Theory of Elasticity. <gl Spri ringer. and Thermal Stresses. Explanations, Problems and Solutions. Jozef Ignaczak. Naotake Noda Yoshinobu Tanigawa

Size: px
Start display at page:

Download "Theory of Elasticity. <gl Spri ringer. and Thermal Stresses. Explanations, Problems and Solutions. Jozef Ignaczak. Naotake Noda Yoshinobu Tanigawa"

Transcription

1 M. Reza Eslami Richard B. Hetnarski Jozef Ignaczak Naobumi Sumi Naotake Noda Yoshinobu Tanigawa Theory of Elasticity and Thermal Stresses Explanations, Problems and Solutions <gl Spri ringer

2 Contents Part I The Mathematical Theory of Elasticity 1 Mathematical Preliminaries Some Formulas in Tensor Algebra Alternative Definitions of a Vector and of a Tensor Using an Orthogonal Tensor Further Definitions Eigenproblem for a Second Order Tensor A Fourth-Order Tensor C Tensor Fields Integral Theorems Irrotational and Solenoidal Fields Time-Dependent Fields Problems and Solutions Related to the Mathematical Preliminaries 13 2 Fundamentals of Linear Elasticity Deformation of an Elastic Body Compatibility Motion and Equilibrium Equations of Motion Constitutive Relations Isotropic Elastic Body The Cauchy Relations Constitutive Relations for a Thermoelastic Body Problems and Solutions Related to the Fundamentals of Linear Elasticity 43 3 Formulation of Problems of Elasticity Boundary Value Problems of Elastostatics Concept of an Elastic State Concept of a Thermoelastic State Formulation of Boundary Value Problems 69 xi

3 xii Contents 3.5 Uniqueness Formulation of Problems of Nonisothermal Elastostatics Initial-Boundary Value Problems of Elastodynamics Concept of an Elastic Process Formulation of Problems of Isothermal Elastodynamics Problems and Solutions Related to the Formulation of Problems of Elasticity 74 4 Variational Formulation of Elastostatics Minimum Principles The Rayleigh-Ritz Method Variational Principles Compatibility-Related Principle Problems and Solutions Related to Variational Formulation of Elastostatics Variational Principles of Elastodynamics The Hamilton-Kirchhoff Principle Problems and Solutions Related to Variational Principles of Elastodynamics Complete Solutions of Elasticity Complete Solutions of Elastostatics Complete Solutions of Elastodynamics Complete Stress Solution of Elastodynamics Problems and Solutions Related to Complete Solutions of Elasticity Formulation of Two-Dimensional Problems Two-Dimensional Problems of Isothermal Elastostatics Two-Dimensional Problems of Nonisothermal Elastostatics Two-Dimensional Problems of Elastodynamics Two-Dimensional Problems of Nonisothermal Elastodynamics Problems and Solutions Related to Formulation of Two-Dimensional Problems Solutions to Particular Three-Dimensional Boundary Value Problems of Elastostatics Torsion of Circular Bars Problems and Solutions Related to Particular Three-Dimensional Boundary Value Problems of Elastostatics Torsion Problems 212

4 Contents xiii 9 Solutions to Particular Two-Dimensional Boundary Value Problems of Elastostatics The Two-Dimensional Version of Boussinesq-Papkovitch-Neuber Solution for a Body Under Plane Strain Conditions Problems and Solutions Related to Particular Two-Dimensional Boundary Value Problems of Elastostatics Solutions to Particular Three-Dimensional Initial-Boundary Value Problems of Elastodynamics A Spherically Symmetric Green's Function of the Dynamic Theory of Thermal Stresses for an Infinite Elastic Body A Spherically Symmetric Green's Function for a Parabolic Heat Conduction Equation in an Infinite Space Problems and Solutions Related to Particular Three-Dimensional Initial-Boundary Value Problems of Elastodynamics Solutions to Particular Two-Dimensional Initial-Boundary Value Problems of Elastodynamics Dynamic Thermal Stresses in an Infinite Elastic Body Under Plane Strain Conditions Subject to a Time-Dependent Temperature Field Dynamic Thermal Stresses in an Infinite Elastic Body Under Generalized Plane Stress Conditions Subject to a Time-Dependent Temperature Field Problems and Solutions Related to Particular Two-Dimensional Initial-Boundary Value Problems of Elastodynamics One-Dimensional Solutions of Elastodynamics One-Dimensional Field Equations of Isothermal Elastodynamics One-Dimensional Field Equations of Nonisothermal Elastodynamics Problems and Solutions Related to One-Dimensional Initial-Boundary Value Problems of Elastodynamics 276 Part II Thermal Stresses 13 Thermal Stresses in Bars Thermal Stresses in Bars 301

5 xiv Contents 13.2 Problems and Solutions Related to Thermal Stresses in Bars Thermal Stresses in Beams Thermal Stresses in Beams Thermal Stresses in Beams Thermal Stresses in Composite Beams Thermal Deflection in Beams Curved Beams Problems and Solutions Related to Thermal Stresses in Beams Heat Conduction Heat Conduction Equation One-Dimensional Heat Conduction Problems Problems and Solutions Related to Heat Conduction Basic Equations of Thermoelasticity Governing Equations of Thermoelasticity Stress and Strain in a Cartesian Coordinate System Navier's Equations, Compatibility Equations and Boundary Conditions General Solution of Navier's Equations Thermal Stresses in a Cylindrical Coordinate System Thermal Stresses in a Spherical Coordinate System Problems and Solutions Related to Basic Equations of Thermoelasticity Plane Thermoelastic Problems Plane Strain and Plane Stress Problems and Solutions Related to Plane Thermoelastic Problems Thermal Stresses in Circular Cylinders One-Dimensional Problems Plane Problems Two-Dimensional Axisymmetric Problems (r, z) Three-Dimensional Problems Problems and Solutions Related to Thermal Stresses in Circular Cylinders 453

6 Contents xv 19 Thermal Stresses in Spherical Bodies One-Dimensional Problems in Spherical Bodies Two-Dimensional Axisymmetric Problems Problems and Solutions Related to Thermal Stresses in Spherical Bodies Thermal Stresses in Plates Basic Equations for a Rectangular Plate Basic Equations for a Circular Plate Problems and Solutions Related to Thermal Stresses in Plates Thermally Induced Instability Instability of Beam-Column Instability of Plate Problems and Solutions Related to Thermally Induced Instability 539 Part III Thermal Stresses Advanced Theory and Applications 22 Heat Conduction Problems in Rectangular Cartesian Coordinates Steady Two-Dimensional Problems: Separation of Variables Fourier Series Double Fourier Series Bessel Functions and Fourier-Bessel Series Nonhomogeneous Differential Equations and Boundary Conditions Problems and Solutions Related to Heat Conduction Lumped Formulation Problems in Cylindrical Coordinates Problems in Spherical Coordinates Steady-State Two- and Three-Dimensional Problems Thermal Stresses in Beams Thermal Stresses in Beams Deflection Equation of Beams Boundary Conditions Problems and Solutions of Beams Thick Cylinders and Spheres Problems and Solutions of Cylinders and Spheres 653

7 xvi Contents 25 Piping Systems Thermal Expansion of Piping Systems Definition of the Elastic Center Piping Systems in Two-Dimensions Piping Systems in Three-Dimensions Problems and Solutions of Piping Systems Coupled Thermoelasticity Governing Equations, Classical Theory Problems and Solutions of Coupled Thermoelasticity 703 Part IV Numerical Methods 27 The Method of Characteristics Basic Equations for Plane Thermoelastic Waves Characteristics and Characteristic Equations Derivation of Difference Equations and Numerical Procedure Finite-Difference Solution for Temperature Problems and Solutions Related to The Method of Characteristics Finite Element of Coupled Thermoelasticity Galerkin Finite Element One-Dimensional Problem Problems and Solutions Related to Coupled Thermoelasticity Boundary Element, Coupled Thermoelasticity Governing Equations Boundary Integral Equation Fundamental Solution Numerical Formulation Problems and Solutions Related to Coupled Thermoelasticity 763 Errata to Three Books 777 Bibliography 781 Index 783

COPYRIGHTED MATERIAL. Index

COPYRIGHTED MATERIAL. Index Index A Admissible function, 163 Amplification factor, 36 Amplitude, 1, 22 Amplitude-modulated carrier, 630 Amplitude ratio, 36 Antinodes, 612 Approximate analytical methods, 647 Assumed modes method,

More information

Tyn Myint-U Lokenath Debnath. Linear Partial Differential Equations for Scientists and Engineers. Fourth Edition. Birkhauser Boston Basel Berlin

Tyn Myint-U Lokenath Debnath. Linear Partial Differential Equations for Scientists and Engineers. Fourth Edition. Birkhauser Boston Basel Berlin Tyn Myint-U Lokenath Debnath Linear Partial Differential Equations for Scientists and Engineers Fourth Edition Birkhauser Boston Basel Berlin Preface to the Fourth Edition Preface to the Third Edition

More information

Laminated Composite Plates and Shells

Laminated Composite Plates and Shells Jianqiao Ye Laminated Composite Plates and Shells 3D Modelling With 62 Figures Springer Table of Contents 1. Introduction to Composite Materials 1 1.1 Introduction 1 1.2 Classification of Composite Materials

More information

HEAT CONDUCTION USING GREEN S FUNCTIONS

HEAT CONDUCTION USING GREEN S FUNCTIONS HEAT CONDUCTION USING GREEN S FUNCTIONS Preface to the first edition Preface to the second edition Author Biographies Nomenclature TABLE OF CONTENTS FOR SECOND EDITION December 2009 Page viii x xii xiii

More information

Nonlinear Problems of Elasticity

Nonlinear Problems of Elasticity Stuart S. Antman Nonlinear Problems of Elasticity With 105 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest Contents Preface vn Chapter I. Background

More information

Contents. I Introduction 1. Preface. xiii

Contents. I Introduction 1. Preface. xiii Contents Preface xiii I Introduction 1 1 Continuous matter 3 1.1 Molecules................................ 4 1.2 The continuum approximation.................... 6 1.3 Newtonian mechanics.........................

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

Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition

Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition C. Pozrikidis m Springer Contents Preface v 1 Introduction to Kinematics 1 1.1 Fluids and solids 1 1.2 Fluid parcels and flow

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

Linear Partial Differential Equations for Scientists and Engineers

Linear Partial Differential Equations for Scientists and Engineers Tyn Myint-U Lokenath Debnath Linear Partial Differential Equations for Scientists and Engineers Fourth Edition Birkhäuser Boston Basel Berlin Tyn Myint-U 5 Sue Terrace Westport, CT 06880 USA Lokenath Debnath

More information

Vibrations and Waves in Continuous Mechanical Systems

Vibrations and Waves in Continuous Mechanical Systems Vibrations and Waves in Continuous Mechanical Systems Peter Hagedorn TU Darmstadt, Germany Anirvan DasGupta IIT Kharagpur, India BICENTENNIAL John Wiley & Sons, Ltd Preface xi 1 Vibrations of strings and

More information

METHODS OF THEORETICAL PHYSICS

METHODS OF THEORETICAL PHYSICS METHODS OF THEORETICAL PHYSICS Philip M. Morse PROFESSOR OF PHYSICS MASSACHUSETTS INSTITUTE OF TECHNOLOGY Herman Feshbach PROFESSOR OF PHYSICS MASSACHUSETTS INSTITUTE OF TECHNOLOGY PART II: CHAPTERS 9

More information

Frequently Asked Questions

Frequently Asked Questions Frequently Asked Questions Why do we have to make the assumption that plane sections plane? How about bars with non-axis symmetric cross section? The formulae derived look very similar to beam and axial

More information

Course Syllabus: Continuum Mechanics - ME 212A

Course Syllabus: Continuum Mechanics - ME 212A Course Syllabus: Continuum Mechanics - ME 212A Division Course Number Course Title Academic Semester Physical Science and Engineering Division ME 212A Continuum Mechanics Fall Academic Year 2017/2018 Semester

More information

An Introduction to the Finite Element Method

An Introduction to the Finite Element Method An Introduction to the Finite Element Method Third Edition J. N. REDDY Department 01 Mechanical Engineering Texas A&M University College Station, Texas, USA 77843 11 Boston Burr Ridge, IL Dubuque, IA Madison,

More information

Table of Contents. Preface... 13

Table of Contents. Preface... 13 Table of Contents Preface... 13 Chapter 1. Vibrations of Continuous Elastic Solid Media... 17 1.1. Objective of the chapter... 17 1.2. Equations of motion and boundary conditions of continuous media...

More information

METHODS OF ENGINEERING MATHEMATICS

METHODS OF ENGINEERING MATHEMATICS METHODS OF ENGINEERING MATHEMATICS Edward J. Hang Kyung K. Choi Department of Mechanical Engineering College of Engineering The University of Iowa Iowa City, Iowa 52242 METHODS OF ENGINEERING MATHEMATICS

More information

Mathematica. 1? Birkhauser. Continuum Mechanics using. Fundamentals, Methods, and Applications. Antonio Romano Addolorata Marasco.

Mathematica. 1? Birkhauser. Continuum Mechanics using. Fundamentals, Methods, and Applications. Antonio Romano Addolorata Marasco. Antonio Romano Addolorata Marasco Continuum Mechanics using Mathematica Fundamentals, Methods, and Applications Second Edition TECHNISCHE INFORM ATIONSB IBLIOTHEK UNIVERSITATSBtBLIOTHEK HANNOVER 1? Birkhauser

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

Quasi Static Thermal Stresses in A Limiting Thick Circular Plate with Internal Heat Generation Due To Axisymmetric Heat Supply

Quasi Static Thermal Stresses in A Limiting Thick Circular Plate with Internal Heat Generation Due To Axisymmetric Heat Supply International Journal of Mathematics and Statistics Invention (IJMSI) E-ISSN: 2321 4767 P-ISSN: 2321-4759 Volume 1 Issue 2 ǁ December. 2013ǁ PP-56-63 Quasi Static Thermal Stresses in A Limiting Thick Circular

More information

COMPUTATIONAL ELASTICITY

COMPUTATIONAL ELASTICITY COMPUTATIONAL ELASTICITY Theory of Elasticity and Finite and Boundary Element Methods Mohammed Ameen Alpha Science International Ltd. Harrow, U.K. Contents Preface Notation vii xi PART A: THEORETICAL ELASTICITY

More information

The Finite Element Method for Solid and Structural Mechanics

The Finite Element Method for Solid and Structural Mechanics The Finite Element Method for Solid and Structural Mechanics Sixth edition O.C. Zienkiewicz, CBE, FRS UNESCO Professor of Numerical Methods in Engineering International Centre for Numerical Methods in

More information

APPLIED PARTIM DIFFERENTIAL EQUATIONS with Fourier Series and Boundary Value Problems

APPLIED PARTIM DIFFERENTIAL EQUATIONS with Fourier Series and Boundary Value Problems APPLIED PARTIM DIFFERENTIAL EQUATIONS with Fourier Series and Boundary Value Problems Fourth Edition Richard Haberman Department of Mathematics Southern Methodist University PEARSON Prentice Hall PEARSON

More information

Mechanics of Viscoelastic Solids

Mechanics of Viscoelastic Solids Mechanics of Viscoelastic Solids Aleksey D. Drozdov Institute for Industrial Mathematics, Beersheba, Israel JOHN WILEY & SONS Chichester New York Weinheim Brisbane Toronto Singapore Contents Preface xi

More information

METHODS FOR SOLVING MATHEMATICAL PHYSICS PROBLEMS

METHODS FOR SOLVING MATHEMATICAL PHYSICS PROBLEMS METHODS FOR SOLVING MATHEMATICAL PHYSICS PROBLEMS V.I. Agoshkov, P.B. Dubovski, V.P. Shutyaev CAMBRIDGE INTERNATIONAL SCIENCE PUBLISHING Contents PREFACE 1. MAIN PROBLEMS OF MATHEMATICAL PHYSICS 1 Main

More information

PARTIAL DIFFERENTIAL EQUATIONS and BOUNDARY VALUE PROBLEMS

PARTIAL DIFFERENTIAL EQUATIONS and BOUNDARY VALUE PROBLEMS PARTIAL DIFFERENTIAL EQUATIONS and BOUNDARY VALUE PROBLEMS NAKHLE H. ASMAR University of Missouri PRENTICE HALL, Upper Saddle River, New Jersey 07458 Contents Preface vii A Preview of Applications and

More information

Boundary-Layer Theory

Boundary-Layer Theory Hermann Schlichting Klaus Gersten Boundary-Layer Theory With contributions from Egon Krause and Herbert Oertel Jr. Translated by Katherine Mayes 8th Revised and Enlarged Edition With 287 Figures and 22

More information

Elasticity 2 nd Edition

Elasticity 2 nd Edition Elasticity 2 nd Edition SOLID MECHANICS AND ITS APPLICATIONS Volume 107 Series Editor: G.M.L. GLADWELL Department of Civil Engineering University of Waterloo Waterloo, Ontario, Canada N2L 3GI Aims and

More information

PHYSICAL PROPERTIES OF CRYSTALS

PHYSICAL PROPERTIES OF CRYSTALS PHYSICAL PROPERTIES OF CRYSTALS THEIR REPRESENTATION TENSORS AND MATRICES BY By J. F. NYE, F.R.S. CLARENDON PRESS OXFORD NOTATION INTRODUCTION xiii xv PART 1. GENERAL PRINCIPLES I. THE GROUNDWORK OF CRYSTAL

More information

THERMOELASTIC ANALYSIS OF THICK-WALLED FINITE-LENGTH CYLINDERS OF FUNCTIONALLY GRADED MATERIALS

THERMOELASTIC ANALYSIS OF THICK-WALLED FINITE-LENGTH CYLINDERS OF FUNCTIONALLY GRADED MATERIALS Journal of Thermal Stresses, 28: 391 408, 2005 Copyright # Taylor & Francis Inc. ISSN: 0149-5739 print/1521-074x online DOI: 10.1080/01495730590916623 THERMOELASTIC ANALYSIS OF THICK-WALLED FINITE-LENGTH

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

FOURIER SERIES, TRANSFORMS, AND BOUNDARY VALUE PROBLEMS

FOURIER SERIES, TRANSFORMS, AND BOUNDARY VALUE PROBLEMS fc FOURIER SERIES, TRANSFORMS, AND BOUNDARY VALUE PROBLEMS Second Edition J. RAY HANNA Professor Emeritus University of Wyoming Laramie, Wyoming JOHN H. ROWLAND Department of Mathematics and Department

More information

Cavity Expansion Methods in Geomechanics

Cavity Expansion Methods in Geomechanics Cavity Expansion Methods in Geomechanics by Hai-Sui Yu School of Civil Engineering, University of Nottingham, U. K. KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON TABLE OF CONTENTS Foreword Preface

More information

Structural Integrity. Volume 1

Structural Integrity. Volume 1 Structural Integrity Volume 1 Series editors José A. F. O. Correia, Faculty of Engineering, University of Porto, Porto, Portugal Abílio M. P. De Jesus, Faculty of Engineering, University of Porto, Porto,

More information

Detailed Outline, M E 521: Foundations of Fluid Mechanics I

Detailed Outline, M E 521: Foundations of Fluid Mechanics I Detailed Outline, M E 521: Foundations of Fluid Mechanics I I. Introduction and Review A. Notation 1. Vectors 2. Second-order tensors 3. Volume vs. velocity 4. Del operator B. Chapter 1: Review of Basic

More information

INTRODUCTION TO THE CALCULUS OF VARIATIONS AND ITS APPLICATIONS

INTRODUCTION TO THE CALCULUS OF VARIATIONS AND ITS APPLICATIONS INTRODUCTION TO THE CALCULUS OF VARIATIONS AND ITS APPLICATIONS Frederick Y.M. Wan University of California, Irvine CHAPMAN & HALL I(J)P An International Thomson Publishing Company New York Albany Bonn

More information

Code No: RT41033 R13 Set No. 1 IV B.Tech I Semester Regular Examinations, November - 2016 FINITE ELEMENT METHODS (Common to Mechanical Engineering, Aeronautical Engineering and Automobile Engineering)

More information

Contents. 1 Basic Equations 1. Acknowledgment. 1.1 The Maxwell Equations Constitutive Relations 11

Contents. 1 Basic Equations 1. Acknowledgment. 1.1 The Maxwell Equations Constitutive Relations 11 Preface Foreword Acknowledgment xvi xviii xix 1 Basic Equations 1 1.1 The Maxwell Equations 1 1.1.1 Boundary Conditions at Interfaces 4 1.1.2 Energy Conservation and Poynting s Theorem 9 1.2 Constitutive

More information

Electromagnetic Theory for Microwaves and Optoelectronics

Electromagnetic Theory for Microwaves and Optoelectronics Keqian Zhang Dejie Li Electromagnetic Theory for Microwaves and Optoelectronics Translated by authors With 259 Figures Springer Contents 1 Basic Electromagnetic Theory 1 1.1 Maxwell's Equations 1 1.1.1

More information

Continuum Mechanics and Theory of Materials

Continuum Mechanics and Theory of Materials Peter Haupt Continuum Mechanics and Theory of Materials Translated from German by Joan A. Kurth Second Edition With 91 Figures, Springer Contents Introduction 1 1 Kinematics 7 1. 1 Material Bodies / 7

More information

Table of Contents. Preface...xvii. Part 1. Level

Table of Contents. Preface...xvii. Part 1. Level Preface...xvii Part 1. Level 1... 1 Chapter 1. The Basics of Linear Elastic Behavior... 3 1.1. Cohesion forces... 4 1.2. The notion of stress... 6 1.2.1. Definition... 6 1.2.2. Graphical representation...

More information

3 2 6 Solve the initial value problem u ( t) 3. a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1

3 2 6 Solve the initial value problem u ( t) 3. a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1 Math Problem a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1 3 6 Solve the initial value problem u ( t) = Au( t) with u (0) =. 3 1 u 1 =, u 1 3 = b- True or false and why 1. if A is

More information

Course No: (1 st version: for graduate students) Course Name: Continuum Mechanics Offered by: Chyanbin Hwu

Course No: (1 st version: for graduate students) Course Name: Continuum Mechanics Offered by: Chyanbin Hwu Course No: (1 st version: for graduate students) Course Name: Continuum Mechanics Offered by: Chyanbin Hwu 2011. 11. 25 Contents: 1. Introduction 1.1 Basic Concepts of Continuum Mechanics 1.2 The Need

More information

VIBRATION PROBLEMS IN ENGINEERING

VIBRATION PROBLEMS IN ENGINEERING VIBRATION PROBLEMS IN ENGINEERING FIFTH EDITION W. WEAVER, JR. Professor Emeritus of Structural Engineering The Late S. P. TIMOSHENKO Professor Emeritus of Engineering Mechanics The Late D. H. YOUNG Professor

More information

The Non-Linear Field Theories of Mechanics

The Non-Linear Field Theories of Mechanics С. Truesdell-W.Noll The Non-Linear Field Theories of Mechanics Second Edition with 28 Figures Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo Hong Kong Barcelona Budapest Contents. The Non-Linear

More information

Viscoelastic Structures Mechanics of Growth and Aging

Viscoelastic Structures Mechanics of Growth and Aging Viscoelastic Structures Mechanics of Growth and Aging Aleksey D. Drozdov Institute for Industrial Mathematics Ben-Gurion University of the Negev Be'ersheba, Israel ACADEMIC PRESS San Diego London Boston

More information

JEPPIAAR ENGINEERING COLLEGE

JEPPIAAR ENGINEERING COLLEGE JEPPIAAR ENGINEERING COLLEGE Jeppiaar Nagar, Rajiv Gandhi Salai 600 119 DEPARTMENT OFMECHANICAL ENGINEERING QUESTION BANK VI SEMESTER ME6603 FINITE ELEMENT ANALYSIS Regulation 013 SUBJECT YEAR /SEM: III

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

Translated from Prikladnaya Mekhanika, Vol. 7, No. 8, pp , August, 1971.

Translated from Prikladnaya Mekhanika, Vol. 7, No. 8, pp , August, 1971. W. Nowacki THE THEORY OF ASYMMETRICAL ELASTICITY* Reviewedby G. N. Savin and Yu. N. Nemish The monograph is a result of studies based on the model of a continuous medium which W. Voigt had proposed in

More information

Boundary. DIFFERENTIAL EQUATIONS with Fourier Series and. Value Problems APPLIED PARTIAL. Fifth Edition. Richard Haberman PEARSON

Boundary. DIFFERENTIAL EQUATIONS with Fourier Series and. Value Problems APPLIED PARTIAL. Fifth Edition. Richard Haberman PEARSON APPLIED PARTIAL DIFFERENTIAL EQUATIONS with Fourier Series and Boundary Value Problems Fifth Edition Richard Haberman Southern Methodist University PEARSON Boston Columbus Indianapolis New York San Francisco

More information

Vibration Dynamics and Control

Vibration Dynamics and Control Giancarlo Genta Vibration Dynamics and Control Spri ringer Contents Series Preface Preface Symbols vii ix xxi Introduction 1 I Dynamics of Linear, Time Invariant, Systems 23 1 Conservative Discrete Vibrating

More information

BHAR AT HID AS AN ENGIN E ERI N G C O L L E G E NATTR A MPA LL I

BHAR AT HID AS AN ENGIN E ERI N G C O L L E G E NATTR A MPA LL I BHAR AT HID AS AN ENGIN E ERI N G C O L L E G E NATTR A MPA LL I 635 8 54. Third Year M E C H A NICAL VI S E M ES TER QUE S T I ON B ANK Subject: ME 6 603 FIN I T E E LE ME N T A N A L YSIS UNI T - I INTRODUCTION

More information

Electromagnetic Theory for Microwaves and Optoelectronics

Electromagnetic Theory for Microwaves and Optoelectronics Keqian Zhang Dejie Li Electromagnetic Theory for Microwaves and Optoelectronics Second Edition With 280 Figures and 13 Tables 4u Springer Basic Electromagnetic Theory 1 1.1 Maxwell's Equations 1 1.1.1

More information

Advanced Vibrations. Distributed-Parameter Systems: Exact Solutions (Lecture 10) By: H. Ahmadian

Advanced Vibrations. Distributed-Parameter Systems: Exact Solutions (Lecture 10) By: H. Ahmadian Advanced Vibrations Distributed-Parameter Systems: Exact Solutions (Lecture 10) By: H. Ahmadian ahmadian@iust.ac.ir Distributed-Parameter Systems: Exact Solutions Relation between Discrete and Distributed

More information

Chapter 3: Newtonian Fluids

Chapter 3: Newtonian Fluids Chapter 3: Newtonian Fluids CM4650 Michigan Tech Navier-Stokes Equation v vv p t 2 v g 1 Chapter 3: Newtonian Fluid TWO GOALS Derive governing equations (mass and momentum balances Solve governing equations

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

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

UNIT-I Introduction & Plane Stress and Plane Strain Analysis

UNIT-I Introduction & Plane Stress and Plane Strain Analysis SIDDHARTH INSTITUTE OF ENGINEERING & TECHNOLOGY:: PUTTUR (AUTONOMOUS) Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : Advanced Solid Mechanics (18CE1002) Year

More information

Introduction. Finite and Spectral Element Methods Using MATLAB. Second Edition. C. Pozrikidis. University of Massachusetts Amherst, USA

Introduction. Finite and Spectral Element Methods Using MATLAB. Second Edition. C. Pozrikidis. University of Massachusetts Amherst, USA Introduction to Finite and Spectral Element Methods Using MATLAB Second Edition C. Pozrikidis University of Massachusetts Amherst, USA (g) CRC Press Taylor & Francis Group Boca Raton London New York CRC

More information

in this web service Cambridge University Press

in this web service Cambridge University Press CONTINUUM MECHANICS This is a modern textbook for courses in continuum mechanics. It provides both the theoretical framework and the numerical methods required to model the behavior of continuous materials.

More information

A FAILURE CRITERION FOR POLYMERS AND SOFT BIOLOGICAL MATERIALS

A FAILURE CRITERION FOR POLYMERS AND SOFT BIOLOGICAL MATERIALS Material Technology A FALURE CRTERON FOR POLYMERS AND SOFT BOLOGCAL MATERALS Authors: William W. Feng John O. Hallquist Livermore Software Technology Corp. 7374 Las Positas Road Livermore, CA 94550 USA

More information

Chapter 3. Load and Stress Analysis

Chapter 3. Load and Stress Analysis Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3

More information

Mechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002

Mechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002 student personal identification (ID) number on each sheet. Do not write your name on any sheet. #1. A homogeneous, isotropic, linear elastic bar has rectangular cross sectional area A, modulus of elasticity

More information

ELASTICITY AND FRACTURE MECHANICS. Vijay G. Ukadgaonker

ELASTICITY AND FRACTURE MECHANICS. Vijay G. Ukadgaonker THEORY OF ELASTICITY AND FRACTURE MECHANICS y x Vijay G. Ukadgaonker Theory of Elasticity and Fracture Mechanics VIJAY G. UKADGAONKER Former Professor Indian Institute of Technology Bombay Delhi-110092

More information

Contact, Adhesion and Rupture of Elastic Solids

Contact, Adhesion and Rupture of Elastic Solids D. Maugis Contact, Adhesion and Rupture of Elastic Solids With 186 Figures Springer Contents г 1. Elements of Surface Physics 1 1.1 Introduction 1 1.2 Van der Waals Forces Between Molecules 3 1.2.1 The

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

Piezoelectric Multilayer Beam Bending Actuators

Piezoelectric Multilayer Beam Bending Actuators R.G. Bailas Piezoelectric Multilayer Beam Bending Actuators Static and Dynamic Behavior and Aspects of Sensor Integration With 143 Figures and 17 Tables Sprin ger List of Symbols XV Part I Focus of the

More information

Solving Direct and Inverse Heat Conduction Problems

Solving Direct and Inverse Heat Conduction Problems Solving Direct and Inverse Heat Conduction Problems Jan Taler Piotr Duda Solving Direct and Inverse Heat Conduction Problems ~ Springer Preface This book is devoted to the concept of simple and inverse

More information

COSSERAT THEORIES: SHELLS, RODS AND POINTS

COSSERAT THEORIES: SHELLS, RODS AND POINTS COSSERAT THEORIES: SHELLS, RODS AND POINTS SOLID MECHANICS AND ITS APPLICATIONS Volume 79 Series Editor: G.M.L. GLADWELL Department of Civil Engineering University of Waterloo Waterloo, Ontario, Canada

More information

Back Matter Index The McGraw Hill Companies, 2004

Back Matter Index The McGraw Hill Companies, 2004 INDEX A Absolute viscosity, 294 Active zone, 468 Adjoint, 452 Admissible functions, 132 Air, 294 ALGOR, 12 Amplitude, 389, 391 Amplitude ratio, 396 ANSYS, 12 Applications fluid mechanics, 293 326. See

More information

Theory of Elasticity

Theory of Elasticity Theory of Elasticity Aldo Maceri Theory of Elasticity 123 Prof. Dr.-Ing. Aldo Maceri Universitá Roma Tre Departimento di Ingegneria Meccanica e Industriale Via della Vasca Navale, 79 00146 Roma Italy

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

Fluid Dynamics Exercises and questions for the course

Fluid Dynamics Exercises and questions for the course Fluid Dynamics Exercises and questions for the course January 15, 2014 A two dimensional flow field characterised by the following velocity components in polar coordinates is called a free vortex: u r

More information

Photoelasticity of Glass

Photoelasticity of Glass H. Aben, C. GuiUemet Photoelasticity of Glass With 218 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest Contents Preface v Part One The Basics of Photoelasticity

More information

Microstructural Randomness and Scaling in Mechanics of Materials. Martin Ostoja-Starzewski. University of Illinois at Urbana-Champaign

Microstructural Randomness and Scaling in Mechanics of Materials. Martin Ostoja-Starzewski. University of Illinois at Urbana-Champaign Microstructural Randomness and Scaling in Mechanics of Materials Martin Ostoja-Starzewski University of Illinois at Urbana-Champaign Contents Preface ix 1. Randomness versus determinism ix 2. Randomness

More information

Table of Contents. Foreword... xiii. Preface... xv

Table of Contents. Foreword... xiii. Preface... xv Table of Contents Foreword.... xiii Preface... xv Chapter 1. Fundamental Equations, Dimensionless Numbers... 1 1.1. Fundamental equations... 1 1.1.1. Local equations... 1 1.1.2. Integral conservation equations...

More information

HANDBUCH DER PHYSIK HERAUSGEGEBEN VON S. FLÜGGE. BAND VIa/2 FESTKÖRPERMECHANIK II BANDHERAUSGEBER C.TRUESDELL MIT 25 FIGUREN

HANDBUCH DER PHYSIK HERAUSGEGEBEN VON S. FLÜGGE. BAND VIa/2 FESTKÖRPERMECHANIK II BANDHERAUSGEBER C.TRUESDELL MIT 25 FIGUREN HANDBUCH DER PHYSIK HERAUSGEGEBEN VON S. FLÜGGE BAND VIa/2 FESTKÖRPERMECHANIK II BANDHERAUSGEBER C.TRUESDELL MIT 25 FIGUREN SPRINGER-VERLAG BERLIN HEIDELBERG NEWYORK 1972 Contents. The Linear Theory of

More information

Finite Element Analysis of Acoustic Scattering

Finite Element Analysis of Acoustic Scattering Frank Ihlenburg Finite Element Analysis of Acoustic Scattering With 88 Illustrations Springer Contents Preface vii 1 The Governing Equations of Time-Harmonic Wave Propagation, 1 1.1 Acoustic Waves 1 1.1.1

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

Geometry for Physicists

Geometry for Physicists Hung Nguyen-Schafer Jan-Philip Schmidt Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers 4 i Springer Contents 1 General Basis and Bra-Ket Notation 1 1.1 Introduction to

More information

Structure of the Comprehensive Examination in the ME Department. For circulation to students

Structure of the Comprehensive Examination in the ME Department. For circulation to students Structure of the Comprehensive Examination in the ME Department For circulation to students i. The qualifying exams will be held up to 3 times every year. ii. Generally, the qualifying examination will

More information

Homogeneous Turbulence Dynamics

Homogeneous Turbulence Dynamics Homogeneous Turbulence Dynamics PIERRE SAGAUT Universite Pierre et Marie Curie CLAUDE CAMBON Ecole Centrale de Lyon «Hf CAMBRIDGE Щ0 UNIVERSITY PRESS Abbreviations Used in This Book page xvi 1 Introduction

More information

CRITERIA FOR SELECTION OF FEM MODELS.

CRITERIA FOR SELECTION OF FEM MODELS. CRITERIA FOR SELECTION OF FEM MODELS. Prof. P. C.Vasani,Applied Mechanics Department, L. D. College of Engineering,Ahmedabad- 380015 Ph.(079) 7486320 [R] E-mail:pcv-im@eth.net 1. Criteria for Convergence.

More information

HANDBOOK OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS for ENGINEERS and SCIENTISTS

HANDBOOK OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS for ENGINEERS and SCIENTISTS HANDBOOK OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS for ENGINEERS and SCIENTISTS Andrei D. Polyanin Chapman & Hall/CRC Taylor & Francis Group Boca Raton London New York Singapore Foreword Basic Notation

More information

1. Introduction, tensors, kinematics

1. Introduction, tensors, kinematics 1. Introduction, tensors, kinematics Content: Introduction to fluids, Cartesian tensors, vector algebra using tensor notation, operators in tensor form, Eulerian and Lagrangian description of scalar and

More information

SEMM Mechanics PhD Preliminary Exam Spring Consider a two-dimensional rigid motion, whose displacement field is given by

SEMM Mechanics PhD Preliminary Exam Spring Consider a two-dimensional rigid motion, whose displacement field is given by SEMM Mechanics PhD Preliminary Exam Spring 2014 1. Consider a two-dimensional rigid motion, whose displacement field is given by u(x) = [cos(β)x 1 + sin(β)x 2 X 1 ]e 1 + [ sin(β)x 1 + cos(β)x 2 X 2 ]e

More information

PART A. CONSTITUTIVE EQUATIONS OF MATERIALS

PART A. CONSTITUTIVE EQUATIONS OF MATERIALS Preface... xix Acknowledgements... xxix PART A. CONSTITUTIVE EQUATIONS OF MATERIALS.... 1 Chapter 1. Elements of Anisotropic Elasticity and Complements on Previsional Calculations... 3 Yvon CHEVALIER 1.1.

More information

GEOPHYSICAL INVERSE THEORY AND REGULARIZATION PROBLEMS

GEOPHYSICAL INVERSE THEORY AND REGULARIZATION PROBLEMS Methods in Geochemistry and Geophysics, 36 GEOPHYSICAL INVERSE THEORY AND REGULARIZATION PROBLEMS Michael S. ZHDANOV University of Utah Salt Lake City UTAH, U.S.A. 2OO2 ELSEVIER Amsterdam - Boston - London

More information

Constitutive models: Incremental (Hypoelastic) Stress- Strain relations. and

Constitutive models: Incremental (Hypoelastic) Stress- Strain relations. and Constitutive models: Incremental (Hypoelastic) Stress- Strain relations Example 5: an incremental relation based on hyperelasticity strain energy density function and 14.11.2007 1 Constitutive models:

More information

Introduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams.

Introduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams. Outline of Continuous Systems. Introduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams. Vibrations of Flexible Strings. Torsional Vibration of Rods. Bernoulli-Euler Beams.

More information

SPECIAL FUNCTIONS OF MATHEMATICS FOR ENGINEERS

SPECIAL FUNCTIONS OF MATHEMATICS FOR ENGINEERS SPECIAL FUNCTIONS OF MATHEMATICS FOR ENGINEERS Second Edition LARRY C. ANDREWS OXFORD UNIVERSITY PRESS OXFORD TOKYO MELBOURNE SPIE OPTICAL ENGINEERING PRESS A Publication of SPIE The International Society

More information

Mechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection

Mechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection Mechanics of Materials II Chapter III A review of the fundamental formulation of stress, strain, and deflection Outline Introduction Assumtions and limitations Axial loading Torsion of circular shafts

More information

NONLINEAR STRUCTURAL DYNAMICS USING FE METHODS

NONLINEAR STRUCTURAL DYNAMICS USING FE METHODS NONLINEAR STRUCTURAL DYNAMICS USING FE METHODS Nonlinear Structural Dynamics Using FE Methods emphasizes fundamental mechanics principles and outlines a modern approach to understanding structural dynamics.

More information

Mechanics of Solids and Structures, Second Edition

Mechanics of Solids and Structures, Second Edition Mechanics of Solids and Structures, Second Edition A revision of a popular textbook, this volume emphasizes the development of analysis techniques from basic principles for a broad range of practical problems,

More information

Thermoelastic Stresses in a Rod Subjected to Periodic Boundary Condition: An Analytical Treatment

Thermoelastic Stresses in a Rod Subjected to Periodic Boundary Condition: An Analytical Treatment Thermoelastic Stresses in a Rod Subjected to Periodic Boundary Condition: An Analytical Treatment Ahmet N. Eraslan Department of Engineering Sciences Middle East Technical University Ankara 06531, Turkey

More information

Table of Contents. Preface... xiii

Table of Contents. Preface... xiii Preface... xiii PART I. ELEMENTS IN FLUID MECHANICS... 1 Chapter 1. Local Equations of Fluid Mechanics... 3 1.1. Forces, stress tensor, and pressure... 4 1.2. Navier Stokes equations in Cartesian coordinates...

More information

Elastic Multibody Dynamics

Elastic Multibody Dynamics H. Bremer Elastic Multibody Dynamics A Direct Ritz Approach Springer TABLE OF CONTENTS 1. INTRODUCTION 1 1.1 Background 1 1.2 Contents 5 2. AXIOMS AND PRINCIPLES 7 2.1 Axioms 7 2.2 Principles - the "Differential"

More information

METHODS OF THEORETICAL PHYSICS

METHODS OF THEORETICAL PHYSICS METHODS OF THEORETICAL PHYSICS Philip M. Morse PROFESSOR OF PHYSICS MASSACHUSETTS INSTITUTE OF TECHNOLOGY Herman Feshbach PROFESSOR OF PHYSICS MASSACHUSETTS INSTITUTE OF TECHNOLOGY PART I: CHAPTERS 1 TO

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

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