Fundamentals of Finite Elements. Mehrdad Negahban. W311 Nebraska Hall Department of Engineering Mechanics University of Nebraska-Lincoln
|
|
- Herbert Walters
- 5 years ago
- Views:
Transcription
1 EGM 98 unamentals f nte Elements Mehra egahban W ebraska Hall Deartment f Engneerng Mechancs Unversty f ebraska-lncln Phne: E-mal: mnegahban@unl.eu
2 Curse escrtn Objectve: Slutn f artal fferental euatns f engneerng mrtance usng EM. Emhaszng the smlarty f the evelment. Develment f cmmn mathematcal an numercal tls. Usng cnsstent an rbust meths. Develng an bject rente rgrammng structure fr EM. Aressng sme avance tcs. 4 Elements 7x77 r 9x99 e Elements 7x7 Element: 6 La stes 7 ewtn Iteratns 9x9 Element: 4 La stes 6 ewtn Iteratns u A v B u w v A B
3 Tcs Curse Object rente rgrammng n EM W Weghte Resual lmeths Lnear Prblems scalar an vectr fels mult hyscs Heat transfer elastcty an thermelastcty Cnstrants n-lnear Prblems nlnear elastcty large efrmatn Intal-Value Prblems Transent thermal analyss Vbratn f beams Bars Plates an Shells Knematcally efne cntnua umercal Imlementatn
4
5 Shells Peanut Sunflwer Eggs Slanum cnereum germnatng Ccnut
6 Shells Ale Re bl cell Cell structure: Prcaryte Crnary artery
7 Shells Plant cells Plant cell wall Plar leaf cell Tallw tree Chlrlast: ste f htsynthess n lant cells
8 Tycal EM rmulatn Shell Knematcs Cnsttutve Characterstcs nte Element rmulatn nte Element Arxmatn Intal an Bunary Cntns umercal Slutn
9 nte Element rmulatn Shell Knematcs nte Element Arxmatn Varatnal rmulatn EM rmulatn Cnsttutve Characterstcs Intal an Bunary Cntns umercal Slutn
10 Shell Knematcs t ρ ζ Q ρ P Drectr Curvlnear Crnate t P Q M -surface s x O Reference rame
11 Shell Knematcs Ressner/Mnln Shell + s s x ς ς j j g g g + + s x g ς ς ς ρ ζ Q ρ P ρ P s x O ς ς
12 Shell Knematcs Makng the mangs nt materal mangs: X x JJ Current cnfguratn Γ Intal cnfguratn D Ω Γ Ω S J X s J x J g e J G e e e e O
13 Shell Knematcs Defrmatn Graent: Dslacement Graent: JJ H I Intal cnfguratn X Current cnfguratn x JJ Strans: D ε H + H T G R I T G L I T J X e e e S O s J x
14 Isarametrc shell x s + ς Current Cnfguratn nne s s 5 nne nne ς ς Isarametrc -D 5 Extrue -D 4 8 s O e e e e e e
15 Isarametrc shell X S + ς D Intal Cnfguratn nne S S nne D D nne ς ς 4 5 D 8 Isarametrc -D Extrue -D 5 e S e e e e e O
16 ρ s + e x J e X J Jacbans ζ s x + ρ s x + Δ Δ D S s s ρ ζ s x + ζ + s x ζ ζ ζ Δ Δ D x s ζ ζ + + Thckness unknwns + nf f a ζ ζ ζ + D S X Thckness base functns ζ ζ + + D D ζ
17 Thckness nterlatn ζ umber f nterlatn functns nf + ζ ζ a f f Legenre lynmals: Materal surface P + P s f P + P s even One term arxmatn: Δζ a f Δζ 0 M-surface
18 EM frmulatn Resual fr EM: mnal stress T J T T R u t Γ X u : T Ω + ρu bω ρu aω Γ t T T t T Ω Intal cnfguratn Γ D Ω X x JJ Ω Current cnfguratn al unknwns: Ω U j Δ s j j U j+ Δ j j U j+ 6 a j... nf j e e e S O J X s J x
19 nlnear elastcty Defrmatn graent: general new new l + & Δt & l + U j Δ t U j l + U j Δ U j U j JJ U g U j U j j J U e J j J g e U g j x x J mnal stress: nnlnear elastc T T new new T T l l + T& Δt + & T : Δt T l + T : U j ΔU j rm shell knematcs T T + E : new l Materal secfc U U Δ j j U j Δ s j j U j+ Δ j j U j+ 6 a j j... nf Tangent mulus f nmnal stress: E T
20 nlnear elastcty Tw arameter nnlnear-elastc materal mel: mnal stress: Tangent mulus: Materal arameters: Shear an bulk mulus matche t lnear resnse
21 Examles frm nlnear Elastcty Cantlevere beam wth strbute en la 6 E. 0 ν 0.0 max h b 4 La stes 4 ewtn teratns L u t w t w v u
22 Examles frmnlnear Elastcty Cantlevere beam wth strbute en mment Sngle 9x-ne element 6 lang stes 75 ewtn teratns M E. 0 ν 0.0 L.0 h 0. b.0 6 M M 60 4 M M 60 w t Theretcal M M 60 u t w v M M 60 u
23 Examles frm nlnear Elastcty Cantlevere beam wth strbute en mment a -4x-60-6LIC-87I b -4x-60-6LIC-47I c 4-4x-60-6LIC-47I -5x-60-6LIC-50I e -5x-60-6LIC-50I f -5x-540-4LIC-4I g -6x-540-4LIC-I h -6x-70 -LIC-09I -7x-70 -LIC-9I
24 Examles frm nlnear Elastcty Bucklng n cmressn f a clumn u t w v u w t E.0 0 ν L 0.5 b h Crtcal bucklng la L
25 Examles frm nlnear Elastcty Transverse lang f an annular rng u w v R R A B A E 0 R 6.0 h 0.0 max ν 0.0 R 0.0 A B wa wb La Stes 4 ewtn stes 5 Elements 7x7-es er element B
26 Examles frm nlnear Elastcty Pnchng f hemshercal shell wth hle 4 Elements 7x7 r 9x9 e Elements 7x7 Element: 6 La stes 7 ewtn Iteratns 9x9 Element: 4 La stes 6 ewtn Iteratns u A v B z Hle rc Symmetrc x Symmetr A R 0 h E 6.85x0 7 ν 0. Hle 8 B y u w v A B
27 Examles frm nlnear Elastcty Pnchng f cylnrcal shell wth free ens 40 La Stes 74 ewtn stes 4 Elements 9x9-es er element w A v C v B A v B v C B w 6 v E ν 0.5 max u L 0.5 R 4.95 h R C L
28 Examles frm nlnear Elastcty Pnt la n a hnge cylnrcal rf R 540 L 54 θ 0. ra E 0.75 ν 0. Hnge ree ree Hnge L R θ
29 ur arameter elastc mel τ T κ G tanh I G τ G I + + B tr B I 5/ 5/ J G J I τ J G τ G G τ κ J et tr C J T C I * G γ
30 Large efrmatn elastc-lastc mel Cauchy stress: e e e tr B T κ J I + G B I 5 e J Over-stress: ΔT Yel functn: e e b T b 0 T T κ G E ν E + ν f : ΔS σ y ΔS ΔS Pwer-law harenng rule: ΔS ΔT tr ΔT I σ + n y σ y a & ΔT T : L
31 Tw mels n tensn ur Parameter Mel Large Defrmatn Elastc-Plastc Mel 000 Stress arameter Elastc-lastc κ G τ G κ G σ y a 0.6 n Stran
32 Beam n cmressn 000 ur Parameter Brck ur Parameter Shell 0000 La C Cmress n u Large Defrmatn Elastc-Plastc Brck L0 b h Dslacement
33 Beam n tensn La ur Parameter Brck ur Parameter Shell Large Defrmatn Elastc-Plastc Brck u L0 b h Dslacement
34 Cantlevere beam v u ur Parameter Brck ur arameter brck 00 Large Defrmatn Elastc-Plastc Brck Large Defrmatn Elastc-Plastc Brck ur Parameter Shell 000 ur Parameter Shell La u v L0 b h Dslacement
35 Mult-scale analyss Each ntegratn nt can have an RVE
36 abro Questns?
CTN 2/23/16. EE 247B/ME 218: Introduction to MEMS Design Lecture 11m2: Mechanics of Materials. Copyright 2016 Regents of the University of California
Vlume Change fr a Unaxal Stress Istrpc lastcty n 3D Istrpc = same n all drectns The cmplete stress-stran relatns fr an strpc elastc Stresses actng n a dfferental vlume element sld n 3D: (.e., a generalzed
More informationelement k Using FEM to Solve Truss Problems
sng EM t Slve Truss Prblems A truss s an engneerng structure cmpsed straght members, a certan materal, that are tpcall pn-ned at ther ends. Such members are als called tw-rce members snce the can nl transmt
More informationA Note on the Linear Programming Sensitivity. Analysis of Specification Constraints. in Blending Problems
Aled Mathematcal Scences, Vl. 2, 2008, n. 5, 241-248 A Nte n the Lnear Prgrammng Senstvty Analyss f Secfcatn Cnstrants n Blendng Prblems Umt Anc Callway Schl f Busness and Accuntancy Wae Frest Unversty,
More information1.050 Content overview Engineering Mechanics I Content overview. Outline and goals. Lecture 28
.5 Content overvew.5 Engneerng Mechancs I Lecture 8 Introucton: Energy bouns n lnear elastcty (cont I. Dmensonal analyss. On monsters, mce an mushrooms Lectures -. Smlarty relatons: Important engneerng
More informationPHY2053 Summer 2012 Exam 2 Solutions N F o f k
HY0 Suer 0 Ea Slutns. he ree-bdy dagra r the blck s N F 7 k F g Usng Newtn s secnd law r the -cnents F a F F cs7 k 0 k F F cs7 (0 N ( Ncs7 N he wrk dne by knetc rctn k r csθ ( N(6 cs80 0 N. Mechancal energy
More informationMode-Frequency Analysis of Laminated Spherical Shell
Mde-Frequency Analyss f Lamnated Sphercal Shell Umut Tpal Department f Cvl Engneerng Karadenz Techncal Unversty 080, Trabzn, Turkey umut@ktu.edu.tr Sessn ENG P50-00 Abstract Ths paper deals wth mde-frequency
More informationIn this section is given an overview of the common elasticity models.
Secton 4.1 4.1 Elastc Solds In ths secton s gven an overvew of the common elastcty models. 4.1.1 The Lnear Elastc Sold The classcal Lnear Elastc model, or Hooean model, has the followng lnear relatonshp
More informationExploiting vector space properties for the global optimization of process networks
Exptng vectr space prpertes fr the gbal ptmzatn f prcess netwrks Juan ab Ruz Ignac Grssmann Enterprse Wde Optmzatn Meetng March 00 Mtvatn - The ptmzatn f prcess netwrks s ne f the mst frequent prblems
More informationIGEE 401 Power Electronic Systems. Solution to Midterm Examination Fall 2004
Jós, G GEE 401 wer Electrnc Systems Slutn t Mdterm Examnatn Fall 2004 Specal nstructns: - Duratn: 75 mnutes. - Materal allwed: a crb sheet (duble sded 8.5 x 11), calculatr. - Attempt all questns. Make
More informationSIMULATION OF THREE PHASE THREE LEG TRANSFORMER BEHAVIOR UNDER DIFFERENT VOLTAGE SAG TYPES
SIMULATION OF THREE PHASE THREE LEG TRANSFORMER BEHAVIOR UNDER DIFFERENT VOLTAGE SAG TYPES Mhammadreza Dlatan Alreza Jallan Department f Electrcal Engneerng, Iran Unversty f scence & Technlgy (IUST) e-mal:
More informationFaculty of Engineering
Faculty f Engneerng DEPARTMENT f ELECTRICAL AND ELECTRONIC ENGINEERING EEE 223 Crcut Thery I Instructrs: M. K. Uygurğlu E. Erdl Fnal EXAMINATION June 20, 2003 Duratn : 120 mnutes Number f Prblems: 6 Gd
More informationSpring 2002 Lecture #17
1443-51 Sprng 22 Lecture #17 r. Jaehn Yu 1. Cndtns fr Equlbrum 2. Center f Gravty 3. Elastc Prpertes f Slds Yung s dulus Shear dulus ulk dulus Tday s Hmewrk Assgnment s the Hmewrk #8!!! 2 nd term eam n
More information4DVAR, according to the name, is a four-dimensional variational method.
4D-Varatnal Data Assmlatn (4D-Var) 4DVAR, accrdng t the name, s a fur-dmensnal varatnal methd. 4D-Var s actually a smple generalzatn f 3D-Var fr bservatns that are dstrbuted n tme. he equatns are the same,
More informationLucas Imperfect Information Model
Lucas Imerfect Infrmatn Mdel 93 Lucas Imerfect Infrmatn Mdel The Lucas mdel was the frst f the mdern, mcrfundatns mdels f aggregate suly and macrecnmcs It bult drectly n the Fredman-Phels analyss f the
More informationTRANSPORT MOMENTS. beyond the leading order. arxiv: Jack Kuipers. University of Regensburg. with. Gregory Berkolaiko.
TRANSPORT MOMENTS beynd the leadng rder arxv:1012.3526 Jack Kupers Unversty f Regensburg wth Gregry Berklak Texas A&M Transprt mments p.1/24 OUTLINE Open systems mments crrelatn functns semclasscal expressn
More informationWYSE Academic Challenge 2014 Sectional Physics Exam SOLUTION SET. [ F][ d] [ t] [ E]
WYSE Aaem Challenge 0 Setnal hss Exam SOLUTION SET. Crret answer: E Unts Trque / unts pwer: [ r ][ ] [ E] [ t] [ r ][ ][ t] [ E] [ r ][ ][ t] [ ][ ] [ r ][ t] [ ] m s m s. Crret answer: D The net external
More informationA New Method for Solving Integer Linear. Programming Problems with Fuzzy Variables
Appled Mathematcal Scences, Vl. 4, 00, n. 0, 997-004 A New Methd fr Slvng Integer Lnear Prgrammng Prblems wth Fuzzy Varables P. Pandan and M. Jayalakshm Department f Mathematcs, Schl f Advanced Scences,
More informationAnalytical Modeling of Natural Convection in Horizontal Annuli
Analytcal Mdelng f Natural Cnvectn n Hrzntal Annul Peter Teertstra, M. Mchael Yvanvch, J. Rchard Culham Mcrelectrncs Heat Transfer Labratry Department f Mechancal Engneerng Unversty f Waterl Waterl, Ontar,
More informationLecture # 02: Pressure measurements and Measurement Uncertainties
AerE 3L & AerE343L Lecture Notes Lecture # 0: Pressure measurements and Measurement Uncertantes Dr. Hu H Hu Deartment of Aerosace Engneerng Iowa State Unversty Ames, Iowa 500, U.S.A Mechancal Pressure
More informationCOMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD
COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,
More informationConduction Heat Transfer
Cnductn Heat Transfer Practce prblems A steel ppe f cnductvty 5 W/m-K has nsde and utsde surface temperature f C and 6 C respectvely Fnd the heat flw rate per unt ppe length and flux per unt nsde and per
More informationDesign of Analog Integrated Circuits
Desgn f Analg Integrated Crcuts I. Amplfers Desgn f Analg Integrated Crcuts Fall 2012, Dr. Guxng Wang 1 Oerew Basc MOS amplfer structures Cmmn-Surce Amplfer Surce Fllwer Cmmn-Gate Amplfer Desgn f Analg
More informationCHAPTER 11. Solutions for Exercises. (b) An inverting amplifier has negative gain. Thus L
CHPTE Slutn fr Exerce E. (a nnnertng amplfer ha pte gan. Thu ( t ( t 50 ( t 5.0 n(000πt (b n nertng amplfer ha negate gan. Thu ( t ( t 50 ( t 5.0 n(000πt E. V V 75 500 + 5+ 75 c 75 V 000 75 500 V + + 500
More informationPlasticity of Metals Subjected to Cyclic and Asymmetric Loads: Modeling of Uniaxial and Multiaxial Behavior
Plastcty of Metals Subjecte to Cyclc an Asymmetrc Loas: Moelng of Unaxal an Multaxal Behavor Dr Kyrakos I. Kourouss Captan, Hellenc Ar Force 1/16 Abstract Strength analyss of materals submtte to cyclc
More informationA/2 l,k. Problem 1 STRATEGY. KNOWN Resistance of a complete spherical shell: r rk. Inner and outer radii
Prblem 1 STRATEGY KNOWN Resstance f a cmplete sphercal shell: R ( r r / (4 π r rk sphere Inner an uter ra r an r, SOLUTION Part 1: Resstance f a hemsphercal shell: T calculate the resstance f the hemsphere,
More informationTHE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS OF A TELESCOPIC HYDRAULIC CYLINDER SUBJECTED TO EULER S LOAD
Journal of Appled Mathematcs and Computatonal Mechancs 7, 6(3), 7- www.amcm.pcz.pl p-issn 99-9965 DOI:.75/jamcm.7.3. e-issn 353-588 THE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS
More informationStability of Steel Columns with Non-Uniform Cross-Sections
The Open Cnstructn and Buldng Technlgy Jurnal, 1, 6, 1-7 1 Stablty f Steel Clumns wth n-unfrm Crss-Sectns Open Access Thedre G. Knstantakpuls, Ianns G. Raftyanns* and Gerge T. Mchaltss Department f Cvl
More informationA nonlinear field theory of deformable dielectrics
A nonlnear feld theory of deformable delectrcs Zhgang Suo Harvard Unversty ork wth X. Zhao,. Greene, e Hong, J. Zhou Talk n Sesson --, 0:00 am - :00 pm, ednesday, 6 June 007, McMat 007, Austn, Texas Sldes
More informationCIRCLE YOUR DIVISION: Div. 1 (9:30 am) Div. 2 (11:30 am) Div. 3 (2:30 pm) Prof. Ruan Prof. Naik Mr. Singh
Frst CIRCLE YOUR DIVISION: Dv. 1 (9:30 am) Dv. (11:30 am) Dv. 3 (:30 m) Prf. Ruan Prf. Na Mr. Sngh Schl f Mechancal Engneerng Purdue Unversty ME315 Heat and Mass ransfer Eam #3 Wednesday Nvember 17 010
More informationCOLUMN GENERATION HEURISTICS FOR SPLIT PICKUP AND DELIVERY VEHICLE ROUTING PROBLEM FOR INTERNATIONAL CRUDE OIL TRANSPORTATION
12/03/2013 CAPD Annual Meetng Carnege Melln Unversty U.S.A. COLUMN GENERATION HEURISTICS FOR SPLIT PICKUP AND DELIVERY VEHICLE ROUTING PROBLEM FOR INTERNATIONAL CRUDE OIL TRANSPORTATION Mathematcal Scence
More informationTransient Conduction: Spatial Effects and the Role of Analytical Solutions
Transent Cnductn: Spatal Effects and the Rle f Analytcal Slutns Slutn t the Heat Equatn fr a Plane Wall wth Symmetrcal Cnvectn Cndtns If the lumped capactance apprxmatn can nt be made, cnsderatn must be
More informationEE 204 Lecture 25 More Examples on Power Factor and the Reactive Power
EE 204 Lecture 25 Mre Examples n Pwer Factr and the Reactve Pwer The pwer factr has been defned n the prevus lecture wth an example n pwer factr calculatn. We present tw mre examples n ths lecture. Example
More informationChapter 12 Equilibrium & Elasticity
Chapter 12 Equlbrum & Elastcty If there s a net force, an object wll experence a lnear acceleraton. (perod, end of story!) If there s a net torque, an object wll experence an angular acceleraton. (perod,
More informationENGI 1313 Mechanics I
ENGI 1313 Mechanics I Lecture 11: 2D and 3D Particle Equilibrium Shawn Kenny, Ph.D., P.Eng. Assistant Prfessr aculty f Engineering and Applied Science Memrial University f Newfundland spkenny@engr.mun.ca
More informationEffects of Polymer Concentration and Molecular Weight on the Dynamics of Visco-Elasto- Capillary Breakup
Effects of Polymer Concentraton and Molecular Weght on the Dynamcs of Vsco-Elasto- Capllary Breakup Mattheu Veran Advsor: Prof. Gareth McKnley Mechancal Engneerng Department January 3, Capllary Breakup
More informationLifetime prediction of EP and NBR rubber seal by thermos-viscoelastic model
ECCMR, Prague, Czech Republc; September 3 th, 2015 Lfetme predcton of EP and NBR rubber seal by thermos-vscoelastc model Kotaro KOBAYASHI, Takahro ISOZAKI, Akhro MATSUDA Unversty of Tsukuba, Japan Yoshnobu
More information55:041 Electronic Circuits
55:04 Electrnc Crcuts Feedback & Stablty Sectns f Chapter 2. Kruger Feedback & Stablty Cnfguratn f Feedback mplfer S S S S fb Negate feedback S S S fb S S S S S β s the feedback transfer functn Implct
More informationCircuits Op-Amp. Interaction of Circuit Elements. Quick Check How does closing the switch affect V o and I o?
Crcuts Op-Amp ENGG1015 1 st Semester, 01 Interactn f Crcut Elements Crcut desgn s cmplcated by nteractns amng the elements. Addng an element changes vltages & currents thrughut crcut. Example: clsng a
More informationModal Identification of the Elastic Properties in Composite Sandwich Structures
Modal Identfcaton of the Elastc Propertes n Composte Sandwch Structures M. Matter Th. Gmür J. Cugnon and A. Schorderet School of Engneerng (STI) Ecole poltechnque fédérale f de Lausanne (EPFL) Swterland
More informationKinetics of Particles. Chapter 3
Kinetics f Particles Chapter 3 1 Kinetics f Particles It is the study f the relatins existing between the frces acting n bdy, the mass f the bdy, and the mtin f the bdy. It is the study f the relatin between
More information( ) ( ) Pre-Calculus Team Florida Regional Competition March Pre-Calculus Team Florida Regional Competition March α = for 0 < α <, and
Flrida Reginal Cmpetitin March 08 Given: sin ( ) sin π α = fr 0 < α
More informationModule B3. VLoad = = V S V LN
Mdule B Prblem The -hase lads are cnnected n arallel. One s a urely resste lad cnnected n wye. t cnsumes 00kW. The secnd s a urely nducte 00kR lad cnnected n wye. The thrd s a urely caacte 00kR lad cnnected
More informationLearn more at
Tensn and Expansn Analyss f Ppe-n-Ppe Rsers: Part A, Theretcal rmulatn Kevn Chuanjan Man, Bn Yue, Adam Szucs, Rcky Theth 2H ffshre nc. Hustn, TX, USA ABSTRACT Ths paper prvdes a mathematcal mdel fr accurate
More informationChapter 7. Systems 7.1 INTRODUCTION 7.2 MATHEMATICAL MODELING OF LIQUID LEVEL SYSTEMS. Steady State Flow. A. Bazoune
Chapter 7 Flud Systems and Thermal Systems 7.1 INTODUCTION A. Bazune A flud system uses ne r mre fluds t acheve ts purpse. Dampers and shck absrbers are eamples f flud systems because they depend n the
More informationPhysic 231 Lecture 33
Physc 231 Lecture 33 Man pnts f tday s lecture: eat and heat capacty: Q cm Phase transtns and latent heat: Q Lm ( ) eat flw Q k 2 1 t L Examples f heat cnductvty, R values fr nsulatrs Cnvectn R L / k Radatn
More informationChapter 6. Dielectrics and Capacitance
Chapter 6. Dielectrics and Capacitance Hayt; //009; 6- Dielectrics are insulating materials with n free charges. All charges are bund at mlecules by Culmb frce. An applied electric field displaces charges
More informationComputing Nonequilibrium Conformational Dynamics of Structured Nucleic Acid Assemblies
Supportng Informaton for Computng Nonequlbrum Conformatonal Dynamcs of Structured Nuclec Acd Assembles Reza Sharf Sedeh,, Keyao Pan,, Matthew Ralph Adendorff, Oskar Hallatschek, Klaus-Jürgen Bathe,*, and
More informationReproducing kernel Hilbert spaces. Nuno Vasconcelos ECE Department, UCSD
Reprucng ernel Hlbert spaces Nun Vascncels ECE Department UCSD Classfcatn a classfcatn prblem has tw tpes f varables X -vectr f bservatns features n the wrl Y - state class f the wrl Perceptrn: classfer
More informationSections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.
Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage
More informationChapter 6 : Gibbs Free Energy
Wnter 01 Chem 54: ntrductry hermdynamcs Chapter 6 : Gbbs Free Energy... 64 Defntn f G, A... 64 Mawell Relatns... 65 Gbbs Free Energy G(,) (ure substances)... 67 Gbbs Free Energy fr Mtures... 68 ΔG f deal
More informationChapter Eight. Review and Summary. Two methods in solid mechanics ---- vectorial methods and energy methods or variational methods
Chapter Eght Energy Method 8. Introducton 8. Stran energy expressons 8.3 Prncpal of statonary potental energy; several degrees of freedom ------ Castglano s frst theorem ---- Examples 8.4 Prncpal of statonary
More informationA density- and stress-dependent elasto-plastic model for sands subjected to monotonic undrained torsional shear loading
Unversty f Wllngng Research Onlne Faculty f Engneerng an Infrmatn Scences - Papers: Part A Faculty f Engneerng an Infrmatn Scences 3 A ensty- an stress-epenent elast-plast mel fr sans subjecte t mntn unrane
More informationOFF-AXIS MECHANICAL PROPERTIES OF FRP COMPOSITES
ICAMS 204 5 th Internatonal Conference on Advanced Materals and Systems OFF-AXIS MECHANICAL PROPERTIES OF FRP COMPOSITES VLAD LUPĂŞTEANU, NICOLAE ŢĂRANU, RALUCA HOHAN, PAUL CIOBANU Gh. Asach Techncal Unversty
More informationMechanical 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 informationSi Oxidation. SiO 2. ! A method of forming SiO 2
S Oxatn! A met f frmn SO wc ue a Ma (e.., fr n mplantatn) Oxe n MOSFET Surface pavatn! Frm perfect S-SO nterface S S ( ) ( ) O ( ) ( ) SO ( ) H O SO H ( ) ( ) SO S O Oxant ffue tru te SO flm Reactn tae
More informationTHE IDENTIFICATION OF MATERIAL PARAMETERS IN NONLINEAR DEFORMATION MODELS OF METALLIC-PLASTIC CYLINDRICAL SHELLS UNDER PULSED LOADING
Materals Physcs and Mechancs (2015) 66-70 Receved: March 27, 2015 THE IDENTIFICATION OF MATERIAL PARAMETERS IN NONLINEAR DEFORMATION MODELS OF METALLIC-PLASTIC CYLINDRICAL SHELLS UNDER PULSED LOADING N.А.
More informationME2142/ME2142E Feedback Control Systems. Modelling of Physical Systems The Transfer Function
Mdellng Physcal Systems The Transer Functn Derental Equatns U Plant Y In the plant shwn, the nput u aects the respnse the utput y. In general, the dynamcs ths respnse can be descrbed by a derental equatn
More informationChapter 3 Kinematics in Two Dimensions; Vectors
Chapter 3 Kinematics in Tw Dimensins; Vectrs Vectrs and Scalars Additin f Vectrs Graphical Methds (One and Tw- Dimensin) Multiplicatin f a Vectr b a Scalar Subtractin f Vectrs Graphical Methds Adding Vectrs
More informationInternational Journal of Engineering Research & Science (IJOER) [Vol-1, Issue-9, December- 2015]
Internatnal Jurnal f Engneerng Research & Scence (IJOER) [Vl, Issue9, December 05] Unstraned Element LengthBased Methds fr Determnng One Optmzed Intal State f CableStayed Brdges MyungRag Jung, Dngju Mn,
More informationApproach: (Equilibrium) TD analysis, i.e., conservation eqns., state equations Issues: how to deal with
Schl f Aerspace Chemcal D: Mtvatn Prevus D Analyss cnsdered systems where cmpstn f flud was frzen fxed chemcal cmpstn Chemcally eactng Flw but there are numerus stuatns n prpulsn systems where chemcal
More informationThis is natural first assumption, unless theory rejects it.
Sectn Smple Regressn What regressn es Relatnshp between varables Often n ecnmcs we beleve that there s a (perhaps causal) relatnshp between tw varables. Usually mre than tw, but that s eferre t anther
More informationFuzzy approach to solve multi-objective capacitated transportation problem
Internatonal Journal of Bonformatcs Research, ISSN: 0975 087, Volume, Issue, 00, -0-4 Fuzzy aroach to solve mult-objectve caactated transortaton roblem Lohgaonkar M. H. and Bajaj V. H.* * Deartment of
More informationAnalysis The characteristic length of the junction and the Biot number are
-4 4 The temerature f a gas stream s t be measured by a thermule. The tme t taes t regster 99 erent f the ntal ΔT s t be determned. Assumtns The juntn s sheral n shae wth a dameter f D 0.00 m. The thermal
More informationFinal Exam Spring 2014 SOLUTION
Appled Opts H-464/564 C 594 rtland State nverst A. La Rsa Fnal am Sprng 14 SOLTION Name There are tw questns 1%) plus an ptnal bnus questn 1%) 1. Quarter wave plates and half wave plates The fgures belw
More informationIntegrating Certified Lengths to Strengthen Metrology Network Uncertainty
Integratng Certfed engths t Strengthen Metrlgy Netwrk Uncertanty Authrs: Jseph Calkns, PhD New Rver Knematcs je@knematcs.cm Sctt Sandwth New Rver Knematcs sctt@knematcs.cm Abstract Calbrated and traceable
More informationChapter 3, Solution 1C.
COSMOS: Cmplete Onlne Slutns Manual Organzatn System Chapter 3, Slutn C. (a If the lateral surfaces f the rd are nsulated, the heat transfer surface area f the cylndrcal rd s the bttm r the tp surface
More informationLecture 12. Heat Exchangers. Heat Exchangers Chee 318 1
Lecture 2 Heat Exchangers Heat Exchangers Chee 38 Heat Exchangers A heat exchanger s used t exchange heat between tw fluds f dfferent temperatures whch are separated by a sld wall. Heat exchangers are
More informationSTATIC ANALYSIS OF TWO-LAYERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION
STATIC ANALYSIS OF TWO-LERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION Ákos József Lengyel István Ecsed Assstant Lecturer Emertus Professor Insttute of Appled Mechancs Unversty of Mskolc Mskolc-Egyetemváros
More information1. An incident ray from the object to the mirror, parallel to the principal axis and then reflected through the focal point F.
Hmewrk- Capter 25 4. REASONING Te bject stance ( = cm) s srter tan te cal lengt ( = 8 cm) te mrrr, s we expect te mage t be vrtual, appearng ben te mrrr. Takng Fgure 25.8a as ur mel, we wll trace ut: tree
More informationENGI 4421 Probability & Statistics
Lecture Ntes fr ENGI 441 Prbablty & Statstcs by Dr. G.H. Gerge Asscate Prfessr, Faculty f Engneerng and Appled Scence Seventh Edtn, reprnted 018 Sprng http://www.engr.mun.ca/~ggerge/441/ Table f Cntents
More informationBuckling analysis of single-layered FG nanoplates on elastic substrate with uneven porosities and various boundary conditions
IOSR Journal of Mechancal and Cvl Engneerng (IOSR-JMCE) e-issn: 78-1684,p-ISSN: 30-334X, Volume 15, Issue 5 Ver. IV (Sep. - Oct. 018), PP 41-46 www.osrjournals.org Bucklng analyss of sngle-layered FG nanoplates
More information( 1 jj) = p + j B (1) j = en (u i u e ) (2) ρu = n (m i u i + m e u e ) (3)
Magnetospheric Physics - Homework, 2/14/2014 11. MHD Equations: a Consider a two component electrons and ions charge neutral ρ c = 0 plasma where the total bulk velocity is defined by ρu = n m i u i +
More informationKinematic Hardening Parameters Identification with Respect to Objective Function
Vol:8, No:4, 04 Knematc Hardenng Parameters Identfcaton wth Respect to Objectve Functon Marna Franulovc, Robert Basan, Bozdar Krzan Internatonal Scence Index, Mathematcal and Computatonal Scences Vol:8,
More informationLecture 8 Modal Analysis
Lecture 8 Modal Analyss 16.0 Release Introducton to ANSYS Mechancal 1 2015 ANSYS, Inc. February 27, 2015 Chapter Overvew In ths chapter free vbraton as well as pre-stressed vbraton analyses n Mechancal
More informationKinematics of Fluid Motion
Knematcs of Flu Moton R. Shankar Subramanan Department of Chemcal an Bomolecular Engneerng Clarkson Unversty Knematcs s the stuy of moton wthout ealng wth the forces that affect moton. The scusson here
More informationTHE EFFECT OF BEAM TO COLUMN CONNECTION IN ARC PORTAL FRAME
THE EFFECT OF BEAM TO COLUMN CONNECTON N ARC PORTAL FRAME Asko Keronen Rakenteden Mekankka, Vol. 26 No 2 1993, ss. 35-5 SUMMARY A full scale rc (renforced concrete) portal frame has been bult n order to
More information2 Analysis of the non-linear aerodynamic loads of hypersonic flow. 1 General Introduction
4 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES PRELIMINARY STUDY OF NON-LINEAR AEROELASTIC PHENOMENA IN HYPERSONIC FLOW Zhang Wewe, Ye Zhengyn, Yang Yngnan Cllege f Aernautcs, Nrthwestern Plytechncal
More informationThe Tangential Force Distribution on Inner Cylinder of Power Law Fluid Flowing in Eccentric Annuli with the Inner Cylinder Reciprocating Axially
Open Journal of Flud Dynamcs, 2015, 5, 183-187 Publshed Onlne June 2015 n ScRes. http://www.scrp.org/journal/ojfd http://dx.do.org/10.4236/ojfd.2015.52020 The Tangental Force Dstrbuton on Inner Cylnder
More informationCourse Stabilty of Structures
Curse Stabilty f Structures Lecture ntes 2015.03.06 abut 3D beams, sme preliminaries (1:st rder thery) Trsin, 1:st rder thery 3D beams 2:nd rder thery Trsinal buckling Cupled buckling mdes, eamples Numerical
More information425. Calculation of stresses in the coating of a vibrating beam
45. CALCULAION OF SRESSES IN HE COAING OF A VIBRAING BEAM. 45. Calulaton of stresses n the oatng of a vbratng beam M. Ragulsks,a, V. Kravčenken,b, K. Plkauskas,, R. Maskelunas,a, L. Zubavčus,b, P. Paškevčus,d
More informationBig Data Analytics! Special Topics for Computer Science CSE CSE Mar 31
Bg Data Analytcs! Specal Tpcs fr Cmputer Scence CSE 4095-001 CSE 5095-005! Mar 31 Fe Wang Asscate Prfessr Department f Cmputer Scence and Engneerng fe_wang@ucnn.edu Intrductn t Deep Learnng Perceptrn In
More informationSpreadsheet Implementations for Solving Power- Flow Problems
Spreadsheets n Educatn (ejse lume Issue 1 Artcle August 008 Spreadsheet Implementatns fr Slvng wer- Flw rblems Mark A Lau Unversdad del Turab, mlau@suagmedu Sastry Kuruganty Unversdad del Turab, ut_skurugant@suagmedu
More informationChapter (10) lbf Ans. 3-2 Body AB: R R. Body OAC: R R. Chapter 3 - Rev. B, Page 1/100. R R 300 lbf Ans 0 R (10) 100(30) 0
Chapter - M 0 8RB 6(00) 0. lbf Ans. RB F y 0 R RB 00 0 R 66.7 lbf Ans. R R. lbf Ans. C B - Bdy AB: F x 0 RAx RBx F y 0 RAy RBy M B 0 RAy (0) RAx (0) 0 R R Ax Ay Bdy OAC: 0 R (0) 00(0) 0 M O RAy Ay 00 lbf
More informationORIGIN 1. PTC_CE_BSD_3.2_us_mp.mcdx. Mathcad Enabled Content 2011 Knovel Corp.
Clck to Vew Mathcad Document 2011 Knovel Corp. Buldng Structural Desgn. homas P. Magner, P.E. 2011 Parametrc echnology Corp. Chapter 3: Renforced Concrete Slabs and Beams 3.2 Renforced Concrete Beams -
More informationInstituto Tecnológico de Aeronáutica FINITE ELEMENTS I. Class notes AE-245
Insttuto Tecnológco de Aeronáutca FIITE ELEMETS I Class notes AE-5 Insttuto Tecnológco de Aeronáutca 5. Isoparametrc Elements AE-5 Insttuto Tecnológco de Aeronáutca ISOPARAMETRIC ELEMETS Introducton What
More informationDUE: WEDS FEB 21ST 2018
HOMEWORK # 1: FINITE DIFFERENCES IN ONE DIMENSION DUE: WEDS FEB 21ST 2018 1. Theory Beam bendng s a classcal engneerng analyss. The tradtonal soluton technque makes smplfyng assumptons such as a constant
More informationComputer Based Porosity Design by Multi Phase Topology Optimization
Computer Based Porosty Desgn by Mult Phase Topology Optmzaton Andreas Burbles and Matthas Busse Fraunhofer-Insttut für Fertgungstechnk und Angewandte Materalforschung - IFAM Wener Str. 12, 28359 Bremen,
More informationM-theory from the superpoint
M-thery frm the superpint Jhn Huerta http://math.ucr.edu/~huerta CAMGSD Institut Superir Técnic Iberian Strings 2017 Lisbn 16 19 January Prlgue Figure : R 0 1 Prlgue Figure : R 0 1 R 0 1 has a single dd
More informationPlan o o. I(t) Divide problem into sub-problems Modify schematic and coordinate system (if needed) Write general equations
STAPLE Physics 201 Name Final Exam May 14, 2013 This is a clsed bk examinatin but during the exam yu may refer t a 5 x7 nte card with wrds f wisdm yu have written n it. There is extra scratch paper available.
More informationSurface force on a volume element.
STRESS and STRAIN Reading: Section. of Stein and Wysession. In this section, we will see how Newton s second law and Generalized Hooke s law can be used to characterize the response of continuous medium
More informationNWACC Dept of Mathematics Dept Final Exam Review for Trig - Part 3 Trigonometry, 9th Edition; Lial, Hornsby, Schneider Fall 2008
NWACC Dept f Mathematics Dept Final Exam Review fr Trig - Part Trignmetry, 9th Editin; Lial, Hrnsby, Schneider Fall 008 Departmental Objectives: Departmental Final Exam Review fr Trignmetry Part : Chapters
More informationMechanics Physics 151
Mechancs Physcs 5 Lecture 3 Contnuous Systems an Fels (Chapter 3) Where Are We Now? We ve fnshe all the essentals Fnal wll cover Lectures through Last two lectures: Classcal Fel Theory Start wth wave equatons
More informationIncrease Decrease Remain the Same (Circle one) (2 pts)
ME 270 Sample Fnal Eam PROBLEM 1 (25 ponts) Prob. 1 questons are all or nothng. PROBLEM 1A. (5 ponts) FIND: A 2000 N crate (D) s suspended usng ropes AB and AC and s n statc equlbrum. If θ = 53.13, determne
More informationCHAPTER 9 CONCLUSIONS
78 CHAPTER 9 CONCLUSIONS uctlty and structural ntegrty are essentally requred for structures subjected to suddenly appled dynamc loads such as shock loads. Renforced Concrete (RC), the most wdely used
More informationSupplementary Course Notes Adding and Subtracting AC Voltages and Currents
Supplementary Curse Ntes Adding and Subtracting AC Vltages and Currents As mentined previusly, when cmbining DC vltages r currents, we nly need t knw the plarity (vltage) and directin (current). In the
More informationThe Two-scale Finite Element Errors Analysis for One Class of Thermoelastic Problem in Periodic Composites
7 Asa-Pacfc Engneerng Technology Conference (APETC 7) ISBN: 978--6595-443- The Two-scale Fnte Element Errors Analyss for One Class of Thermoelastc Problem n Perodc Compostes Xaoun Deng Mngxang Deng ABSTRACT
More informationSolution ME 323 EXAM #2 FALL SEMESTER :00 PM 9:30 PM Nov. 2, 2010
Solution ME 33 EXAM # FALL SEMESTER 1 8: PM 9:3 PM Nov., 1 Instructions 1. Begin each problem in the space provided on the eamination sheets. If additional space is required, use the paper provided. Work
More informationTrigonometry, 8th ed; Lial, Hornsby, Schneider
Trignmetry, 8th ed; Lial, Hrnsby, Schneider Trignmetry Final Exam Review: Chapters 7, 8, 9 Nte: A prtin f Exam will cver Chapters 1 6, s be sure yu rewrk prblems frm the first and secnd exams and frm the
More informationP a g e 3 6 of R e p o r t P B 4 / 0 9
P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J
More informationGrade 12 Physics Exam Review
Grade 12 Physcs Exam Revew 1. A 40 kg wagn s pulled wth an appled frce f 50 N [E 37 degrees abve the hrzntal. The wagn mves 8 m [E] hrzntally whle 5 N f frctn act. Fnd the wrk dne n the wagn by the...
More information