Theory of linear elasticity. I assume you have learned the elements of linear
|
|
- Natalie Morgan
- 7 years ago
- Views:
Transcription
1 Physial Metallurgy Frature mehanis leture 1 In the next two letures (Ot.16, Ot.18), we will disuss some basis of frature mehanis using ontinuum theories. The method of ontinuum mehanis is to view a solid as a ontinuous distribution of material partiles. ah material partile onsists of many atoms. The material partile represents the olletive behavior of many atoms. Following topis will be disussed. Trouble with linear elasti theory of strength. The Griffith approah. Frature energy. nergy release rate. Appliations of frature mehanis. The problem to be solved in frature mehanis. A body is subjet to a load. What is the magnitude of the load that will ause the body to frature? Let us begin with a body of a silia glass, whih deforms elastially by small strains. A proedure has been taught in strength of materials probably goes as follows. We first determine the imum stress in the body. Then we determine the strength of the material. The body is supposed to frature when the imum stress in the body reahes the strength of the material. I will first review this proedure, so that we agree exatly what this proedure is. I will then explain why this proedure is diffiult to y in pratie. Theory of linear elastiity. I assume you have learned the elements of linear elastiity. Imagine a body subjet to an ied stress,. At eah material partile, the state of stress is a tensor, with 6 omponents. In the body, the state of stress varies from one material partile to another. Thus, the state of stress in a body is desribed by a field. The field is determined by solving the boundary-value problem. A list of notes of solving boundary-value problems in elastiity are following: Governing equations. Geometri relations. Fore balane equations. Constitutive law. Boundary onditions. Tration or displaement boundary onditions. Approximate solutions. Beams and plates. xat analytial solutions. Few problems an be solved exatly. Theory of lastiity, S. P. Timoshenko and J. N. Goodier, MGraw-Hill, New York. Numerial solutions. Finite element methods. Commerial software suh as ABAQUS. Maximum stress in a body. Solving boundary-value problem is a big task by itself, but is not the subjet of this lass. Let s say we already have the solution. That is, we know all six omponents of stress at every material partile in the body, ( x, x, x ), ( x, x, x ) What do we do with this massive amount of data? We are interested in 1
2 prediting the onditions of frature of the body. For example, if the ied stress is small enough, the body will not frature. How small is small enough? Here is the proedure taught in strength of materials. From the field of stress we determine the imum stress in the body,. The imum omponent of stress at eah material partile is determined by priniple stresses, solved by an eigenvalue problem. Then we look for the largest value of the priniple stress by omparing all material partiles in the body. Today, all this proedure is embodied in ommerial finite element software. So you know the imum omponent of stress of the body,. Stress onentration fator. The equations in elastiity are linear, so that the imum stress in the body is proportional to the ied stress. = C, where C is a dimensionless number. The basi phenomenon that the stress is higher at some material partile in a body than others is known as stress onentration. The number C is known as the stress onentration fator. When a irular hole is embedded in a muh larger plate, this boundary-value problem is solved analytially by Timoshenko and Goodier. The imum stress ours at the surfae of the hole. The stress onentration fator is = 3. Consider an ellipti hole in an infinite plate subjet to a remote stress. This boundary-value problem an still be solved analytially (Stresses in a plate due to the presene of raks and sharp orners, C.. Inglis, 1913). The imum stress given by is a = 1+, b where a and b are semi-axes of the ellipse. The stress onentration fator depends on the shape of the hole, haraterized by the ratio a/b. When a=b, the hole is irular, and the stress onentration fator is 3. When the ellipse is very elongated, a>>b, the stress onentration fator is very large. Denote the radius of urvature at the tip of the ellipse as ρ, after some math you an find ρ = b / a. You an express the above formula in terms of a and ρ, namely, a. ρ This formula may be used to estimate the stress onentration fator for a flaw of
3 some other shapes, where a is interpreted as the overall size of the flaw, and ρ is the radius at the root of the flaw. Strength of a material. Now we have alulated the imum stress the body. Will the body sustain this stress? The theory of elastiity will not answer this question. You need to find the strength of the material somewhere else. For example, you may estimate the theoretial strength of a material by S th =. 10 For a glass, Young s modulus is 70 GPa, so that the estimated theoretial strength is 7 GPa. Prof. Ju Li has told you this value is about two orders of magnitude higher than the strength measured in a bulk sample. You an determine the strength of the material experimentally. You pull a sample until it breaks, then reord the stress that breaks the sample. We all this stress as the experimental strength of the material. The experimental values of vlass are on the order of S ~100 MPa. Design for strength based on linear elastiity. What is the imum load that an be sustained by a body? We now summarize the proedure as follows. Calulate the stress field by solving boundary-value problems. Loate the imum stress in the body. Assume the material has a definite strength. That is, the same material has the same strength, independent of the shape of the body. Measure the strength S using a simple sample of the material, suh as a tensile bar. Make sure the imum stress in the body is below the strength of the material. in Why is this proedure hard to use in pratie? The imum stress in a body is sensitive to the shape of the flaw. The shape of the flaw is a body is seldom known in pratie. The proedure assumes that the body is linearly elasti everywhere, whih is never true. The proedure assumes that the strength of a material is independent of the sample used in experiments. In reality, strengths measured from different samples are different, beause eah sample has different flaws. That is, the proedure is hit in both ways: the imum stress is impossible to alulate, and the strength is impossible to measure. 3
4 Qualitative ontent of the Griffith paper. After the atomisti nature of matter was onfirmed by many experimental observations, it beame useful to relate marosopi phenomena to atomi proesses. In 191, the British engineer A. A. Griffith published a paper on frature of a glass. The main puzzle had been that the glass breaks under a stress several orders of magnitude below the strength of atomi ohesion. Griffith took up the notion that a piee of a glass is never perfet: small raks pre-exist in a body of the glass. The tip of suh a rak onentrates stresses. The intense stress at the tip breaks atomi bonds one by one, like opening a zipper. The rak advanes, leading to the frature of the body. Consider a pre-existing rak in a body subjet to an external load. Regard the body and the external fore together as a thermodynami system, haraterized by two thermodynami variables: the area of the rak and the displaement of the loading grips. To fous on the essential ideas, suppose that, after a ertain amount of displaement, the loading grips are held fixed, but the rak is allowed to advane. Beause the loading grips are fixed, the external load does no work. The energy of the system is the sum of the elasti energy in the body, and the surfae energy in the faes of the rak. The energy of the system is the sum of the elasti energy in the body, and the surfae energy in the faes of the rak. The energy of the system is a funtion of a single thermodynami variable: the area of the rak. When the rak advanes, the stress in the sample is partially relieved, so that the elasti energy is redued. At the same time, the advaning rak reates more surfae area, so that the surfae energy inreases. Thermodynamis ditates that the proess should go in the diretion that redues the total free energy. If the derease in elasti energy prevails, the rak grows. If the inrease in surfae energy prevails, the rak heals. The nonlinear zone, loalized around the tip of the rak, remains invariant as the rak advanes. Consequently, the presene of the nonlinearity does not affet the aounting of energy. To sum up, the qualitative ontent of the Griffith paper is following In a body of glass raks pre-exist. The tip of suh a rak onentrates stresses. The intense stress breaks atomi bonds one by one, like opening a zipper. As the rak advanes, fresh surfaes are reated. The surfae energy inreases, but the elasti energy dereases. The rak advanes if the advane redues the sum of the surfae energy and elasti energy. The theory. A large sheet of a glass is under stress. The sheet has unit thikness. For the time being, assume that the loading grips are rigidly held, so that the displaement is fixed, and the loading devie does no additional work after a fixed displaement is ied. The state of referene is a stressed sheet with no rak. The state that interests us is the sheet with a rak of length a. We now alulate the differene in energy between the two states. The surfae energy inreases by 4aγ. 4
5 The elasti energy redues. To determine the amount of the redution, one has to solve the boundary-value problem. This tough elastiity problem is for professional elastitians. Look how ompliated the stress field must be near the rak. Griffith used the elastiity solution of Inglis, beause a rak is just a speial ase of an ellipse when b/ a 0. This part of the Griffith paper is diffiult to read, and is not very interesting. In the end he made small errors. An alternative approah is to invoke linearity and dimensional onsiderations. For a linearly elasti problem, the stress field is linearly proportional to the ied stress. The elasti energy per unit volume is proportional to /. The elasti energy in an infinite sheet is infinite. However, we are interested in the differene in elasti energy between the raked sheet and the unraked sheet. Note that the rak length a is the only length sale in the boundaryvalue problem. Consequently, the differene in elasti energy between the two sheets takes the form β a, where β is a numerial value. Thus, from very basi onsiderations, we get nearly everything exept for a pure number. This number must be determined by solving the elastiity boundary value problem. The solution turns out to be β = π. You an find the solution of the full problem in Timoshenko and Goodier. Relative to the unraked sheet, in the raked sheet the ombined surfae energy and elasti energy is U( a) =+ 4aγ π a. The rak length, a, is the thermodynami variable. The surfae energy density γ and the ied stress are taken to be onstant for the time being. As expeted, when the rak length inreases, the surfae energy inreases, but the elasti energy dereases. Critial rak size. Plot the free energy as a funtion of the rak length. The free energy first goes up, reahes a peak, and then goes down. Beause there is no minimum free energy, the rak annot reah equilibrium. The free energy reahes the peak at the rak length γ a* =. π Let us examine the physial signifiane of this partiular rak length. Let a be the length of the rak pre-existing in the sheet. Distinguish two situations. 5
6 Crak healing. If a< a*, the surfae energy prevails over the elasti energy. To redue the free energy, the rak length must derease. The rak does so by healing, i.e., forming atomi bonds one by one, like losing a zipper. In reality rak healing is not often observed. This is not beause the thermodynamis is wrong, but beause surfaes are not flat to the atomi dimension, so that atoms annot meet aross the gap and form bonds. Several examples show that rak healing happens. Adhesives. Soft material an heal readily by flows. Wafer bonding. If the surfaes are indeed made flat, they will join. Sintering. At elevated temperatures, atoms an diffuse, so that the two surfaes hange shape and an join. Crak growth. If a> a*, the elasti energy prevails over the surfae energy. To redue the free energy, the rak must grow. The rak does so by breaking atomi bonds one by one, like opening a zipper. This is the situation studied in this ourse. The Griffith experiments. The main predition of the Griffith theory an be written as γ a =. π He performed several experiments to asertain various parts of the equation. xperiment 1. Confirm that a = onstant, independent of the size of the rak. Start with several glass sheets (large spherial bulbs atually). Introdue a rak in eah sheet. Measure the strength of eah sheet. Two important points: (1) The rak introdued is in the mm to m range, muh longer than any natural flaws in the sheets, so that the natural flaws are negligible. In this way Griffith irumvented the unertainties assoiated with the natural flaws. () The introdued raks in different sheets have different lengths, and the measured strengths are also different. His data onfirmed that a = onstant. xperiment. Confirm that the onstant is indeed γ / π. Young s modulus for the glass used by Griffith was = 6 GPa. The surfae energy inferred from the measured breaking strength is γ = 1.75 J/m. Griffith needed an independent measurement of the surfae energy. He did the reeping fiber experiment. The value he obtained was γ = 0.54 J/m. The agreement was fair. xperiment 3. Measure strengths of glass fibers. For a fixed pre-existing rak size a, there is a ritial stress: γ =. π a 6
7 This is the stress needed to frature the sample. This relation shows that the frature strength depends on the rak size. Beause different samples have different rak sizes, the frature strength is not a material property. The measured strength has large satter. Take representative values γ = 1 J/m, 11 = 10 N/m, strength is 50 MPa. This orresponds to the experimental strength. a 6 = 10 m, the Sine the Griffith paper, the siene of frature was born. 7
Chapter 5 Single Phase Systems
Chapter 5 Single Phase Systems Chemial engineering alulations rely heavily on the availability of physial properties of materials. There are three ommon methods used to find these properties. These inlude
More informationTHE PERFORMANCE OF TRANSIT TIME FLOWMETERS IN HEATED GAS MIXTURES
Proeedings of FEDSM 98 998 ASME Fluids Engineering Division Summer Meeting June 2-25, 998 Washington DC FEDSM98-529 THE PERFORMANCE OF TRANSIT TIME FLOWMETERS IN HEATED GAS MIXTURES John D. Wright Proess
More informationIn order to be able to design beams, we need both moments and shears. 1. Moment a) From direct design method or equivalent frame method
BEAM DESIGN In order to be able to design beams, we need both moments and shears. 1. Moment a) From diret design method or equivalent frame method b) From loads applied diretly to beams inluding beam weight
More informationSHAFTS: TORSION LOADING AND DEFORMATION
ECURE hird Edition SHAFS: ORSION OADING AND DEFORMAION A. J. Clark Shool of Engineering Department of Civil and Environmental Engineering 6 Chapter 3.1-3.5 by Dr. Ibrahim A. Assakkaf SPRING 2003 ENES 220
More informationHEAT CONDUCTION. q A q T
HEAT CONDUCTION When a temperature gradient eist in a material, heat flows from the high temperature region to the low temperature region. The heat transfer mehanism is referred to as ondution and the
More informationImpact Simulation of Extreme Wind Generated Missiles on Radioactive Waste Storage Facilities
Impat Simulation of Extreme Wind Generated issiles on Radioative Waste Storage Failities G. Barbella Sogin S.p.A. Via Torino 6 00184 Rome (Italy), barbella@sogin.it Abstrat: The strutural design of temporary
More informationCapacity at Unsignalized Two-Stage Priority Intersections
Capaity at Unsignalized Two-Stage Priority Intersetions by Werner Brilon and Ning Wu Abstrat The subjet of this paper is the apaity of minor-street traffi movements aross major divided four-lane roadways
More informationSebastián Bravo López
Transfinite Turing mahines Sebastián Bravo López 1 Introdution With the rise of omputers with high omputational power the idea of developing more powerful models of omputation has appeared. Suppose that
More informationChapter 1 Microeconomics of Consumer Theory
Chapter 1 Miroeonomis of Consumer Theory The two broad ategories of deision-makers in an eonomy are onsumers and firms. Eah individual in eah of these groups makes its deisions in order to ahieve some
More informationEarthquake Loss for Reinforced Concrete Building Structures Before and After Fire damage
Earthquake Loss for Reinfored Conrete Building Strutures Before and After Fire damage Pai-Mei LIU, Yi-Hsuan Tu and Maw-Shyong SHEU 3 ABSTRACT The purpose of this paper is to propose a rational analytial
More information) ( )( ) ( ) ( )( ) ( ) ( ) (1)
OPEN CHANNEL FLOW Open hannel flow is haraterized by a surfae in ontat with a gas phase, allowing the fluid to take on shapes and undergo behavior that is impossible in a pipe or other filled onduit. Examples
More informationCHAPTER J DESIGN OF CONNECTIONS
J-1 CHAPTER J DESIGN OF CONNECTIONS INTRODUCTION Chapter J of the addresses the design and heking of onnetions. The hapter s primary fous is the design of welded and bolted onnetions. Design requirements
More informationChapter 1: Introduction
Chapter 1: Introdution 1.1 Pratial olumn base details in steel strutures 1.1.1 Pratial olumn base details Every struture must transfer vertial and lateral loads to the supports. In some ases, beams or
More information10.1 The Lorentz force law
Sott Hughes 10 Marh 2005 Massahusetts Institute of Tehnology Department of Physis 8.022 Spring 2004 Leture 10: Magneti fore; Magneti fields; Ampere s law 10.1 The Lorentz fore law Until now, we have been
More informationMeasurement of Powder Flow Properties that relate to Gravity Flow Behaviour through Industrial Processing Lines
Measurement of Powder Flow Properties that relate to Gravity Flow ehaviour through Industrial Proessing Lines A typial industrial powder proessing line will inlude several storage vessels (e.g. bins, bunkers,
More informationDSP-I DSP-I DSP-I DSP-I
DSP-I DSP-I DSP-I DSP-I Digital Signal Proessing I (8-79) Fall Semester, 005 IIR FILER DESIG EXAMPLE hese notes summarize the design proedure for IIR filters as disussed in lass on ovember. Introdution:
More information1.3 Complex Numbers; Quadratic Equations in the Complex Number System*
04 CHAPTER Equations and Inequalities Explaining Conepts: Disussion and Writing 7. Whih of the following pairs of equations are equivalent? Explain. x 2 9; x 3 (b) x 29; x 3 () x - 2x - 22 x - 2 2 ; x
More informationHow To Fator
CHAPTER hapter 4 > Make the Connetion 4 INTRODUCTION Developing seret odes is big business beause of the widespread use of omputers and the Internet. Corporations all over the world sell enryption systems
More informationIntelligent Measurement Processes in 3D Optical Metrology: Producing More Accurate Point Clouds
Intelligent Measurement Proesses in 3D Optial Metrology: Produing More Aurate Point Clouds Charles Mony, Ph.D. 1 President Creaform in. mony@reaform3d.om Daniel Brown, Eng. 1 Produt Manager Creaform in.
More information4.15 USING METEOSAT SECOND GENERATION HIGH RESOLUTION VISIBLE DATA FOR THE IMPOVEMENT OF THE RAPID DEVELOPPING THUNDERSTORM PRODUCT
4.15 USNG METEOSAT SECOND GENEATON HGH ESOLUTON VSBLE DATA FO THE MPOVEMENT OF THE APD DEVELOPPNG THUNDESTOM PODUCT Oleksiy Kryvobok * Ukrainian HydroMeteorologial nstitute Kyiv, Ukraine Stephane Senesi
More informationSuggested Answers, Problem Set 5 Health Economics
Suggested Answers, Problem Set 5 Health Eonomis Bill Evans Spring 2013 1. The graph is at the end of the handout. Fluoridated water strengthens teeth and redues inidene of avities. As a result, at all
More informationPhysical and mathematical postulates behind relativity
Physial and mathematial postulates behind relativity Tuomo Suntola Physis Foundations Soiety, Finland, www.physisfoundations.org In this presentation we look for answers to questions: What was the problem
More informationResidual strength evaluation by DBEM for a cracked lap joint
Residual strength evaluation b DBEM for a raked lap joint R. Citarella Department of Industrial Engineering, via Giovanni Paolo II, 132, Fisiano (SA), Universit of Salerno, Ital ritarella@unisa.it ABSTRACT.
More informationStatic Fairness Criteria in Telecommunications
Teknillinen Korkeakoulu ERIKOISTYÖ Teknillisen fysiikan koulutusohjelma 92002 Mat-208 Sovelletun matematiikan erikoistyöt Stati Fairness Criteria in Teleommuniations Vesa Timonen, e-mail: vesatimonen@hutfi
More informationWeighting Methods in Survey Sampling
Setion on Survey Researh Methods JSM 01 Weighting Methods in Survey Sampling Chiao-hih Chang Ferry Butar Butar Abstrat It is said that a well-designed survey an best prevent nonresponse. However, no matter
More informationEffects of Inter-Coaching Spacing on Aerodynamic Noise Generation Inside High-speed Trains
Effets of Inter-Coahing Spaing on Aerodynami Noise Generation Inside High-speed Trains 1 J. Ryu, 1 J. Park*, 2 C. Choi, 1 S. Song Hanyang University, Seoul, South Korea 1 ; Korea Railroad Researh Institute,
More informationElectrician'sMathand BasicElectricalFormulas
Eletriian'sMathand BasiEletrialFormulas MikeHoltEnterprises,In. 1.888.NEC.CODE www.mikeholt.om Introdution Introdution This PDF is a free resoure from Mike Holt Enterprises, In. It s Unit 1 from the Eletrial
More informationprotection p1ann1ng report
f1re~~ protetion p1ann1ng report BUILDING CONSTRUCTION INFORMATION FROM THE CONCRETE AND MASONRY INDUSTRIES Signifiane of Fire Ratings for Building Constrution NO. 3 OF A SERIES The use of fire-resistive
More informationA Three-Hybrid Treatment Method of the Compressor's Characteristic Line in Performance Prediction of Power Systems
A Three-Hybrid Treatment Method of the Compressor's Charateristi Line in Performane Predition of Power Systems A Three-Hybrid Treatment Method of the Compressor's Charateristi Line in Performane Predition
More information3 Game Theory: Basic Concepts
3 Game Theory: Basi Conepts Eah disipline of the soial sienes rules omfortably ithin its on hosen domain: : : so long as it stays largely oblivious of the others. Edard O. Wilson (1998):191 3.1 and and
More informationClassical Electromagnetic Doppler Effect Redefined. Copyright 2014 Joseph A. Rybczyk
Classial Eletromagneti Doppler Effet Redefined Copyright 04 Joseph A. Rybzyk Abstrat The lassial Doppler Effet formula for eletromagneti waves is redefined to agree with the fundamental sientifi priniples
More informationRelativistic Kinematics -a project in Analytical mechanics Karlstad University
Relativisti Kinematis -a projet in Analytial mehanis Karlstad University Carl Stigner 1th January 6 Abstrat The following text is a desription of some of the ontent in hapter 7 in the textbook Classial
More informationHeat Generation and Removal in Solid State Lasers
Chapter 1 Heat Generation and Removal in Solid State Lasers V. Ashoori, M. Shayganmanesh and S. Radmard Additional information is available at the end of the hapter http://dx.doi.org/10.577/63 1. Introdution
More informationHenley Business School at Univ of Reading. Pre-Experience Postgraduate Programmes Chartered Institute of Personnel and Development (CIPD)
MS in International Human Resoure Management For students entering in 2012/3 Awarding Institution: Teahing Institution: Relevant QAA subjet Benhmarking group(s): Faulty: Programme length: Date of speifiation:
More informationA Static Friction Model for Elastic-Plastic Contacting Rough Surfaces
Lior Kogut 1 Mem. ASME e-mail: mekogut@tx.tehnion.a.il Izhak Etsion Fellow ASME e-mail: etsion@tx.tehnion.a.il Dept. of Mehanial Engineering, Tehnion, Haifa 32000, Israel A Stati Frition Model for Elasti-Plasti
More informationHOW TO CALCULATE PRESSURE ANYWHERE IN A PUMP SYSTEM? Jacques Chaurette p. eng. www.lightmypump.com April 2003
HOW TO CALCULATE PRESSURE ANYWHERE IN A PUMP SYSTEM? Jaques Chaurette p. en. www.lihtmypump.om April 003 Synopsis Calulatin the total head of the pump is not the only task of the pump system desiner. Often
More informationLecture 24: Spinodal Decomposition: Part 3: kinetics of the
Leture 4: Spinodal Deoposition: Part 3: kinetis of the oposition flutuation Today s topis Diffusion kinetis of spinodal deoposition in ters of the onentration (oposition) flutuation as a funtion of tie:
More informationSUBSTRUCTURE EXAMPLE. Full Height Abutment on Spread Footing
SUBSTRUCTURE EXAMPLE Full Height Abutment on Spread Footing This example illustrates the design of a full height abutment on spread footings for a single span ast-in-plae post-tensioned onrete box girder
More informationHEAT EXCHANGERS-2. Associate Professor. IIT Delhi E-mail: prabal@mech.iitd.ac.in. P.Talukdar/ Mech-IITD
HEA EXHANGERS-2 Prabal alukdar Assoiate Professor Department of Mehanial Engineering II Delhi E-mail: prabal@meh.iitd.a.in Multipass and rossflow he subsripts 1 and 2 represent the inlet and outlet, respetively..
More informationIsaac Newton. Translated into English by
THE MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY (BOOK 1, SECTION 1) By Isaa Newton Translated into English by Andrew Motte Edited by David R. Wilkins 2002 NOTE ON THE TEXT Setion I in Book I of Isaa
More information10 UNSTEADY FLOW IN OPEN CHANNELS
0 UNTEY FLOW IN OEN CHNNEL 0. Introdution Unsteady flow in open hannels differs from that in losed onduits in that the eistene of a free surfae allows the flow ross-setion to freely hange, a fator whih
More informationChapter 6 A N ovel Solution Of Linear Congruenes Proeedings NCUR IX. (1995), Vol. II, pp. 708{712 Jerey F. Gold Department of Mathematis, Department of Physis University of Utah Salt Lake City, Utah 84112
More information5.2 The Master Theorem
170 CHAPTER 5. RECURSION AND RECURRENCES 5.2 The Master Theorem Master Theorem In the last setion, we saw three different kinds of behavior for reurrenes of the form at (n/2) + n These behaviors depended
More informationRISK-BASED IN SITU BIOREMEDIATION DESIGN JENNINGS BRYAN SMALLEY. A.B., Washington University, 1992 THESIS. Urbana, Illinois
RISK-BASED IN SITU BIOREMEDIATION DESIGN BY JENNINGS BRYAN SMALLEY A.B., Washington University, 1992 THESIS Submitted in partial fulfillment of the requirements for the degree of Master of Siene in Environmental
More informationRESEARCH SEMINAR IN INTERNATIONAL ECONOMICS. Discussion Paper No. 475. The Evolution and Utilization of the GATT/WTO Dispute Settlement Mechanism
RESEARCH SEMINAR IN INTERNATIONAL ECONOMICS Shool of Publi Poliy The University of Mihigan Ann Arbor, Mihigan 48109-1220 Disussion Paper No. 475 The Evolution and Utilization of the GATT/WTO Dispute Settlement
More informationAnother Look at Gaussian CGS Units
Another Look at Gaussian CGS Units or, Why CGS Units Make You Cool Prashanth S. Venkataram February 24, 202 Abstrat In this paper, I ompare the merits of Gaussian CGS and SI units in a variety of different
More informationProcurement auctions are sometimes plagued with a chosen supplier s failing to accomplish a project successfully.
Deision Analysis Vol. 7, No. 1, Marh 2010, pp. 23 39 issn 1545-8490 eissn 1545-8504 10 0701 0023 informs doi 10.1287/dea.1090.0155 2010 INFORMS Managing Projet Failure Risk Through Contingent Contrats
More informationOptimal Health Insurance for Multiple Goods and Time Periods
Preliminary draft for review only 0R.P. Ellis, S. Jiang, and W.G.Manning MultipleGood_ 00630.dox June 30, 0 Optimal Health Insurane for Multiple Goods and Time Periods Randall P. Ellis a,, Shenyi Jiang
More informationIntuitive Guide to Principles of Communications By Charan Langton www.complextoreal.com
Intuitive Guide to Priniples of Communiations By Charan Langton www.omplextoreal.om Understanding Frequeny Modulation (FM), Frequeny Shift Keying (FSK), Sunde s FSK and MSK and some more The proess of
More informationProgramming Basics - FORTRAN 77 http://www.physics.nau.edu/~bowman/phy520/f77tutor/tutorial_77.html
CWCS Workshop May 2005 Programming Basis - FORTRAN 77 http://www.physis.nau.edu/~bowman/phy520/f77tutor/tutorial_77.html Program Organization A FORTRAN program is just a sequene of lines of plain text.
More informationTHE EFFECT OF WATER VAPOR ON COUNTERFLOW DIFFUSION FLAMES
THE EFFECT OF WATER VAPOR ON COUNTERFLOW DIFFUSION FLAMES by Jaeil Suh and Arvind Atreya Combustion and Heat Tkansfer Laboratory Department of Mehanial Engineering and Applied Mehanis The University of
More informationExplanatory Examples on Indian Seismic Code IS 1893 (Part I)
Doument No. :: IITK-GSDMA-EQ1-V.0 inal Report :: A - Earthquake Codes IITK-GSDMA Projet on Building Codes Explanatory Examples on Indian Seismi Code IS 1893 (Part I) by Dr. Sudhir K Jain Department of
More informationRetirement Option Election Form with Partial Lump Sum Payment
Offie of the New York State Comptroller New York State and Loal Retirement System Employees Retirement System Polie and Fire Retirement System 110 State Street, Albany, New York 12244-0001 Retirement Option
More informationImproved SOM-Based High-Dimensional Data Visualization Algorithm
Computer and Information Siene; Vol. 5, No. 4; 2012 ISSN 1913-8989 E-ISSN 1913-8997 Published by Canadian Center of Siene and Eduation Improved SOM-Based High-Dimensional Data Visualization Algorithm Wang
More informationMasters Thesis- Criticality Alarm System Design Guide with Accompanying Alarm System Development for the Radioisotope Production L
PNNL-18348 Prepared for the U.S. Department of Energy under Contrat DE-AC05-76RL01830 Masters Thesis- Critiality Alarm System Design Guide with Aompanying Alarm System Development for the Radioisotope
More informationAgile ALM White Paper: Redefining ALM with Five Key Practices
Agile ALM White Paper: Redefining ALM with Five Key Praties by Ethan Teng, Cyndi Mithell and Chad Wathington 2011 ThoughtWorks ln. All rights reserved www.studios.thoughtworks.om Introdution The pervasiveness
More informationFixed-income Securities Lecture 2: Basic Terminology and Concepts. Present value (fixed interest rate) Present value (fixed interest rate): the arb
Fixed-inome Seurities Leture 2: Basi Terminology and Conepts Philip H. Dybvig Washington University in Saint Louis Various interest rates Present value (PV) and arbitrage Forward and spot interest rates
More informationComputer Networks Framing
Computer Networks Framing Saad Mneimneh Computer Siene Hunter College of CUNY New York Introdution Who framed Roger rabbit? A detetive, a woman, and a rabbit in a network of trouble We will skip the physial
More informationA Holistic Method for Selecting Web Services in Design of Composite Applications
A Holisti Method for Seleting Web Servies in Design of Composite Appliations Mārtiņš Bonders, Jānis Grabis Institute of Information Tehnology, Riga Tehnial University, 1 Kalu Street, Riga, LV 1658, Latvia,
More informationPolyethylene glycol (PEG) is a hydrophilic nonionic polymer
Effet of polyethylene glyol on the liquid liquid phase transition in aqueous protein solutions Onofrio Annunziata, Neer Asherie, Aleksey Lomakin, Jayanti Pande, Olutayo Ogun, and George B. Benedek* Department
More informationSoft-Edge Flip-flops for Improved Timing Yield: Design and Optimization
Soft-Edge Flip-flops for Improved Timing Yield: Design and Optimization Abstrat Parameter variations ause high yield losses due to their large impat on iruit delay. In this paper, we propose the use of
More informationChannel Assignment Strategies for Cellular Phone Systems
Channel Assignment Strategies for Cellular Phone Systems Wei Liu Yiping Han Hang Yu Zhejiang University Hangzhou, P. R. China Contat: wliu5@ie.uhk.edu.hk 000 Mathematial Contest in Modeling (MCM) Meritorious
More informationThe Reduced van der Waals Equation of State
The Redued van der Waals Equation of State The van der Waals equation of state is na + ( V nb) n (1) V where n is the mole number, a and b are onstants harateristi of a artiular gas, and R the gas onstant
More informationTrade Information, Not Spectrum: A Novel TV White Space Information Market Model
Trade Information, Not Spetrum: A Novel TV White Spae Information Market Model Yuan Luo, Lin Gao, and Jianwei Huang 1 Abstrat In this paper, we propose a novel information market for TV white spae networks,
More informationPrice-based versus quantity-based approaches for stimulating the development of renewable electricity: new insights in an old debate
Prie-based versus -based approahes for stimulating the development of renewable eletriity: new insights in an old debate uthors: Dominique FINON, Philippe MENNTEU, Marie-Laure LMY, Institut d Eonomie et
More informationBEARING CAPACITY OF SOIL
BEARING CAPACITY OF SOIL Dr. S. K. Prasad Professor of Civil Engineering S. J. College of Engineering, Mysore 7.0 Syllabus. Definition of ultimate, net and safe bearing apaities, Allowable bearing pressure
More informationInternational Journal of Supply and Operations Management. Mathematical modeling for EOQ inventory system with advance payment and fuzzy Parameters
nternational Journal of Supply and Operations Management JSOM November 0, Volume, ssue 3, pp. 60-78 SSN-Print: 383-359 SSN-Online: 383-55 www.ijsom.om Mathematial modeling for EOQ inventory system with
More informationPerformance Analysis of IEEE 802.11 in Multi-hop Wireless Networks
Performane Analysis of IEEE 80.11 in Multi-hop Wireless Networks Lan Tien Nguyen 1, Razvan Beuran,1, Yoihi Shinoda 1, 1 Japan Advaned Institute of Siene and Tehnology, 1-1 Asahidai, Nomi, Ishikawa, 93-19
More informationRobust Classification and Tracking of Vehicles in Traffic Video Streams
Proeedings of the IEEE ITSC 2006 2006 IEEE Intelligent Transportation Systems Conferene Toronto, Canada, September 17-20, 2006 TC1.4 Robust Classifiation and Traking of Vehiles in Traffi Video Streams
More informationFOOD FOR THOUGHT Topical Insights from our Subject Matter Experts
FOOD FOR THOUGHT Topial Insights from our Sujet Matter Experts DEGREE OF DIFFERENCE TESTING: AN ALTERNATIVE TO TRADITIONAL APPROACHES The NFL White Paper Series Volume 14, June 2014 Overview Differene
More information1 CHAPTER 6 PROPERTIES OF GASES
CHAPTER 6 PROPERTIES OF GASES 6. The Ideal Gas Equation In 660, the Honorable Robert Boyle, Father of Chemistry and seventh son of the Earl of Cork, and one of the founders of the Royal Soiety of London,
More informationAUDITING COST OVERRUN CLAIMS *
AUDITING COST OVERRUN CLAIMS * David Pérez-Castrillo # University of Copenhagen & Universitat Autònoma de Barelona Niolas Riedinger ENSAE, Paris Abstrat: We onsider a ost-reimbursement or a ost-sharing
More informationMotorcycle Accident Reconstruction Part I - Physical Models
Motoryle Aident Reonstrution Part I - Physial Models Oren Masory Wade Bartlett Bill Wright Dept. of Oean & Mehanial Engr. Mehanial Forensis Engineering Servies IPTM Florida Atlanti University 179 Cross
More informationarxiv:astro-ph/0304006v2 10 Jun 2003 Theory Group, MS 50A-5101 Lawrence Berkeley National Laboratory One Cyclotron Road Berkeley, CA 94720 USA
LBNL-52402 Marh 2003 On the Speed of Gravity and the v/ Corretions to the Shapiro Time Delay Stuart Samuel 1 arxiv:astro-ph/0304006v2 10 Jun 2003 Theory Group, MS 50A-5101 Lawrene Berkeley National Laboratory
More informationAn integrated optimization model of a Closed- Loop Supply Chain under uncertainty
ISSN 1816-6075 (Print), 1818-0523 (Online) Journal of System and Management Sienes Vol. 2 (2012) No. 3, pp. 9-17 An integrated optimization model of a Closed- Loop Supply Chain under unertainty Xiaoxia
More informationState of Maryland Participation Agreement for Pre-Tax and Roth Retirement Savings Accounts
State of Maryland Partiipation Agreement for Pre-Tax and Roth Retirement Savings Aounts DC-4531 (08/2015) For help, please all 1-800-966-6355 www.marylandd.om 1 Things to Remember Complete all of the setions
More informationOptimal Sales Force Compensation
Optimal Sales Fore Compensation Matthias Kräkel Anja Shöttner Abstrat We analyze a dynami moral-hazard model to derive optimal sales fore ompensation plans without imposing any ad ho restritions on the
More informationJournal of Colloid and Interface Science
Journal of Colloid and Interfae Siene 338 (9) 93 Contents lists available at SieneDiret Journal of Colloid and Interfae Siene www.elsevier.om/loate/jis Contat angle of a emisperial bubble: An analytial
More informationDeadline-based Escalation in Process-Aware Information Systems
Deadline-based Esalation in Proess-Aware Information Systems Wil M.P. van der Aalst 1,2, Mihael Rosemann 2, Marlon Dumas 2 1 Department of Tehnology Management Eindhoven University of Tehnology, The Netherlands
More informationWATER CLOSET SUPPORTS TECHNICAL DATA
WATER CLOSET SUPPORTS TECHNICAL DATA Smith engineers have developed an unusually omplete line of fixture supports for mounting all types of "off the floor" fixtures. Supports have been designed for water
More informationCombining refractive and topographic data in corneal refractive surgery for astigmatism
Combining refrative and topographi data in orneal refrative surgery for astigmatism A new method based on polar value analysis and mathematial optimization Kristian Næser Department of Ophthalmology, Randers
More informationAvailability, Reliability, Maintainability, and Capability
Availability, Reliability, Maintainability, and Capability H. Paul Barringer, P.E. Barringer & Assoiates, In. Humble, TX Triplex Chapter Of The Vibrations Institute Hilton Hotel Beaumont, Texas February
More informationINCOME TAX WITHHOLDING GUIDE FOR EMPLOYERS
Virginia Department of Taxation INCOME TAX WITHHOLDING GUIDE FOR EMPLOYERS www.tax.virginia.gov 2614086 Rev. 07/14 * Table of Contents Introdution... 1 Important... 1 Where to Get Assistane... 1 Online
More informationFig. 1.1 Rectangular foundation plan.
Footings Example 1 Design of a square spread footing of a seven-story uilding Design and detail a typial square spread footing of a six ay y five ay seven-story uilding, founded on stiff soil, supporting
More informationSupply chain coordination; A Game Theory approach
aepted for publiation in the journal "Engineering Appliations of Artifiial Intelligene" 2008 upply hain oordination; A Game Theory approah Jean-Claude Hennet x and Yasemin Arda xx x LI CNR-UMR 668 Université
More informationStructural Integrity Analysis
Structural Integrity Analysis 1. STRESS CONCENTRATION Igor Kokcharov 1.1 STRESSES AND CONCENTRATORS 1.1.1 Stress An applied external force F causes inner forces in the carrying structure. Inner forces
More informationJournal of Engineering Science and Technology Review 6 (5) (2013) 143-148. Research Article
Jestr Journal o Engineering Siene and Tehnology Review 6 (5) (13) 143-148 Researh Artile JOURNAL OF Engineering Siene and Tehnology Review www.jestr.org Numerial Analyses on Seismi Behaviour o Conrete-illed
More informationMechanics of the tapered interference fit in dental implants
ARTICLE IN PRESS Journal of Biomehanis 36 (2003) 1649 1658 Mehanis of the tapered interferene fit in dental implants Din@er Bozkaya, Sinan M.uft.u* Department of Mehanial Engineering, Northeastern University,
More informationTHERMAL TO MECHANICAL ENERGY CONVERSION: ENGINES AND REQUIREMENTS Vol. I - Thermodynamic Cycles of Reciprocating and Rotary Engines - R.S.
THERMAL TO MECHANICAL ENERGY CONVERSION: ENGINES AND REQUIREMENTS Vol. I - Thermodynami Cyles of Reiproating and Rotary Engines - R.S.Kavtaradze THERMODYNAMIC CYCLES OF RECIPROCATING AND ROTARY ENGINES
More informationINCOME TAX WITHHOLDING GUIDE FOR EMPLOYERS
Virginia Department of Taxation INCOME TAX WITHHOLDING GUIDE FOR EMPLOYERS www.tax.virginia.gov 2614086 Rev. 01/16 Table of Contents Introdution... 1 Important... 1 Where to Get Assistane... 1 Online File
More informationConversion of short optical pulses to terahertz radiation in a nonlinear medium: Experiment and theory
PHYSICAL REVIEW B 76, 35114 007 Conversion of short optial pulses to terahertz radiation in a nonlinear medium: Experiment and theory N. N. Zinov ev* Department of Physis, University of Durham, Durham
More informationHenley Business School at Univ of Reading. Chartered Institute of Personnel and Development (CIPD)
MS in International Human Resoure Management (full-time) For students entering in 2015/6 Awarding Institution: Teahing Institution: Relevant QAA subjet Benhmarking group(s): Faulty: Programme length: Date
More informationVOLUME 13, ARTICLE 5, PAGES 117-142 PUBLISHED 05 OCTOBER 2005 DOI: 10.4054/DemRes.2005.13.
Demographi Researh a free, expedited, online journal of peer-reviewed researh and ommentary in the population sienes published by the Max Plank Institute for Demographi Researh Konrad-Zuse Str. 1, D-157
More informationCustomer Efficiency, Channel Usage and Firm Performance in Retail Banking
Customer Effiieny, Channel Usage and Firm Performane in Retail Banking Mei Xue Operations and Strategi Management Department The Wallae E. Carroll Shool of Management Boston College 350 Fulton Hall, 140
More information1. Introduction. Three Different Behaviors of Liquid Water Path of Water Clouds in Aerosol-Cloud Interactions
Three Different Behaviors of Liquid Water Path of Water Clouds in Aerosol-Cloud Interations Qingyuan Han 1, William B. Rossow 2, Jian Zeng 1, and Ronald Welh 1 1 University of Alabama in Huntsville Huntsville,
More informationThe analysis of brushing tool characteristics
ARCHIVES OF CIVIL AND MECHANICAL ENGINEERING Vol. IV 004 No. 4 The analysis of rushing tool harateristis Kiele University of Tehnology, al. Tysiąleia P. P. 7, 5-34 Kiele In this paper, an analytial proedure
More informationDraft Notes ME 608 Numerical Methods in Heat, Mass, and Momentum Transfer
Draft Notes ME 608 Numerial Methods in Heat, Mass, and Momentum Transfer Instrutor: Jayathi Y. Murthy Shool of Mehanial Engineering Purdue University Spring 2002 1998 J.Y. Murthy and S.R. Mathur. All Rights
More informationi e AT 21 of 2006 EMPLOYMENT ACT 2006
i e AT 21 of 2006 EMPLOYMENT ACT 2006 Employment At 2006 Index i e EMPLOYMENT ACT 2006 Index Setion Page PART I DISCRIMINATION AT RECRUITMENT ON TRADE UNION GROUNDS 9 1 Refusal of employment on grounds
More informationGranular Problem Solving and Software Engineering
Granular Problem Solving and Software Engineering Haibin Zhu, Senior Member, IEEE Department of Computer Siene and Mathematis, Nipissing University, 100 College Drive, North Bay, Ontario, P1B 8L7, Canada
More informationFinite Element Modelling of Vibro-Acoustic Systems for Active Noise Reduction
ECHNISCHE MECHANIK, Band 25, Heft 3-4, (25), 24-247 Manuskripteingang:. Dezember 25 Finite Element Modelling of Vibro-Aousti Systems for Ative Noise Redution J. Lefèvre, U. Gabbert Over the past years
More information