME C218 Introduction to MEMS Design

EE C245 ME C218 Introduction to MEMS Design EE C245 ME C218 Introduction to MEMS Design Fall 2007 Prof. Clark T.-C. Nguyen Dept. of Electrical Engineering & Computer Sciences University of California at Berkeley Berkeley, CA 94720 Lecture 16: Energy

More information

CHAPTER 5. Beam Theory

CHAPTER 5. Beam Theory CHPTER 5. Beam Theory SangJoon Shin School of Mechanical and erospace Engineering Seoul National University ctive eroelasticity and Rotorcraft Lab. 5. The Euler-Bernoulli assumptions One of its dimensions

More information

N = Shear stress / Shear strain

N = Shear stress / Shear strain UNIT - I 1. What is meant by factor of safety? [A/M-15] It is the ratio between ultimate stress to the working stress. Factor of safety = Ultimate stress Permissible stress 2. Define Resilience. [A/M-15]

More information

4/14/11. Chapter 12 Static equilibrium and Elasticity Lecture 2. Condition for static equilibrium. Stability An object is in equilibrium:

4/14/11. Chapter 12 Static equilibrium and Elasticity Lecture 2. Condition for static equilibrium. Stability An object is in equilibrium: About Midterm Exam 3 When and where Thurs April 21 th, 5:45-7:00 pm Rooms: Same as Exam I and II, See course webpage. Your TA will give a brief review during the discussion session. Coverage: Chapts 9

More information

Iraq Ref. & Air. Cond. Dept/ Technical College / Kirkuk

Iraq Ref. & Air. Cond. Dept/ Technical College / Kirkuk International Journal of Scientific & Engineering Research, Volume 6, Issue 4, April-015 1678 Study the Increasing of the Cantilever Plate Stiffness by Using s Jawdat Ali Yakoob Iesam Jondi Hasan Ass.

More information

Lecture notes Models of Mechanics

Lecture notes Models of Mechanics Lecture notes Models of Mechanics Anders Klarbring Division of Mechanics, Linköping University, Sweden Lecture 7: Small deformation theories Klarbring (Mechanics, LiU) Lecture notes Linköping 2012 1 /

More information

Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras. Module - 01 Lecture - 11

Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras. Module - 01 Lecture - 11 Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras Module - 01 Lecture - 11 Last class, what we did is, we looked at a method called superposition

More information

Mechanics of Irregular Honeycomb Structures

Mechanics of Irregular Honeycomb Structures Mechanics of Irregular Honeycomb Structures S. Adhikari 1, T. Mukhopadhyay 1 Chair of Aerospace Engineering, College of Engineering, Swansea University, Singleton Park, Swansea SA2 8PP, UK Sixth International

More information

ANALYTICAL PENDULUM METHOD USED TO PREDICT THE ROLLOVER BEHAVIOR OF A BODY STRUCTURE

ANALYTICAL PENDULUM METHOD USED TO PREDICT THE ROLLOVER BEHAVIOR OF A BODY STRUCTURE The 3rd International Conference on Computational Mechanics and Virtual Engineering COMEC 2009 29 30 OCTOBER 2009, Brasov, Romania ANALYTICAL PENDULUM METHOD USED TO PREDICT THE ROLLOVER BEHAVIOR OF A

More information

FEA A Guide to Good Practice. What to expect when you re expecting FEA A guide to good practice

FEA A Guide to Good Practice. What to expect when you re expecting FEA A guide to good practice FEA A Guide to Good Practice What to expect when you re expecting FEA A guide to good practice 1. Background Finite Element Analysis (FEA) has transformed design procedures for engineers. Allowing more

More information

VORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NON-LINEAR MATERIALS

VORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NON-LINEAR MATERIALS The 4 th World Conference on Earthquake Engineering October -7, 008, Beijing, China VORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NON-LINEAR MATERIALS K.

More information

Physical Science and Engineering. Course Information. Course Number: ME 100

Physical Science and Engineering. Course Information. Course Number: ME 100 Physical Science and Engineering Course Number: ME 100 Course Title: Course Information Basic Principles of Mechanics Academic Semester: Fall Academic Year: 2016-2017 Semester Start Date: 8/21/2016 Semester

More information

Computational Analysis for Composites

Computational Analysis for Composites Computational Analysis for Composites Professor Johann Sienz and Dr. Tony Murmu Swansea University July, 011 The topics covered include: OUTLINE Overview of composites and their applications Micromechanics

More information

Computational models of diamond anvil cell compression

Computational models of diamond anvil cell compression UDC 519.6 Computational models of diamond anvil cell compression A. I. Kondrat yev Independent Researcher, 5944 St. Alban Road, Pensacola, Florida 32503, USA Abstract. Diamond anvil cells (DAC) are extensively

More information

University of Sheffield The development of finite elements for 3D structural analysis in fire

University of Sheffield The development of finite elements for 3D structural analysis in fire The development of finite elements for 3D structural analysis in fire Chaoming Yu, I. W. Burgess, Z. Huang, R. J. Plank Department of Civil and Structural Engineering StiFF 05/09/2006 3D composite structures

More information

Advanced Analysis of Steel Structures

Advanced Analysis of Steel Structures Advanced Analysis of Steel Structures Master Thesis Written by: Maria Gulbrandsen & Rasmus Petersen Appendix Report Group B-204d M.Sc.Structural and Civil Engineering Aalborg University 4 th Semester Spring

More information

COURSE TITLE : APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4017 COURSE CATEGORY : A PERIODS/WEEK : 6 PERIODS/ SEMESTER : 108 CREDITS : 5

COURSE TITLE : APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4017 COURSE CATEGORY : A PERIODS/WEEK : 6 PERIODS/ SEMESTER : 108 CREDITS : 5 COURSE TITLE : APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4017 COURSE CATEGORY : A PERIODS/WEEK : 6 PERIODS/ SEMESTER : 108 CREDITS : 5 TIME SCHEDULE MODULE TOPICS PERIODS 1 Simple stresses

More information

Computation Time Assessment of a Galerkin Finite Volume Method (GFVM) for Solving Time Solid Mechanics Problems under Dynamic Loads

Computation Time Assessment of a Galerkin Finite Volume Method (GFVM) for Solving Time Solid Mechanics Problems under Dynamic Loads Proceedings of the International Conference on Civil, Structural and Transportation Engineering Ottawa, Ontario, Canada, May 4 5, 215 Paper o. 31 Computation Time Assessment of a Galerkin Finite Volume

More information

Modelling and numerical simulation of the wrinkling evolution for thermo-mechanical loading cases

Modelling and numerical simulation of the wrinkling evolution for thermo-mechanical loading cases Modelling and numerical simulation of the wrinkling evolution for thermo-mechanical loading cases Georg Haasemann Conrad Kloß 1 AIMCAL Conference 2016 MOTIVATION Wrinkles in web handling system Loss of

More information

Alternative numerical method in continuum mechanics COMPUTATIONAL MULTISCALE. University of Liège Aerospace & Mechanical Engineering

Alternative numerical method in continuum mechanics COMPUTATIONAL MULTISCALE. University of Liège Aerospace & Mechanical Engineering University of Liège Aerospace & Mechanical Engineering Alternative numerical method in continuum mechanics COMPUTATIONAL MULTISCALE Van Dung NGUYEN Innocent NIYONZIMA Aerospace & Mechanical engineering

More information

Elements of Continuum Elasticity. David M. Parks Mechanics and Materials II February 25, 2004

Elements of Continuum Elasticity. David M. Parks Mechanics and Materials II February 25, 2004 Elements of Continuum Elasticity David M. Parks Mechanics and Materials II 2.002 February 25, 2004 Solid Mechanics in 3 Dimensions: stress/equilibrium, strain/displacement, and intro to linear elastic

More information

A BEAM FINITE ELEMENT MODEL INCLUDING WARPING

A BEAM FINITE ELEMENT MODEL INCLUDING WARPING A BEAM FINITE ELEMENT MODEL INCLUDING WARPING Application to the dynamic and static analysis of bridge decks Diego Lisi Department of Civil Engineering of Instituto Superior Técnico, October 2011 ABSTRACT

More information

Fundamentals of Linear Elasticity

Fundamentals of Linear Elasticity Fundamentals of Linear Elasticity Introductory Course on Multiphysics Modelling TOMASZ G. ZIELIŃSKI bluebox.ippt.pan.pl/ tzielins/ Institute of Fundamental Technological Research of the Polish Academy

More information

INTRODUCTION TO THE EXPLICIT FINITE ELEMENT METHOD FOR NONLINEAR TRANSIENT DYNAMICS

INTRODUCTION TO THE EXPLICIT FINITE ELEMENT METHOD FOR NONLINEAR TRANSIENT DYNAMICS INTRODUCTION TO THE EXPLICIT FINITE ELEMENT METHOD FOR NONLINEAR TRANSIENT DYNAMICS SHEN R. WU and LEI GU WILEY A JOHN WILEY & SONS, INC., PUBLICATION ! PREFACE xv PARTI FUNDAMENTALS 1 1 INTRODUCTION 3

More information

1.103 CIVIL ENGINEERING MATERIALS LABORATORY (1-2-3) Dr. J.T. Germaine Spring 2004 LABORATORY ASSIGNMENT NUMBER 6

1.103 CIVIL ENGINEERING MATERIALS LABORATORY (1-2-3) Dr. J.T. Germaine Spring 2004 LABORATORY ASSIGNMENT NUMBER 6 1.103 CIVIL ENGINEERING MATERIALS LABORATORY (1-2-3) Dr. J.T. Germaine MIT Spring 2004 LABORATORY ASSIGNMENT NUMBER 6 COMPRESSION TESTING AND ANISOTROPY OF WOOD Purpose: Reading: During this laboratory

More information

COURSE TITLE : THEORY OF STRUCTURES -I COURSE CODE : 3013 COURSE CATEGORY : B PERIODS/WEEK : 6 PERIODS/SEMESTER: 90 CREDITS : 6

COURSE TITLE : THEORY OF STRUCTURES -I COURSE CODE : 3013 COURSE CATEGORY : B PERIODS/WEEK : 6 PERIODS/SEMESTER: 90 CREDITS : 6 COURSE TITLE : THEORY OF STRUCTURES -I COURSE CODE : 0 COURSE CATEGORY : B PERIODS/WEEK : 6 PERIODS/SEMESTER: 90 CREDITS : 6 TIME SCHEDULE Module Topics Period Moment of forces Support reactions Centre

More information

Course in. Geometric nonlinearity. Nonlinear FEM. Computational Mechanics, AAU, Esbjerg

Course in. Geometric nonlinearity. Nonlinear FEM. Computational Mechanics, AAU, Esbjerg Course in Nonlinear FEM Geometric nonlinearity Nonlinear FEM Outline Lecture 1 Introduction Lecture 2 Geometric nonlinearity Lecture 3 Material nonlinearity Lecture 4 Material nonlinearity it continued

More information

Discrete Analysis for Plate Bending Problems by Using Hybrid-type Penalty Method

Discrete Analysis for Plate Bending Problems by Using Hybrid-type Penalty Method 131 Bulletin of Research Center for Computing and Multimedia Studies, Hosei University, 21 (2008) Published online (http://hdl.handle.net/10114/1532) Discrete Analysis for Plate Bending Problems by Using

More information

Numerical Solutions of 2-D Linear Elastostatic Problems by Network Method

Numerical Solutions of 2-D Linear Elastostatic Problems by Network Method Copyright 2011 Tech Science Press CMES, vol.76, no.1, pp.1-18, 2011 Numerical Solutions of 2-D Linear Elastostatic Problems by Network Method J.L. Morales 1, J.A. Moreno 2 and F. Alhama 3 Abstract: Following

More information

ME 475 Modal Analysis of a Tapered Beam

ME 475 Modal Analysis of a Tapered Beam ME 475 Modal Analysis of a Tapered Beam Objectives: 1. To find the natural frequencies and mode shapes of a tapered beam using FEA.. To compare the FE solution to analytical solutions of the vibratory

More information

The CR Formulation: BE Plane Beam

The CR Formulation: BE Plane Beam 6 The CR Formulation: BE Plane Beam 6 Chapter 6: THE CR FORMUATION: BE PANE BEAM TABE OF CONTENTS Page 6. Introduction..................... 6 4 6.2 CR Beam Kinematics................. 6 4 6.2. Coordinate

More information

The Finite Element Method for Mechonics of Solids with ANSYS Applicotions

The Finite Element Method for Mechonics of Solids with ANSYS Applicotions The Finite Element Method for Mechonics of Solids with ANSYS Applicotions ELLIS H. DILL 0~~F~~~~"P Boca Raton London New Vork CRC Press is an imprint 01 the Taylor & Francis Group, an Informa business

More information

Engineering Physics. In the Science Program, Engineering Physics contributes to the following program goals described in the Exit Profile:

Engineering Physics. In the Science Program, Engineering Physics contributes to the following program goals described in the Exit Profile: Engineering Physics Objectives: 00UV Discipline: Physics Ponderation: 3-2-3 Course Code: 203-BZE-05 Prerequisite: 00UR (Mechanics ) Course Credit: 2 2/3 Corequisite: 00UP (Calculus II) Semester: 4 Introduction

More information

Laminated Beams of Isotropic or Orthotropic Materials Subjected to Temperature Change

Laminated Beams of Isotropic or Orthotropic Materials Subjected to Temperature Change United States Department of Agriculture Forest Service Forest Products Laboratory Research Paper FPL 375 June 1980 Laminated Beams of Isotropic or Orthotropic Materials Subjected to Temperature Change

More information

ME 243. Mechanics of Solids

ME 243. Mechanics of Solids ME 243 Mechanics of Solids Lecture 2: Stress and Strain Ahmad Shahedi Shakil Lecturer, Dept. of Mechanical Engg, BUET E-mail: sshakil@me.buet.ac.bd, shakil6791@gmail.com Website: teacher.buet.ac.bd/sshakil

More information

FINAL EXAMINATION. (CE130-2 Mechanics of Materials)

FINAL EXAMINATION. (CE130-2 Mechanics of Materials) UNIVERSITY OF CLIFORNI, ERKELEY FLL SEMESTER 001 FINL EXMINTION (CE130- Mechanics of Materials) Problem 1: (15 points) pinned -bar structure is shown in Figure 1. There is an external force, W = 5000N,

More information

Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method

Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method Objectives In this course you will learn the following Deflection by strain energy method. Evaluation of strain energy in member under

More information

AE3160 Experimental Fluid and Solid Mechanics

AE3160 Experimental Fluid and Solid Mechanics AE3160 Experimental Fluid and Solid Mechanics Cantilever Beam Bending Claudio Di Leo 1 Learning Objectives 1. On Structural Mechanics: a) Mechanics of Slender Beams b) Strain Transformation Theory c) Principal

More information

Mechanics PhD Preliminary Spring 2017

Mechanics PhD Preliminary Spring 2017 Mechanics PhD Preliminary Spring 2017 1. (10 points) Consider a body Ω that is assembled by gluing together two separate bodies along a flat interface. The normal vector to the interface is given by n

More information

: APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4021 COURSE CATEGORY : A PERIODS/ WEEK : 5 PERIODS/ SEMESTER : 75 CREDIT : 5 TIME SCHEDULE

: APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4021 COURSE CATEGORY : A PERIODS/ WEEK : 5 PERIODS/ SEMESTER : 75 CREDIT : 5 TIME SCHEDULE COURSE TITLE : APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4021 COURSE CATEGORY : A PERIODS/ WEEK : 5 PERIODS/ SEMESTER : 75 CREDIT : 5 TIME SCHEDULE MODULE TOPIC PERIODS 1 Simple stresses

More information

MAAE 2202 A. Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work.

MAAE 2202 A. Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work. It is most beneficial to you to write this mock final exam UNDER EXAM CONDITIONS. This means: Complete the exam in 3 hours. Work on your own. Keep your textbook closed. Attempt every question. After the

More information

FREE VIBRATION ANALYSIS OF THIN CYLINDRICAL SHELLS SUBJECTED TO INTERNAL PRESSURE AND FINITE ELEMENT ANALYSIS

FREE VIBRATION ANALYSIS OF THIN CYLINDRICAL SHELLS SUBJECTED TO INTERNAL PRESSURE AND FINITE ELEMENT ANALYSIS FREE VIBRATION ANALYSIS OF THIN CYLINDRICAL SHELLS SUBJECTED TO INTERNAL PRESSURE AND FINITE ELEMENT ANALYSIS J. Kandasamy 1, M. Madhavi 2, N. Haritha 3 1 Corresponding author Department of Mechanical

More information

Institute of Structural Engineering Page 1. Method of Finite Elements I. Chapter 2. The Direct Stiffness Method. Method of Finite Elements I

Institute of Structural Engineering Page 1. Method of Finite Elements I. Chapter 2. The Direct Stiffness Method. Method of Finite Elements I Institute of Structural Engineering Page 1 Chapter 2 The Direct Stiffness Method Institute of Structural Engineering Page 2 Direct Stiffness Method (DSM) Computational method for structural analysis Matrix

More information

Linearized theory of elasticity

Linearized theory of elasticity Linearized theory of elasticity Arie Verhoeven averhoev@win.tue.nl CASA Seminar, May 24, 2006 Seminar: Continuum mechanics 1 Stress and stress principles Bart Nowak March 8 2 Strain and deformation Mark

More information

Nonlinear Theory of Elasticity. Dr.-Ing. Martin Ruess

Nonlinear Theory of Elasticity. Dr.-Ing. Martin Ruess Nonlinear Theory of Elasticity Dr.-Ing. Martin Ruess geometry description Cartesian global coordinate system with base vectors of the Euclidian space orthonormal basis origin O point P domain of a deformable

More information

A *69>H>N6 #DJGC6A DG C<>C::G>C<,8>:C8:H /DA 'D 2:6G - ( - ) +"' ( + -"( (' (& -+" % '('%"' +"-2 ( -!"',- % )% -.C>K:GH>IN D; AF69>HH>6,-+

A *69>H>N6 #DJGC6A DG C<>C::G>C<,8>:C8:H /DA 'D 2:6G - ( - ) +' ( + -( (' (& -+ % '('%' +-2 ( -!',- % )% -.C>K:GH>IN D; AF69>HH>6,-+ The primary objective is to determine whether the structural efficiency of plates can be improved with variable thickness The large displacement analysis of steel plate with variable thickness at direction

More information

MECHANICS OF MATERIALS

MECHANICS OF MATERIALS STATICS AND MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr, John T. DeWolf David E Mazurek \Cawect Mc / iur/» Craw SugomcT Hilt Introduction 1 1.1 What is Mechanics? 2 1.2 Fundamental

More information

CE 221: MECHANICS OF SOLIDS I CHAPTER 1: STRESS. Dr. Krisada Chaiyasarn Department of Civil Engineering, Faculty of Engineering Thammasat university

CE 221: MECHANICS OF SOLIDS I CHAPTER 1: STRESS. Dr. Krisada Chaiyasarn Department of Civil Engineering, Faculty of Engineering Thammasat university CE 221: MECHANICS OF SOLIDS I CHAPTER 1: STRESS By Dr. Krisada Chaiyasarn Department of Civil Engineering, Faculty of Engineering Thammasat university Agenda Introduction to your lecturer Introduction

More information

Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian

Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian ahmadian@iust.ac.ir Dynamic Response of MDOF Systems: Mode-Superposition Method Mode-Superposition Method:

More information

Numerical and experimental analysis of a cantilever beam: A laboratory project to introduce geometric nonlinearity in Mechanics of Materials

Numerical and experimental analysis of a cantilever beam: A laboratory project to introduce geometric nonlinearity in Mechanics of Materials Numerical and experimental analysis of a cantilever beam: A laboratory project to introduce geometric nonlinearity in Mechanics of Materials Tarsicio Beléndez (1) and Augusto Beléndez (2) (1) Departamento

More information

DUCTILITY BEHAVIOR OF A STEEL PLATE SHEAR WALL BY EXPLICIT DYNAMIC ANALYZING

DUCTILITY BEHAVIOR OF A STEEL PLATE SHEAR WALL BY EXPLICIT DYNAMIC ANALYZING The 4 th World Conference on arthquake ngineering October -7, 008, Beijing, China ABSTRACT : DCTILITY BHAVIOR OF A STL PLAT SHAR WALL BY XPLICIT DYNAMIC ANALYZING P. Memarzadeh Faculty of Civil ngineering,

More information

Excerpt from the Proceedings of the COMSOL Conference 2010 Boston

Excerpt from the Proceedings of the COMSOL Conference 2010 Boston Excerpt from the Proceedings of the COMSOL Conference 21 Boston Uncertainty Analysis, Verification and Validation of a Stress Concentration in a Cantilever Beam S. Kargar *, D.M. Bardot. University of

More information

Two Tier projects for students in ME 160 class

Two Tier projects for students in ME 160 class ME 160 Introduction to Finite Element Method Spring 2016 Topics for Term Projects by Teams of 2 Students Instructor: Tai Ran Hsu, Professor, Dept. of Mechanical engineering, San Jose State University,

More information

Structural Analysis Lab

Structural Analysis Lab Structural Analysis Lab Session 4 Shear Walls With Openings Group 3 Daniel Carroll James Loney Brian Keating Eoghan Russell Table of Contents Introduction... 2 Modelling of structure... 3 Theoretical Calculations...

More information