FEA by nitin gokhale

1 Practical Finite Element Analysis Firrt Edition



r- Practical Finite Element Analysic - NitinSGokhale - Sanjay SDeshpande -Sanjeev V Bedekar -AnandN Thite -FiniteToInfinire, Pune

Pubiished by:FiniteTo Infinite686, Budhwar Peth, Shivganga Chambers, Near PrabhatTalkiesPune - 411002. Maharashtra, India.Tek 0091 - 20 - 24454981Mobile:0091- 9423571952E-mail: [email protected]: www.finitetoinfinite.comCopyrights 0 2008 by FiniteTo lnfiniteAll rights strictiy reservedNo part of this publication may be reproduced, stored in a retrieval system ortransniitted in any form or by any means,electronic,mechanical, photocopying,recording or otherwise without the prior written permission from Finite ToInfinite.ISBN 978-81-906195-0-9The export rights ofthis bookarevested solely with the publisher.First Printing: January 2008iniages sourced from AltairCalendar2005,2006,2007 and 2008 are copyright ofAitair Engineering, lndia and have been used with prior consent.Commercial software nanies, Company names, other product trademarks,registeredtrademark logos are the properties of their respectiveowners.Price: Us. 6501-Disclaimer:Every efforts have been made to keep the book free from technical as well asother mistakes. However, publishers and authors will not be responsible forloss, damage in any form and consequences arising directly or indirectly fromthe use of this book.Our Bankers: Bank of Maharashtra, Shaniwar Peth Branch, PunePrlnted at: K Joshi & Co.,1745/2, Sadashiv Peth, Near Bhikardas Maruti Temple,Pune- 30Cover Designed by: Mooon Design StudioComposed by: Shailesh Bhingare

- DrPeterFischer m)ikmyral,...a complicated mathematical theory for camputer specialists; or anindispensabletoolfor 011-day industrialproduct development?FiniteElement Analysis...a myth which allows to solve most of the warlds technical problems;... oran analysis method which produces just results that 'L. have to be checkedby further testing ...?\" Al1 the answers may be correct. However, none of the answersreallydescribes Finite Element Analysis properly.Originally FiniteElementsweredeveloped to approximatecontinuousstructures by discreteequationsystems. That's al/. These equation systems can then be solved by anynumericaland computeraided technique.The method of Finite Elements was developed at perfectly right times:growing computercapacities,growing human skills andindustry demandsfor ever faster and cost effective product development made it a synonymfor high-techengineeringandnearly unlimitedpassibilitiesof the technicalcommunity In this context, thename \"FiniteElementAna1ysis\"is nowadayscammonly used fora widerangeofcomputation techniques in engineeringpractice.

This book summarizes the most important techniques of current FiniteElement applications. It is dedicoted to the needs of practising engineersand provides clearly structured, well understandable information formanagers, design & test engineers, students and al1interested technicians.Basing on demonstrative exarnples the fundamenta1theory is summarized.The focus is to exploin those principles, which have most important affectson the practical work, for understanding and for interpreting the results.Most valuable are the guidelines, tips, tricks and checklists, which resultfrom long term experiences and many successfulprojects of the authors.The book aims to understand Finite Element Analysis as a computationalengineering tool and to share the knowledge and experiences in this field.It willprovide appreciation between various disciplines working togetherinengineeringprojects. But 1wish, that this book will be also a seedfor betterunderstanding between al1people working for common objectives of ourlives, societies and cultures, our world and our spirits. -Dr Peter Fischer Manoging Director DTECH STEYR - Dynamics &TechnologyServices GmbH Austria

Foreward1 have great pleosure and feel honored in sharing my thoughts with thereaders through thisprefoce, becauseof following reosons -1) This is O unique book of its kind in the sense it is combining many yearsof actual hands on experience with adequate coverage of theoreticoltreatment.2)1 personolly know the authors Nitin Gokhale, Sonjeev Bedekar, SanjayDeshpande and Dr Anond Thite. We have worked together in reseorchand development for some years and 1had many occasionsto discuss theproblems related with FiniteElementAnalysis.3) This book is going to be a standard reference for the CAE (CornputerAided Engineering)engineersfor many years to corne.When westartedthe CAEDEPARTMENTN)ourcomponyin 1995 (wewereallnew to this technique),arrangedfor intensive trainingof aspeciallyselectedgroup of highly tolented young engineers. The training was impartedby many experts of international repute and also by university ond IITprofessors. The authorswere in this group.The group showedoutstandingresultswhich surprisedeventhe teachers. Very quickly they couldgrospthefundomentalconcepts,get a deep insight and develop Ofeelof FEA (whichisvery essentiolfor one to be really competent).They hod enough confidenceto take a plunge in this very new field fit wasnotevenknown widelyinlndioin thosedays)bystartingtheirowncompanysolely to provide this technology service and training to engineeringindustryglobally.They have not looked bocksince.Itisthis feelond thesixthsensewhichtheyhavesincerelyattemptedtopasson to the serious students through many examples, thumb rules, empiricolrules etc. Theseore generally regarded as professional secrets which most

experts are not willing to shore. This is that knowledge which (in the truelndian style) the disciples learn at the feet of their 'GURU'From this point of view also, 1feel this is a rare book written with a true andsincere desire to spread knowledge.In the last few years, not only have they been relentlessly devouring al1available technicalliteratureonFEA, but alsoassimilating itandputting it totest by taking newer ondnewer (more and more formidable) challenges.Jhey must certainlyhave falteredmany a times. Foilurescomeonly to thosewho are courageous enough to venture in to new lands. They have leornt alot from eoch andevery mistake andsprang back with double the energyand enthusiasm to achieve and conquer even more exalted heights.Jhey have very sincerelydocumented thesemistakesand 'the lessonslearnt'and included in this book for the benefit of devoted students. This -in myopinion- one of the rnost valuoble feature of this book which sets it apartfrom rnost other books on the subject. This is not anly a book which oddsto your knowledge and makes you aware of new technology but it is alsoapracticalguide which tells you about the nuts and bolts of this techniqueand tells you which mistakes you should guard against, whot are the tricksof this trade and where ore thepitfalls.1wish a most enriching learning experience to al1 those who want to take adip in this'Gyan kund' (source of knowledge). - Ashok R Sonalkar R &D Head (Retired) Mahindra &MahindraLtd. FE5 - TracfarDivision

Why the book has been writtenFEA is gaining popularity day by day and is a sought after dream career formechanical engineers.Enthusiasticengineers and managers who want torefresh or update the knowledge on FEA are encounteredwith volumes ofpublished books.Oftenprofessionalsrealizethat they ore not in touchwiththeoretical concepts as being pre-requisite and find it too mathematicaland Hi-Fi Many a times these books just end up being decoration in theirbookshelves...Authorsofthis bookarefromIIT's&IIScandafterjoiningtheindustryrealizedgop between university education& the pmctical FEA. Over the years theylearned it via interaction with experts from international community,sharing experiencewith each other and hard route of trial & errormethod.The basic aim of this book is to share the knowledge andpractices used inthe industry with experienced and in particular beginners so as to reducethelearning cuweandavoidreinventionof the cycle. Emphasis is an simplelanguage, practical usage, minimum mathematics& n o pre-requisites.Al1basic concepts of engineering are included as and where it is required. Itis hoped that this book would be helpful to beginners, experienced users,managers, group leaders and as additional reading materialfor universitycourses. - Nitin 5 Gokhale Dec.21,2007

AcknowledgementThanks t o the teachers Heimut Dannbauer,Dr Peter Fischer,Thanks toco-authors for their contributions Dr P Seshu, DrVijay Ukadgaonkar, Dr S K MaitiCFDNon-linear analysis Sanjay S DeshpandeCrash Anaiysis Sanjay S Deshpande, Chanian Lal SahuThermal Anaiysis Sanjay S Deshpande, Rajesh S KoliNVH SanjeevV BedekarExperimentalvalidation and Data acquisition : Dr Anand N ThiteThanks for image contribution Prashant R Pawar, Dr Anand NThiteThanks t o softwares companies Altair Engineering, ApolloTyresLtd., ARAI,Aitair Engineering Ashok Leyland, Bajaj Auto Ltd., BHEL,UGS Bharat Forge Ltd., DOW India,FEMFAT Emerson CiimateTechnoiogies,Thanks t o colleagues and students EngineeringCenter Steyr, Lear Corporation, L&T Ltd. (SwitchGear Div.), Maruti Udyog Ltd.,Thanks tofamily members Mahindra & Mahindra Ltd. (Tractor Div.),Thanks for painstaking DTP efforts Mahindra & Mahindra Ltd. (Automotive Sector),Thanksfor Cover Design & BookLayout Piaggio Vehicle Ltd.,Tata Motors Ltd.,Thanks t o printer Tata Johnson Controis Automotive Ltd.,Thanks t o o u r bank TV5 Motor Company Ltd. R a p ~ e r lSi ninde, he son L h s , A R 5oiialkar N liii Krnirraoar.5 K Ma~atlic M. R. Saraf, G j a y P~atharkar Rohit Sadalge, AmalrajTatapudi, JagdishTahaiyani,Sujatha KG Nawdeep Puranik, KaushikChoudhuri Axei Werkhausen, Eberhard Dutzler Mandar Kulkarni,Tushar Akoikar, Sachin Mate, Manoj Gothe, Balaji Rajmane, Shakti Chavan, Jitendra Pawar, Sachin Dani, Nitin Karhade, D 5 Bhalerao, Prasanna Shanbhag, Parag Shimpi, Prashant Khedkar, C. L. Patel, Ajay Sohani, Swapnil Wadkar, Rahul Pardesi, Santosh Belure, Jitendra Chaugule, Shrikant Sheodey Parents and specially to brother Sandeep Siiailesh Bhingare Mooon Design Studio 'K. Joshi & Co:, Anii Joshi and team M K Deval,P S Bagade, S S Deo Bank of Maharashtra.Shaniwar Peth BranchThanks t o al1who have helped directly or indirectly

rn Contents 1. Introductionto FiniteElement Analysis 1.1 Methods Solve any Engineering Problem 1.2 Procedure for Solving any Analytical or Numerical Problem 1.3 Brief Introduction ta DifferentNumerical Methods 1.4 What E DOF 1.5 Why daweCarty0ut Merhing.What is FFM 1.6AdvantagesofFEA 1.7 CerignCycler 1.8 Absolute vs. RelaliveDesign 1.9 Ir FEA a K~placcmrnftoi Costlyand TimeConsumingTerring 2. Fast, Present and Futureof FEA 2.1 History of Finite Element Method 2.2 Present 2.3 Theoretical Flnite Element Analysis 2.4 Software Based FEM 2 5 PracticalApplicationsof FEA 2.6 Failure Analysis 2.7 Future of FEA 3. Typesof Analyses (BriefIntroduction) 3.1 Linpar Sratir Ana1ys:r 3.2 Non Iincar Analyrir 3.3 Dynainic Analyrir 3.4 L ncar Riickling An.~ly$is3.5 Thermal Andlys r 3dFarigrra~lyris3ïOptiniization 38Computationalrluid Dynamics 3.9Crash Analysis 3.10Noise Vibrationand Harshness,NVH 4. Basicsof Staticsand Strength of Materials 4.1 What is Stress 4.2Types of Stress 43Types of Forces 4ATypes of Moments 4.5 Uniaxial Stress 4.661 axial Sness 4 7Triaxial Stress 4.8What is\"1\"Area Moment of 1nertiaand\"J\"Polar Moment of lnertia 5. Introductionto Meshing 5.1 Why do We Carry Out Meshing 5.2Types of Elements 5.3 How to Decide Element Type 5A Can We Solve Same Problem Using 1-d, 2-d, 3-d Elemems 5.5 How to DecideElement Length 5.6 How to Start Meshing 5.7 Meshing Techniques 5 8 Meshing in Critical Areas 5.9 Mesh DisplayOptions 6. l-D Meshing 6.1 When toUse1-d Elements 6.25tlffness Matrix Derivation 6 3 Stiffness Matrix- Assembly of Two RddElements 6.4 Beam Element 6.5 SpeciaiFeaturesof BeamElements 7. 2-DMeshing 7.1 Whento Use 2-d Elements 7.2 Family of 2 d Elements 7.3Thin Shell Elements 7.4 Effect ofMesh DensityIntheCriticaIRegion 7.5 Effectof Biaslngin thecritical Region 7.6Symmetrlc BaundaryConditions 7.7 Different ElementTypeOptions for Shell Meshing 7.8 Geometry Associative Mesh 7 9 QualityChecks 7.10 OtherChecks for 2-d Meshing 7.1 1 How Not ta Mesh xiil

- 8.1 When 10 Ure 3-d Elerncnts 8.2 UOrr for Solid Elrrnents 8.3 Tetra Mcjhing Techniques 8.4 Quality Checks for Tetra Mesiiing 8.5 Olliei Checks for étra Merliing R.6 Brick Mrshing 8.1 R r k k MrshQuality Chccir 8.8Other Checks for Bi:ckMeshing 8.9 How Nol toMeih 9. SpecialElementsand SpecialTechniques 9.1 Connection of Solid Elements with Bearnsand Sheilr 9.2 Llnear 10Parabolic and Brick to Tetra Connection 9.3 HybridMeshing [Hex-Pyram-Tetra) 9.4GAPElement 9.5 Masr Eiement 9.6 Spring and Damper Eiement 9.7 Rigid & ConstraintElements 9.8 Simple Linear Static AnalysisTechniquesI oSimulateContact 10. Weld, Bolt, Bearing and Shrink Fit Simuiatlon 10.1 Weiding Simulation 10.2 Howto Modei Spot Weld 10.3 How I o Model Arc Weld 10.4 Practical Considerations for Welded Joints 10.5 Boited Joint 10.6 Bearing Simulation 10.7ShrinkFit Simuiation 11. Material Properties and Boundary Conditions 11.1 E,G&u 11.2 MaterialClassification 11.3 MaterialProperties 11.4 BoundaryCondit~ons 11.5 How to ApplyConstraints 11.6 Syrnmetry 12. Linear Static Analysis 12.1 Definition 12.2 While Startlng any FiniteElement Analysis Project 12.3 How 10 Check Mesh Model Submitted by a Vendor or Colleague 12.4 Design Modifications Based on Linear Static Anaiysis: A CaieStudy 12.5 Linear Static Salverr 12.6 SolutionRestart Method 12.7 h-elementvs. p-element 128Sub-modellng 129Linwr Buckling Analysir 13. Non Linear Analysis 13.1Introdcction 13.2 Cun~pdrironof Linwr and Nonlnca. FEA 13.3 Types of Nonlineariiy 13.4 Stress-Strain Measuresfor Noniinea~Anaiysis 13.5 So.utionTechniquer foi Non inrar Analysis 13.6 issues RrlatedtotheConverqenceof Newton Raphson Method 13.7 Errentiol Steps I o Start with Nonlinear FEA 13.8 i ~ e n e r aPl rocedure for Nonlinear Static Analysis Project 13.9 ExerciseProblem 14. DynamicAnalysis 14.1 Why Dynarnic Analysis 14.2 Static Analysis vs. Dynarnic Analysis 14.3 Definitlonr 14.4What is DifferenceBetweenTirne Domainand Frequency Domain 14.5 Typesof Loading 14.6 Simple Harmonic Motion 14.7 Free Vibration 148 Free - Free Run 14.9 How to Avoid Resonance 14.10 Damping Consideration 14.1 1 Forced Vibration 14.12 Single DOF Svstem FreauencvRemonseAnalmis 14.13 Sinde DOFSvstern. Transient Resoonse Analvsis 14.14 ~ynainic~nalysisSolvers i4.15 Twci DO; Syrtem.ireq&nry Rcrponsb Anaiysis Éase Exritaton 14.16 Bracke1,Tiansienl Responre Anaiys:s (Short Uuratwn Corcr) 14.17 What is PSD (PowerSpectralDensity) 15. Thermal Analysis 15.1 Introduction 15.2ConductionHeatTransfer 15.3SteadvStateConduction IS.4Unsteadv State Conduction 15.5 Convection Heat Transfer 15.6 Forced Convection (Interna1Flow) 15.7 ForcedConvection (ExternalFlow) 15.8 Meshing forThermal Analysis 15.9 FreeINaturai Convection 15.10 RadiationHeat Transfer 15.11 PracticalApplication ofniermal Analysis 16. Computatlonal Fluld Dynamics 16.1 What 1s CFD 162Various Levelsof Approximationsin Fluid Dynamics 16.3 Equilibrium Equations fora Fiuid 16.4The Physrs of the Navter Stokes Equations 16.5Conservation Farm of FluldFlow Equations 16.6 lntegrai Form of the Conservation Laws 16.7 Model Equations for Convection and Diffusion: Their Mathematical and Physicai Aspects 16.8 NumericalSchemesfora ModelConvection Equation 16.9 Numerical Schemesforastandard Diffusion Equation 16.10 Explicit and Implicit Numerical Schemes 16'11 DffferentTypes ofxiv

Codes Ured farCFD Caicuiationi 16.12 DifferentTypesofGridsUsed for CFD 16.13 Difference BetWeen Me~hesUsed in Comoutational Stmctural Mechanics and Cornoutational Fluld Dynamics 16 14 Strrngthsand Wraknrsws of CrD Agalnst Exp~i~mrntaFiuid DynamKs or Win0 Tunnrl Terting 16.15 CFD Projert Irackiny Sheer 16.16 Typicdl Applicationsof ComputationalFluid Dynamics in Various lndusbies17. Fatigue Analysis 17.1 Why Fatigue Analysis 17.2 Static, DynamicandFatigueAnalysisComparison 17.3 What is Fatigue 17.4 Historyof Fatigue 17.5 Definifions 17.6Various Approachesin Fattgue Analysis 17.7 Stress Life Approach 17.8 Strain Lire Approach 17.9 Fracture Mechanics Approach 17.10Cycle Counting 17.11 Muiti-Mal Fafigue 17.12 Weiding Analysls 17.13 CAE (Fatigue) andTestData Correlation18. Crash Analysis 18.1 Introduction 18.2 What do WP ~ V inPStructural Ciarh Worthincrs 18.3 Transmt Dynamics Solution Methaluluqy 18.4 Inrrearinq the rpeed of Explicit Mrthods for Quasi Statir Sirn~ldtion 18.5 ~om&son of Expi'cil S;. Inipllcit Methods 18.6 Typicai Issues in Contdct Analysis 18.7 Some Aspects d Shell Clement Technology 18.8 Contact Impact Aigoiithrns 18.9 Full Dynamir I lmpact vs. Quasi Static Simulatinns 18.10 Lagrangian and EulerianCodes 18.1 1 E l k t of Procerr and Resldual Stress on Crash Analyiis 18.12 Typicdl Application of Crash Worthlness Slniuiations invariousindustries19. NVH Analysis 19.1 Introduction to NVHConcepts 19.2 Frequency Range of FE DynamfcAnalysir 19.3 FEA for StructuralDynamics 19.4 FEA for Acoustics 19.5 ModelValidation 19.6 Modei Updating 19.7 Design Modification 14.8Vibration and Noise Connoi20. Post P r o c e s ~ i nTgechniques 20 1 I(ow to Vddate &CheckArcuracyuf tne Herult 20.2 Haw toView Herults 20.3 Average and UnaveiageStresses 20.4 SpeclalTrlckrfor Pori Processing 20.5 lnterpretationof Results and DerignModifications 20.6CAE Reportr21. Experimental Validation a n d Data Acquisition 21.1 StrainGauge21.2 Photo elasticily 21.3 LoadCeils21.4T0rqueSensorsToqueTransducers 21.5 How Io Collect Force vs. Time Data (Dynamic Test) 21.6 How I o Measure Acceleiatlon 21.7 How ro MeasureFatigue i.ik21.8 How 10 MrasureNawralFreqiiency22. Common Mistakesand Errors23. Preparation for InterviewAbbreviationsAppendix



YPIintroauction to te tiement malysis- Clasricalapproach b,i-Mathematicalreprewntation Actual measurement - 100%accurateresults -Approximate,assumptionsma e -Tirne consuming &needr-Closedfarm sdution -Applicableeven if physical expensiveset up- App~icab~eonf~oyr simple prototype notavaiiable(initial - AppUcabkonlyif physicai' problems likecantllever &simply supportedbeams etc. design phase) prototype is available -Completein itself --Real lifecomplicatedprobiems Resultscannot be believed Thouah analytlcalmethods could alsogiveapproximate resultsif - Resultscan not be believed blindly &min. 3 to 5 prototypes the solution isnot closedform, blindly & mustbe verifiedby must be tested but in general andbroadsense, analyticalmethodsare considered experimentalmethodor hand as closedform solutions ie. calcuiationfor knowingthe range 1W % accurate. of results Finlte Ekment Method: Unear, - Stralnq-au-qe Nonlinear, Butkling,Thermal, Dynamic&Fatigueanalyrir -Photo elasticity Boundary Elemheethnodt: -Vibration measurements ~~~~~~Ni~W~ - Sensorsfor temp. &pressureetc. -Fatiguetest FlniteVolumeMethad: CFD (Com~utationaFiluid Dvnamics)& ~om&tational~lectro&gnetics Flnite DifferenceMethod: Thermal &Fluid flowanalysis(in combination with FVM)There are 2 stepsStep 1) Writing governing equation - Problem Definition or in other words formulating theprobiem in the form of amathematicalequationStep 2) Mathematical solution of governing equationFinal result is summation of step 1 & step 2. Result will be 100 % accurate when there is noapproximation at either of the steps (Analytical method).Numerical methods make approximationat step 1 as well as at step 2 & hence al1the numericalmethods are approximate.

Accurac.y\" Little or no approximation J Approximateresults Little or no approximation Hig-h accuracya. Cantilever beam deflection - Analytical approachAim :To determine deflection of cantileverbeam (y)Step1:Governing equation GoverningEquation (unknown = y )Step 2: Mathematical solution of governing equation -El d2y/dx2=M = -P x (Origin a t free end, moment at a distancexfrom origin = -Px)lntegrating it w.r.t. x, 1\" integration+El dy/dx = -P x2/2 C,integration constant C, could be determinedby substituting known boundary conditions i.e, at* +x = L, dyldx = 0 O = - P L2/2 Cl=1Cl = P L2l2-2nd integrationEI~=-PX~/~+PL'X/Z+C,lntegration constant C, could be determined by substitutingatx=L, y = 0

** O = - PL3/6+PL3/2+C, c, = - PL3/3Substitutingvalues of constants C, and C,For cantileverbeam, deflection is maximum, when force is applied at free end of beam Le. x = O&above equation reduces toy = -PL3/3El (-sign indicotesdeflectionin downworddirection)Obvious question is, if analyticalmethods are accurate then why are they not used for solvingreal life problems. Primary reason is step 1, the governing equation. For above problem beambending equation was readily available as starting point but this type of equations are notavailablefor solving real lifeproblems like say for transmissioncasing or hydraulichousing. Basicbeam bending equation is also based on many assumptionssuch as small deflection, isotropicmaterial, c/s of the beam remains plane and perpendicular to the neutral axis and radius ofcurvatureis largein comparison to cross-sectional dimensionsetc.How does nurnericslrnethodssolvetheproblem?Numerical methods like FEM are based on discretization of integral form of equation. Basictheme of al1 numerical methods is to make calculations a t only limited number of points& then interpolate the results for entire domain (surface or volume). Even before getting thesolution we assume how the unknown is going to Vary over a domain. Say for example, whenmeshing is carried out using linear quadrilateral elements, assumption made i s linear variationof displacement overthedomain and for 8noded quadrilateralelement, assumption is parabolicvariation.This may or may not be the case in real life & hence al1numericalmethods are basedon an initial hypothetical assumption. Afîer getting the results there are several ways to checknumericalas well as practical or field result correlation accuracy & minimizationof errors.1) FiniteElementMethod (FEM):FEM is the most popular numerical method.Applications - Linear, Nonlinear, Buckling, Thermal, Dynamic & Fatigue analysis. FEM will bediscussed in detail at later stage.Are FEA and FEM different?-FiniteElement Method (FEM) and finite Element Analysis (FEA)both are one &the same. Term\"FEKis more popular in industries while\"FEMat universities.Many times there is confusion between FEA, FEM &one more similar but different term FMEA

Introductionto Finite Eiemenr Analysis (EailureMode EffectAnalysis). FEA/FEM is used by design or R&Ddepartment only while FMEA is applicable to al1the departments. 2) Boundary Element Method (BEM): It is a very powerful and efficient technique to solve acoustics or NVH problems. Just like finite element method it also requires nodes and elementsbut as the name suggest it considers only outer boundary of the domain. So in case if the problem is of a volume, only outer surfaces are considered. If the domain is area then only outer periphery is considered. This way it reduces dimensionality of the problem by a degree of one & thus solving it faster. 3) FiniteVolumeMethod (FVM): All Qmputational EluidDynamics (CFD)softwaresare based on FVM. Unit volumei s considered in Finite Volume Method (similar to element in finite element analysis). Variable properties a t nodes are pressure, velocity, area, mass etc. It is based on Navier - Stokes equations (Mass, Momentum and Energy conservation equilibriumequations). 4) FiniteDifferenceMethod (FDM): Finite Element and Finite difference share many common things. In general Finite Difference Method is described as a way to solve differential equation. It uses Taylor's seriez to convert differential equation to algebraic equation. In the conversion process higher order terms are neglected. Itis used in combinationof BEM or otherwlse FVM to solveThermaland CFD coupled problems. Finite Dlfference Method is discretization of partial dliierential equatlan while \"Finite ~ l e i e n t Method, Boundary EiementMethodand Finite VolumeMethod'ore discretization oflntegralformof equatlons. ib It p e d k b u a dl th. ab.*. kt4 nntlrodi OEA, &A, CVM, Fm)to r p i h sqni piabteta (uycantiiinw pmûlum)? The answer is YES! But the difference is in accuracy achieved, programming ease & t h e required to obtain the solution. When interna1 details are required (such as stresses inside the 3-d object) BEM will lead to poor results (as it considers only outer bwndary), while FEM or FDM or FVM are preferable. FVM has been used for solving stress problem but it is well suited for computational fluid dynamics problems whereconservation& equilibrium is quitenatural. FDM has limitations with complicated geometry, assembly of different materialcomponents and combination of various types of elements (1-D, 2-D & 3-D).For this type of problems FEM is far ahead of i t s competitors. Discretization of problem: All real life objectsare continuous. Meansthere is no physicalgap between any two consecutive particles. As per materialscience, any object is made up of small particles, particlesof molecules, moleculesof atomsand so on and they are bonded together by force of attraction.Solving a real I

life problem with continuous material approach is difficult and basic of al1numerical methodsis to simplify the problem by discretizing (discontinuation)it. In simple words nodes work likeatoms and with gap in between filled by an entity called as element. Calculations are made atnodes and resultsare interpolated for elements. There are two approachesto solveany problem continuousapproa<h DisrrsteappiaachAll real lifecomponentsare Eqqivalent Mathematicai Continuous modelingReallifecontinuausproblem Discrere(mathemoricalequivalent)rnodel, chair represented byshellandbeam dementspersmvi0lurnpedm~sotC.GFrom mechanical engineeringpoint of view any component or system could be representedbythree basic elements -Mass'm' EiSpring'k'Damper'c' 4 thAll the numencalmethods including FiniteElement follows discreteapproach. Meshing [nodesand elements) is nothing but discretization of a continuous system with infinite degree offreedoms tofinite degreeof freedoms.

Object is fixed atone end. Force is appliedat point\"P Due to force object deforms and Point Pget shifted to new position P!When can we saythat we know solution of aboveproblem?If and only if we are able to define deformed position of each & every particlecompletely.Minimum number of parameters (motion, coordinates, temp. etc.) required to defineposition of anyentity compietely in the space is known as&greeofheedom (dof).Consider following 2-d (planer)problem. Suppose origin is at bottom left corner and is known.To define positionof point A completely with respect to the origin we need two pararneters i.ex, and y, in other words 2 dofs (translation x and y).

- Practical Finite Element AnalysisConsider that the point A is a part of line, now one anqle should also be defined in addition totwo translations Le. 3 dofs (two translations and one rotation).Suppose points A and B are shifted out of the plane and the line is rotated arbitrarily wrt ail thethree axes. Minimum parameters to define position of point A compietely would be 6 dofs(3translations (Ur, Uy,UJ and 3 rotations (ex,€IyûJ,1.Dof is a very important concept.In FEA we use it for individual calculationpoints Le. nodes(totaldofs for a given mesh model = number of nodesx dof per node) while theory of machines andmechanism uses this concept for body as a whole.It is not like always al1 the elements have 6 dofs per node.Degree of freedom depends on typeof element (Pd, 2-d, 3-d),family of element (thin shell, plane stress, plane strain, membrane etc.)and type of analysis (for structural analysis a thin shell element has 6 dofhode (displacementunknown, 3 translationsand3 rotations) whilethe sameelement when used for thermal analysishas single dof h o d e (temperatureunknown)).Fora new user it isa bit confusingbutthere is lotof logical,engineering&mathematicalthinkingbehind assigningspecific number of dofs to different element types & families. No. of Points =m No. of Noder =8 dof per Point =6 -dof per Node= 6Total equations= m Tatal equatlons 48

Introduction to FiniteElementAnolysis l FEM - Anumericalmethod - Mathematical representation of actual problem - Approximatemethod Definition of FEM is hiddenin its words itself. Basic theme is to make calculationsat only limited (Finite)numberof points and then interpolatethe results for entire domain (surfaceor volume). Finite- Any contlnuousobject has infinitedegreesof freedom & it's just not possibleto solvethe problemin thisformat.FiniteElementMethodreducesdegrees of freedom from Infiniteto Finite with the help of discretization i.e. meshing (nodes& elements). Element - All the calculations are made at limited number of points known as nodes. Entity joining nodes and forming a specific shape such as quadrilateral or triangular etc. is known as Element.Toget value ofvariable(Saydisplacement)any where in betweenthe calculationpoints, interpolation function (as per the shape of element) is used. Method-Thereare3 methodstosolveanyengineeringproblem. Finiteelem,e~.t.~.~.ablye~lginsqs to numericalmethod category. r no1necerrory to rememD~rmothe~noticdaelfinillonofFEM wo/d Dy wordor glvenln rh~oretirorlexfbook the, wholIr imporronlir 10 uiiderrrondthe~oncep&t thenbeoble roder<ribeirin own wordr. It Ir experienre How the resultsare interpolated from few calculationpoints it is okthat FEA is makingal1the calculationsat limitednumberof points, but the question ishow it calculates value of the unknown somewherein betweencalculationpoints. This is achieved by interpolation. Consider4 nodedquadrilateralelement as shownin the figure. Quad4element uses following linear interpolation formula - u=a,+a,x+a,y+a,xy FEA calculates values a t outer nodes 1,2,3,4 i.e. a, a, a, a, are known.Value of the variable any where in betweencould be easily determined just by specifying x & ycoordinatesin aboveequation.For 8 noded quadrilateral,following parabolic interpolation function is used~=a,+a,x+a,y+a,xy+a,x'+a,y'+a,x~y+a,xy~

-Practicai Finite Eiement Anaiysis 8noded(parabaiicl quad dbcmt m mMW* inaw-nutnkr dubammmlmRodnsrrlmmYes, in general increasingcalculation points improves accuracy.Supposesomebodygivesyou 3 straight linesand askto bestfit it inthecircle, find area oftriangle&compare it with circle and then repeat the exercise with 4,6,8,16,32 & 64 lines.006 Unes 8 Lines ShndedAreuisFrrorBy increasing numberof lines, error margin reduces. Number of straight lines are equivalent tonumber of elementsin FiniteElement Analysis.Assume exact answer for area of circle (n r2)i s 100.3 linesgive answer =41 while 4 as 64 & so on.Answer 41 or 64 is not at al1acceptable but 80 or 90 is, considering time spent & relative designconcept.

introduction to Finite Elemenr Anolysis If higher number of nodesand elements leads t o higher accuracy then why not to always create a very fine mesh with maximum possible nodes and elements ?The reason i s solution time is directly proportional t o (dof)\". n = 1 t o 4, depending o n type of analyses and solver. Al50 large size models are not easy to handle on the computer due to graphics card memory limitations. Anaiyst has t o make a fine balance between desired levelof accuracy and element size (dof) that could be handled satisfactorilyusing the availablehardwareresources. Assume Analvtical Method ao~roachgives answers very close to 100 and time taken = 1 month and Finite Elemem Anaiysis with reasonablemesh size gives answer 90 within 1 day. In industry getting fast solutions with logical or reasonable accuracy is more important than absolute accuracy. Thot's why Analytical method approoch is olso known as Scientist way ro solve any problern whil, &nericalmethodis Englneersway tosolvetheproblem. - Visualization . Design cycle t h e $ . 4No. of prototypes 4Testing Optimum design Visualization of results: For simple geometries such as simply supported beam or cantilever beam it is easy to visualize point of maximum stress and displacement. But in real life for parts or assemblies with complex geometrical shapes, made up of different materials with many discontinuities subjected to flexible constraints, complex loading varying wrt t h e and point of application, further complicated by residual stresses and joints like spot and arc welds etc., it is not easy to predict failure location. Imagine someone shows you a complicated engine biock and ask to predict failure location for given set of forces. It is not easy to predict it successfully unless and until you have years of experience in the similar field. But with tools like CAD & CAE, if modelled in appropriate fashion. one can easily get stress contour plots clearly indicating locations of high stress or displacement. Previously components used to be designed by highly experiencedengineers who had seen lot of testing &failures of the components in real life.These days in most of the organizationsdesign engineers arevery Young, using tools like CADICAM /CAE and confident about their designs.

+ -Practical FiniteElernent Analysls Chah Cycle Concurrent Engineering (Currentor new derlgn(Old or conventional cycle& moreefficient) designcycle) r i lMarketingCbnventionalorlradltlonai design cycleItwas used before 1980'sin developedcountriesand in lndia up to late 90's.Consider a simple bracket designed via conventional cycle, failed after conducting the test asshown below Failure Farce location DriginolDesignWhat couldbe the probablesolutions to above problem1) lncrease thickness : Design dept. would release the drawing, purchase engineer submit it to vendor and then test the new prototype. If faiture is reported again then increase the thickness further by repeating the process. Say test is successful after three iterations but the componentbecomes too heavy and not acceptable.

Introduction toFihiteElementAndlysis Jhickness lncreased 2) Next alternativecould be to add fillet a t the sharp corner introduction offillet assume this modificationis also not working 3) Another alternativeis to change the material(high strength material), say test is successful but this suggestion is rejected by marketing dept. due to excessivecost. 4) Further tryouts could be carried out by adding stiffeners Addition ofRib This is a very long & time consumingprocess. Before finalizing the design at component level minimum 3 to 5 prototypes were required to be tested. This design cycle is called as a chain design cycle because just like links of a chain al1the departments are connected to each other in a specific format &function similar to the chain i.e. when the force i s applied at the last linkit will get transferredto topmostlink in a sequentialmanner (from bottomto second last one & so on one by one). Total Design Time In the conventionalchain design cycle effectivetime as well idle time are very high. There is no12

- Practical Finite Element Analysiscoordination among the departments. R&D department i s not a t al1 aware or concern aboutthe project unless & until drawings are delivered to them. Likewise Purchase dept. has no ideaabout what is going on in design or status of the project at R&D. It gets involvedonly after R&Dapproveddrawings are handed overto them.It attacks simultaneouslyon idleas well effective time by using- CAD/CAM/CAE softwares- Smart management techniquesWhy it is called Concurrent?In statics if you remember one of the force system is concurrentforces; ali the forces acting or emerging simultaneously from a single point.In concurrent design cycle similar concept is used. Right from the first day of project a teamof representative from al1 the departments is formed.They seat & work together with specifictargets assigned to them. All the people have access to CAD software. Library or data storageis a very useful and nice facility provided by the commercial softwares. It not only work as safebackup, but also as fast & perfect tool to keep posted al1 the team rnembers about currentstatus of design / project. Whenever design modifications are carried out, al1team members areintimated automatically.ldle time reduction : Say after 2 weeks, design engineer is ready with primary design of acomponent.Now whilehe i s deciding tolerances,manufacturingprocess, surfacefinish methodsetc., CAE engineer starts analysis, simultaneously purchase engineer contacts vendor, transferbasic CAD data with the advance information of the job order. So that by the time design i sfinalized,vendorwill also be prepared to start the job immediately.When prototype activity is inthe process, test engineer will schedule the test.This i s how idletirne is minimized.Effective time reduction :CAE plays important role in reducing no. of prototypes.Test resultsof the first prototype are compared with finite element model. 10 to 15 % difference in FEA &experimental res& is considered as good correlation. FE model behaving in the same way aspredicted by test is key to success. Now further permutations & combinations (likechangingthickness, material, fillet, addition of ribs etc.) could be performed very fast and in an optimumway with the help of CAE. Say for example changing thickness of a sheet metal part from 1.5mm to 2 mm is just a matter of literallyone minute! CAE engineer has to create a new propertywith thickness of 2 mm, assign it to mesh & run the analysis which will not take more than fewminutes. While earlier approachof conventionaldesign would have consumed3 to 6 months forthe same.Oh man, what a magic!The workof 3 monthsfinished within %day!!Thatsoundsgreatand is cost effective too. Its win-win situation for manufacturer as well as customers.

_ - -1.â A ~ S O ~ UW.~ R. eleUurDurp,- DesignRelative design ~bsolu&design1) Relative design:In industry usuallybasic design of a category of componentsremains sameover the years. Say for example existing vehicle power is to be increased from 100 hp to 125hp. Basic design (shape and concept) of components would remain same with minor changeslike scaling the basic design in appropriate proportions. Suppose CAE model & analysis of theprevious version which is performing satisfactorilyin the field, is available. If Analysis of newdesign (using same element type and size with appropriate loads)shows stress magnitude lessthanorequal topreviousmodel thenit couldbe concluded that the new upgradeddesignis alsosafe & will perform satisfactorily.This way one can also avoid test correlationfor new model.Some timestoo muchemphasisis givento test correlation& accuracy of the FE modelto minutelevel.Too much attention to capture each and every detail complicatesFE modeling & analysisunnecessarily (suchas modeling bolt threads when main objective is component design ratherthan bolt, definingnon linearcontactswhen simplelinearconnectioncanworkordensemeshinthe nameof accuracy without due consideration for hardware and softwarecapabilities etc.).Keepingthethingssimple, sticking to thebasics, useof commonsenSe&engineeringjudgment is th1basisof RelativeDesign -21 narojute design:This apprudLii 1s usriui w!irii the piuuu~Vcomponenits designed for thefirst time'i.e. innovativedesignand no previousrecordof similar product is available.The designengineer himseif not very sure about boundary conditions & various load cases. CAE results ofsuch a design must be verified properlyvia testingandFE model should be correçted in case ofvariationin the test & FEA results.\"Finite Element Analysis has minimlzedtesting requirementbut it will be wrong to assume thatit has or will totally replace testing.\"In fact FEA andTestingare not rivalsbut friends. One thing is for sure that al1the good designsare product of excellent coordination betweentestingand CAE.ACAE engineer depends on testing for following reasons1)Input data for CAE (data acquisition)2) Validation of the CAE resultsThough in industrythere are CAE experts who just by looking at FE results can tell whether thedesign is acceptable or not and in 99% cases their statement matches with the test results. Itis possible for them because of their past experience say for example someone is analyzinggear box for 15 years. In past he has calibrated many models and seen how it fails in the field.But believing words of a novice CAE engineer who has no prior experience or just becausethesoftware used is impressive and very costly would be a big mistake.

Past, Present a n d Future of FEA1906 -Civil Engineering applications, Structuresanalysedby l - d beams fiand calculationsJ.1909 - Ritz: Variational Method1915 -Galerkin : Weighted residuals1940's -Courant, Prager & Synge:Mathematicalfoundation for present form of FEA-1950's Argyris, Kelsey, Turner : Direct continuum elements, Aerospace industry engineersformulated stiffnessequations. 100 dofs problem was supposed to be very largeat that time.1960 -Ciough coined the narne FiniteElernent Method.Late 60's - Mechanical industry recognized FEM as useful tool for solving real life problems.Many of the presentlypopuiar FEA softwares were launched in the market.1980's - Graphical& computationaldevelopment.1990's- Emergence of low cost, powerful PC work stations &FEA adopted by mid & small scaleindustriesYear 1961 1966 1971 1976 1986 2006Papers 10 134 844 7,000 20,000 infinitel2.2 PresentStatus of FEM as on Today as post graduate course only at few FEA software types ofjob orders universities 1. NewDesign 1. Proprocesring 2. Costcutting1 - Solid modeling Optimization 1995 and onwards: lntroduced at graduate level. - MeshingI - 8oundaryconditions Theory courses mainlydeals with 1. Various methods to derive [KI 2. Assemblvof M 3. Postprocelring -Result interpzetatiProgrammingIanguages used tor most commercial softwaresare Fortran and C++.

fast, PresmtandFutureof FEA 2.3 TheoreticalFiniteElement Analysis Till 7995 FEM was offered as post graduatecourse only at few universitiesin India. Theory courses deaismainly with 1) Various methods to derivestiffness matrix [KI 2) Assembly of [KI 3) Solution techniques Element stiffnessmatrix Stiffnessmatrixislikepasswordor PIN to thetreasuryof FEA.[KIstiffnessmatrix,thecharacteristic property of element dependson geometry as well as material. If you refer to any theoretical text book on FEM, most of the volume is devoted for methods describinghowto determine [KIfor a given shapeof element&its assembly.Thereare3 methods for deriving [KI. 1) Direct Method - Easy to understand but difficult to program. It is not used for commercial software codegeneration. 2) Variational Method - Rayleigh- Ritz Method : difficult to understand, moderate from code writing point of view. 3) Weiahted Residual Method - Galerkin Method : difficult to understand but easy from programmingpoint of view.This method is used in most of the commercial softwares. What i s stiffness ? StiffnessK= F (Force)/ D (Displacement) Stiffness is defined as force required to produceunit displacement. Itdepends on Geometry as well as Materialproperties. Steel Çonsider 2 rods of identical geometry but different materials Say Steel &Aluminium.Which one is more stiffer ? && becauseof its higher elasticmodulus ( For same force:6s,a,<66,)16

Now consider, same material(steel) but different area of cross section.In thiscasetherod havingmore area of d s is more stiffer.Tensilestiffness = Y_,\" = AVLBending stiffness for cantilever beam = K,, = 3 El 1L3Torsionalstiffness= =GJ/ LIra pentagon or hexagonor any arbitrary shape elementpossible?Why in FEM wealways seeonly limitedregularshapeslike quad,tria, LttL, wedge&tetra only, isit not possibleto use other shape of elements 7Finite Element started with Trianaular (tria) element. Later Quadrilateral (quad) element wasformulated. Theoretically one can use any arbitrary shape element. Only thing required is toknow the stiffness matrix. But in practice since we are able to mesh any kind of geometry rightfrom structural components to aerospaceapplications with available5 or 6 basic shapes, needfor other shapesis not reallyfelt.If it is so then why quad element was introduced at all, was it not possibleto mesh and continuewith only triangular shape? The need for quad element was felt from result accuracy pointof view. Trianguiar element being stiffer results in less stress & displacement. Generally a tprofessionalleveltria-quadcombination(mixed)mesh is used.Trias are avoided in critical areasand restrictedto 5%.Having said that, it would be appropriate to mention about development related to polyhedralmesh; polyhedral mesh is in research phase at the moment and some of the CFD softwareslike Star CCM + have already started providingpolyhedral meshing options. Typical shapes ofpolyhedralelements are hexagonal or octagonalfor 2-d elements and 10,12 or 14 faces for 3-delements.Theidea ofpolyhedralmeshwastakenfrom Bee'shoneycombstructureandformationof special structure onTortoise's back.

Past, Presenf ondFurureofFEA Why number of tria elements are restricted t o 5 96& avoided ln critical areas?- Quad element is more accurate than triangular element (due to better interpolationfunction). iTria element is stiffer than quad, results in lesser stress & displacement if used in criticallocations.Consider any standard problem of plate vibration for which analytical answer of naturalfrequency is known. Create two Finite Element models (femodels) based on only triam)elements and only quad elements (sameelement length).Tria mesh will show higher valueof natural frequency (wn = & wlll deviate more from the exact answer,2.4 Software Based FEMFor usingany commercial software there are 3 steps-1) Preorocessing-Consumes most t h e out of the three steps.2) Processinq(or solution) - just click on\"Solve\"& it's the software's turn to do the job3) Post urocessinq-Result viewing & interpretation-Step1 Pre processing a) CAD data b)Meshing (or discretizationto convert infinitedof to finite one) C)Boundary conditionsIn early stage of industrial applications of FiniteElement Analysis, CAD, meshing & analysis al1used to be carried out by a single engineer only. Soon it was realizedthat separationof the jobs&forming dedicated subgroups i.e. CAD group, Meshing group & Analysis orcalculation group isnecessaryfor optimum output and efficiency.CAD &Meshing -There are specialized softwares for CAD, Meshing & Analysis. CAD & meshingconsumes most of the t h e . For example - Typical time for a single person to mode1 (CAD) 4cylinder engine block i s 6 weeks & for brick meshing 7 weeks (For tetra mesh about 2 weeks).BoundaryConditions -Consumesleast timebut it is the most Importantstep (typicallyapplying10 load cases is about 1 day job). 3 months hard work of meshing & CAD data preparation ofengine block would be undonein just 1 day if boundaryconditions are not applied properly.Aftercompletionof preprocessingLe.CAD, MeshingandBoundaryconditions, softwareinternallyforms mathematicalequations of the form [FI = [KI [61.Step 2 - Processing or SolutionDuringpreprocessinguser has to work hardwhile solution step is the turn of computer to do thejob. User has to just clickon soive icon & enjoy a cup of tea! lnternally software carriesout matrix

formations, inversion, multiplication& solutionfor unknown e.g. displacement& then find strain&stress for static analysis.Today we are using FEA just because of availability of computers. FEM has been known tomathematicians & engineers right from late 50's but since solving so many equations manuallywas not possible, in true sense FEA got recognition only after emergence of high capaciiycomputers.-Step 3 Post processingPost processing is viewing results, verifications, conclusions & thinking about what steps coutdbe taken to improvethe design.Considera simple example which involvesal1the above SepsProbably at the moment you are sitting on a chair or stool & reading this book. In this examplewe will analysethe stool itselffor stress & displacementfor aloadof 200 kq- (assumingit could beused for siting as wellas supportingany object up to max. 200 kg wt.)1. CAD modelII,Meshing and BoundaryConditions flement type-Brick 8 Noder= 17950 Elemenrs= 13392 'X IzVery small length spring elements created a t leg base, stiffness in x and z direction as per F=p N

Part, Present andFutureofFEA (p=friction betweenlegs and ground)and along vertical (y)axisvery high stiffness. At the spring end al1translations Le.U, U, Uz=Oor fixed. III.Solution & Postprocessing Type of analysis - Linear Static, Material-Steel No. of equations or unknowns = no. of nodes 'dof per node = 17950 * 3 = 53850 (All the solid elements have 3 dof Inode) Max. stress (4.68 N/mm2)< < yield stress (250 N/mmz). Analysis conclusion The stool i s over designed. There is scope for cost reduction by changing cross section of leg, thickness of top plate etc. Material could be changed to low cost alternative(having yield stress >6 N/mm3 Max. stress at the sharp corners could be reduced by providing smooth fillet or addition of stiffeners in the localized region. 2.5 Pradcal Applicationsof FEA CAE group responsible for FEA related activities, receive following types of job orders - Newdesign Optimizationor cost cutting projects Failure analysis

New Design:New or innovativekind of design i s a real challenge for designengineer. In automobileindustry,when new version of existing vehicle is launched (upgradedversion), most of the componentsare quite similar to the existing one (scaledproportionately).lnnovative kind of components areusuallynot more than15 96.Atleast initial run ofthis category ofjob i s easyforCAEengineer.Sit with design&testengineertodecideboundaryconditions and then run theanalysis.Real work startsonly when the prototypeis prepared and test & FEA result correlation process is initialized. After achieving correlationvarious permutations and combinations could be carried out to make the product better andoptimum from cost as well designpoint of view.Costcutting or optimization projects:At the moment lndian Auto sector is experiencing a boom but from 1995 to 2003 there wasa slack. During the period most of industries were busy with cost cutting measures for theirsurvival.In lndian markettill late80%samekind ofvehicleswererunning on theroad with outany change(do you remember old designs of lndian cars and heavy, bulky & noisy trucks). These designswere transferred to lndian companies in 50's & 60's from their overseas collaborators (mainlyAmerican & Europeans). Design philosophy was different at that time i.e. design for infinitelife. But slack in the market and emergence of new tools like CAD/CAM/CAE, new cost efficientmanufacturing techniques and availability of low cost materials forced auto manufacturers toadapt to the changing circumstances via optimization of design.Suppose selling price of the product is Rs. 100 & actualmanufacturing cost is Rs.60. Reduction ofcost even by say Rs. 1 by usingCAD / CAM / CAE (reductionin thickness, change in materialetc.)will result in lot of profitfor the company. 1 Earlierdaysdesignphilosophy was - Design for inhnitelife 9 Survivalfor years > Heavy & overslzedcomponents 9 Noisy &rough operations b Highcost -a days designphilosophyis Design for warranty life 9 Use & throwconcept 9 Lifejust greater than warrantyoffered by company 9 Additionalsourœ ofincome; aftersales services Light weightcomponents CLowcostWarranty : Every company offers warranty on its product. Company is under legal binding toreplace the componentfailing within warranty period, free of cost. Itis not only additional cost

Pnst, Present andkiture ofFEA which is incurred but also bad name to the product and company. Probable reasons of failure improper process Manufacturing defects Faulty material Environmentai conditions Weather Road condition Design abuse Genuine Design problem Warranty yard meetings & throwing the bal1i n other's court : Every medium or large scale industry has a warranty yard (a separate place where failed components are displayed and systematic record is maintained). Once in a month managers from different departments meet at warranty yard to discuss about failed components and corrective actions. Imagine a hypothetical meeting of different departments at warranty yard as an independent observer. Say current meeting is to discuss large number of warranty claims for some xyz component. In lndustrial world, it's an open secrete, nobody is interested in taking responsibility for failures and finding the remedy on their own. lnstead we play the game as per the rule : \"Always be safe & throw the bal1in other departments court': Most of the time R&D and Design departments are soft target and hold responsibie for al1 the faiiures. lnside the company its Design and R&D & outside the company service engineers who are the scapegoat and takes most of the biame. Manager, Manufacturing : We are strictly following al1 the instructions as mentioned on the drawing released by design / R&D, Ican assure you that it is nota manufacturing probiem, R&D is clearly responsiblefor the failure. Manager, Purchase: We are working so hard you know! Moving around the globe to find the best quality materiai/ vendors that too at lowest possible cost as per the requirement by design 1 R&D. Manager, Quality : 1 guaranteeyou that ali the tolerances, surfacefinishes, paint quaiity etc. are as per standard. Manager, MarketingISales: Marketing peopleareborn showmanandexpert in giving speeches. Automatically leadershipof the meeting goes to them.They fire Design / R&D manager claiming that because of their poor work, marketing and sales team has to adopt to face saving tactics and manage the things diplomaticaily with dealers and customers. They Say \"our company is investing millions of dollars on Design & R&D, people are given such a handsomesalary, they are always seating (what they actually mean is sleeping!) in AC'Sin front of high capacity computers but see what is the output!\" Managers - Process, lndustrial engineering, Maintenance : Other dept. people feeling naturally happy becausethefinger is not pointed towards them, with a pieasure they join others



fast Present nndFuture ofFEA R&D submitted the CAE report, after going through the report, in the meeting other department heads just fired R&D manager saying that real life failure is at different location & your team is saying it is safe and no need of modification. Later CAE engineer was informed about al1 the proceeding & gravity of the situation. After going through failure reports & observing failed components, he visited manufacturing site and machine shop. After spending 3 days a t various locations like manufacturing, quality, warranty yard, he detected very small sudden step at the location of failure on some of the components. It was due to faulty tool settings on one of the turning machine.Therewere 8 turning machines and setting was faulty on only one of them. CAD model and meshing was modified so as to accommodate this step. Now analysis showed exactly same location of failure as per the field report i.e. at sudden step. Clearly this was n o t a design problem but problem due to defective machine setting. Climatic conditions: A road construction equipment & farm equipment accessories manufacturing Company was facing failure problems. Region wise segregation showed failures mainly from specific States i.e. mainly South lndia only. Samedesign,samecomponents working successfullyin restofthe India. This is because South lndian soi1is acidic and causes faster rusting (components are merged in mud & water most of the time). Rusting eats/consumes material and reduces thickness and life of the component. Should a CAE engineer be assigned the responsibility of rusting analysis. Could FEA help in solving rusting problem. Answer is No! lnstead a material science or chemical engineer or paint shop expert should be consulted. Since this problem is specific to a particular region.One of the solution could be to separate out batch of vehicles meant for South lndia and provide special anti corrosion primer (coating) on the components. Road conditions & limitations of manufacturing techniques: A new 2-wheeler was launched in the market by an lndian manufacturer (in collaboration with a foreign company).The design was very successful abroad, first lot of vehicles were imported from overseas and things worked wellfor a short duration. Soon manufacturing started in lndian plant and then there were many warranty claimsforchassis.kwas becauseof poor manufacturing, low quality materialand also bad condition of roads in India. It was decided to redesignthe chassisas per lndian manufacturing standards, materialand rough road conditions. CAE group carried out FEA (Static, Dynamic and Fatigue) to improve life as per the new input data and modifications proved successful. Design abuse: Design abuse means component is designed for some specific application or function but i t s been used by the customer in a different or creative way. Clients in particular in Asian countries24

are so clever that they can use the product in a manner which design engineer might not havethought about in his most creative and imaginative dreams!a.Tractor Fender (mudguard): Basic purposeof mudguard is to guard the driver against mud,but if you visit a village 3 to 4 people sitting on the mudguard is a quite common scene.Tractoris not only used for agricultural application but also for transporting people from one place toother. In developed countriesthe manufacturer i s bound to replace thefailed component free ofcost only if it was used as per given instruction and not otherwise. But in Asia, could you imaginea Companysaying village people, please do not use Our tractor mudguards for sitting purposeorinstructions like one person per fender please!What could be the remedy to above problem?Design it for 250 kg load!b. Lassi making (washing) machine : In Punjab people are fond of Lassi (specially preparedsweet butter milk). One day in a hotel, group of 25 students arrived and ordered lassi. Hotelsin Punjab usually have a electrical lassi making machine. But on that particular day hotel's lassimaking machine was out of order. Hotel owner, took stock of the situation & thought manualpreparation wouid take lot of time & these young students will become impatient & angry, butat the same time it was not wise to loose such a big order. He saw the washing machine in thebasement and shouted Eureka ! Eureka !! Washing machine also work similar to lassi machinethen why not to prepare the lassi using washing machine itself. He ordered his staff to pour alithe basic ingredients in appropriate proportion in washing machine. He started the machineand coliected lassi from outlet meant for drain (soap water). Lassi was very bubbly & tasty. Tohis surprise the group of students immediately ordered for another round & started visiting thehotel frequently. In short time the hotel became so famous for lassi that people started visitingit from even other corner of the city. Neighbouring hoteliers got jealous and got the secret bybribing the staff. Later every hotel in the region ordered same brand of washing machine andstarted using it as lassi making machine.Washing machine is not designed and made for lassie preparation and imagine it rnight havegot out of order after some time (say within warranty period). The hotelier would first clean thewashing machine perfectly and then cal1service engineer.He will abuse him using special words!and demand for immediate replacement of failed machine, without telling him the real reasonfor failure.Now during the rnonthly warranty meetings al1 the departments will point their finger towarddesign or R&D department, without actually thinking about the basic / root cause of failure.And the responsibility of the analysis will be transferred to a poor CAE engineer like you andme, supposed to solve the problem in a very short time. He will start from the basic drawing,generation of CAD model, meshing & analysis without thinking about and taking in to accountthe actual manner in which the machine has been used, and prepare and submit nice colourfulreport within the deadline .... Foilure o~iolysisolv/oyr corisunies lot of rime. Ir is respor~sibiliryof CAL engilieer & CA€ monoger to co~ivincetlie It&D/Desiyri cliief thot failure onolysis requires more t m e & insieodof storting the FEA jus! for !lie sake ofreporlsubn~issionp. /ioriry sliouldbegi~ento understarid tlieproblem ondfinding ilie rootcouse.

Post, Presentand Future ofFEA But at the same t h e there is no need to fear failure analysis problems. Failure analysis is the most challengingtype of job for any CAE engineer. The process of failure analysis and problem fixing teacheslot of things thm could neverbe learnedby just doing routinemeshing, boundary condkion and result type of activities using software. 2JFtmRreofFam Research related to solution techniques & post processing tools is more or less saturated and in future focus will be mainly towards reducing t h e , improving quality & flow pattern of mesh generated by auto meshing. Also one can expect very powerful & user friendly commands for brick meshing (hopefullyauto brick meshingtoo!). At the moment lndian companies are competent with structural analysis.In near future demand will befor high end analyses like NVH, CFD, Fatigue and Crash. For reducing meshing time apart from conventional types of elements, research is also going on about polyhedral meshing and meshless (or meshfree) analysis. 2-d hexagonal elements dividesa given surface into regionsof equal area with least total perimeter.While 3-d polyhedral elementsaremoreefficientduetomorefacessharedby neighbouringelements(tetra has4while brick has 6, typically polyhedralhas 10 and more faces). Advantageof polyhedral meshing could be described as less meshing t h e (supports automatic mesh like tetra elements) with higher accuracy(likehex elements)and that too a t less number of dofs. In short it combines advantage of tetra and hex elements. Some of the CFD softwareshave already startedproviding polyhedral meshing option. But at the moment it would be too early to answer whether polyhedral mesh would be a regular feature of structural as well other types of analysesalso. Mesh free analysis is an attempt to integrate CAD and Solution steps directly i.e. without conventional & time consuming linking step \"meshing': There are several theories coming up based on creating calculation points during CAD geometry preparation itself, using integrals based on big blocks created automaticallyby softwares and using a special methods based on FiniteDifferenceMethod. One thing isfor sure after 10to 15 years, conventionalmeshing would be either very fast and easy or otherwise there will be no need of meshing at all.

T y p af Analyses [(BriefIntroduaion)The term CAE [Cornputer Aided Engineerbrg) includes following types ofanalyses:1) Linear static analysis 6) Fatigue analysis2 ) Non linear analysis 7) Optimization3) Dynamic analysis 8 ) CFD analysis4) Bucklinganatysis 9) Crash analysis5) Thermal analysis 10) NVH analysis Software follows thir pathfor linear staticcalculation Actual strerritrain curveStress StrainLinear:Linear means straight line. o =e E is equation of straight line (y = m x) passing through origin.\"E\" Elastic Modulus is slope of the curve & is a constant. In real life after crossing yield pointmaterial follows non liner curve but software follows same straight iine. Component brake intotwo separate piecesafter crossing ultimate stress but software basedanalysis nevershow failurein this fashion. It shows single unbroken part with red colour zone at the location of failure.Analyst has t o conclude whether the component is safe or failed by comparing the maximumstress value with yield or ultimate stress.Static:There are two conditions for static analysis1) Force is static i.e. no variation with respect to time (dead weight)

Types ofAnalyses (Brieflntroduction) 2 ) Equilibrium condition - 1forces (Fx, F,, Fz) and 1Moments (Mx,My,M2)= O. FE model fulfils this condition at each and every node. For complete rnodel summation of external forces and moment is equal to reaction forces and moments. PracticalAuulications: Most commonly used analysis. All Aerospace, Automobile, Offshore and Civil engineering industriesperform linear static analysis. Commonlv used softwares: Nastran, Ansys, Abaqus, i-deas NX, Radioss, Cosmos, UG, Pro- Mechanica, Catia etc.3.2 Non Linear Analysis t L 7 \"\"Material Gap ekmentr & Large Conlacl rirnulaticmDeformatlm Within Elanicümn'E' hep BeyondBastic Limtt 'E' 'Non metals' (Progresrive)daformationof 'met& material a t constant stress. -Longlime pracerr. Force (stress)Vs. Displacement [strain) curvenon linear (polynomial). Stiffness [KI is function of displacement [dl (for linear analysis [KI is constant, independent of id11 Deals with true stress & strain (unlikeengineering stress & strain in linear static analysis)A. Materialbasednon linearity:Wlthln E (non-metal) BeyondE (metals)Stress-strain diagramalong with hardening rulefor the materialis required as input data.

Metallicnonlinearitvaoolicatlons: Automobile, Aerospace, Ship industries.To know exact valueof stress / strain when it crossesyield point. For low cycle fatigueanalysis this data is consideredas input for strain life approach.NonmetallicnonlinearitvauulicationrAutomobile, Aerospaceindustry, analysisof rubber, plastic,asbestos, fibre components. - At elevated temperature even small magnitude force if kept applied over long timeperiod (for months and years) would causes failure. Applications - Nuclear / Thermal powerplants, Civil engineering etc.B. Geometricnon linearityThough component is within the elastic limit but due to very large length even smallforce causes large deformation. Regular formulas of strength of material like deflection6 = PL3/3 El, not applicable as these are basedon small displacement assumption.C. Contact - To simulate physical gap between two parts e.g. bearlng and shaft or press fitbetween two cylinders etc.Cornmonlvusedsaftwares:Abaqus, Nastran, Ansys, Marc, Radloss, LS Dyna etc.3.3 Dynamic Analysis 7 Forced Free l 1 1 1 Résponsetothe ExternalexcitationNatural frequencyThe frequency with C Transient reswnse ndom vibrationswhlch any oblect will Freqyenwreswnrr:vibrate if disturbed& Random nature of Frequencydomain, Timedomaln, loading, usuaily input inltsOwn wit'hIbourtaatOneny Steady state slnusoidalexternal force. excitation Arbitrarybut welldefine the form of PSD (Power Limitedm linear elastic excitation Spectral Density) structures Constant acceteration Rotatlng machinery, unbalancedtyres or force at a given Helicopterblade fiequency, Road excitationsetc.x = d2x ldt2 = acceleratlon, x = dxldt = velocity, x= displacement

Types ofAnalyses (Brieflntroductionl[Ml x = O, [Cl x = O, [KI & F(t)= Constant - Linear Static[Ml 2 = O [Cl = O, [KI is a function of Iul, F(t)= constantF(t)= O, [Cl x = O and [Ml, [KI= constant - Non Linear StaticAl1the term in above equation are present - Free Vibration - ForcedVibrationPractical au~licatlons:Natural frequency is characteristic and basic design property of anycomponentwhilefo~edvibrationsisapplicableforcomponentssubjectedtoforce/displacementIvelocity /axeleration varying with respect t o tirne1frequency.Common/vusedsoftwares: Nastran, Ansys, Abaqus, Matlab, 1-deasNX, Radioss etc.3.4 Linear BuddingAnalysis Applicable for oniy compressiveioad Slender beams &sheet metal parts Bending stiffness <<<Axial stiffness Large LateraldeformationO u t ~ ufrtomsoftware: Criticalvalue of load.Practlca1a~~lications:Comrnonulysed forcivii engineering appiications. Mechanical engineeringappiications - vacuum vessel, long gear shifter rod analysis etc.Commonlvusedsoftwares: Nastran, Ansys, Abaqus etc.

3.5 Thermal Analysis +m&dl*L(T*a(hl Convectlon RadiationSteady State Unrteady State t NaNral Conductlon ConvectionConductfon Fwced I convectionPracticalo~alicationsE: ngine, radiator, exhaust system, heat exchangers, power plants, satellitedesign etc.Commonlvusedsoftwares: Ansys, Nasttan, Abaqus, 1-deasNX etc.3.6 Fatigue Analysis Calculations for lifeof the structure when subjected to repetitive load. 5 - N curve (alternating stress vs. cycles) or E - N (alternating strain vs. reversals) is the base for fatigue calculations (like O - Ediagram for static analysis). Low cycle Hlgh cyclefatigue fatigue Alternating StressDamage= n/N EndurenceFactor of Safety (EFS)= = No.of cycles appliedllife Endurance rtrengthl FE stress ...low cycle fatigue ...high cycle fatigueDarnage < 1 safe EFS < 1 failDamage > 1 fail EFS > 1 safe

Types ofAnalyses (8riefIntroduction) Static and dynamic analysis can not tell how long the component will survive for given load. Also there is n o consideration for factors like surface finish, heat treatment, decarburizinq, alloyinq elements, realistic representationof spot & arc welds. Practicalo~~licationsA:pplicable t o al1 the components subjected t o dynamic loading i.e. ail automobile components. Fatigue accounts for 90 % o f failure in the real life. Common!vusedsoftwares: MSC Fatigue, FEMFAT, FE SAFE, LMS etc. 3.7 Optimization Geometrical Parameters Shape Optimization- Optimization for geometry - Usually restricted to onlyparameters, work well atindividual component levei linear static & normal moderather than complicated dynamics.assemblies. - Good tool for innovative- Software can not add or kind of products (whenremove geometry on its own initial shape to start with isbut can play with only pre not known or fixed).defined parameters withinspecified limits. - Software can give hint for addition or removal of geometry.Practicala~ulications:Applicable t o any component which is over or under designed.Cornmon1.vusedsoftwares:OptiStruct,Tosca. Nastran, Ansys etc.3.8 ComputationalFluid Dynamics (CFD)A fluid is a substancethat continuously deforms under an applied shear stress regardless of themagnitude of the applied stress. Gas and liquid both arefluid. Fluid mechanicsdeals with studyof fluid, its properties and behaviour.

Fluld Moehanln I Fluid Statics (Hydrostetics) Fluid DynamicsFluid at rest Fluid in motionEasy from calculationpointofview - Cai~ulationasre more cornplex Variation wrt tirneconsideredNOvariationwrt the, iess realisticresults Non-linearequationsLinear equationsCivil engineering: Dam design Aerospace, automobiie&valvesComputational fluid dynamics (CFD) is the branch of fluid mechanics which uses numericalmethods to analyse fluid dynamics problems. It is based on Navier -Stokes equations (Mass,Momentum and Energy conservation equilibrium equations). 1 1 1DimensionsViscority T'urbnuinieanrt' Comoressibilitv VelocitvPracticalaoulications: Drag prediction and Streamlining of a car, combustion chamber design €0check an optimum fuel -air mixing, Aeroplane design etc.Commonlvusedsoftwares:Fluent, Star CD, CFX, CFDExpertetc.

Types ofAnalysesfBriefIntroduction) 3.9 Crash Analysis I uccupanr aarery A+c&mS:B(arkbaxd m ak ci&, niab(lephone,Common~usedsoftwareLrS-Dyna, Pamcrash, Radioss, Abaqus-Expiicit, Madymo etc.3.10 Noise Vibration and Harshness, NVHUncoupled Problernr 1 CoupledOrVibroacousticr PrablemrNVHproblemsarebroadlyclassifiedinto stmctureborneandairbornesounddiscussed in detailsin the NVH chapter.Practical aoolications: Computing the sound pressure ievels is of utmost importance toautomobile,aeroplaneand aerospacedesigners as customers always prefer a low noise level.Computing the response a t the driver'sfeet (brake pedal ), mirror mounts, steering columnand seats plays a crucial role as the driver must be comfortable. Also predicting the soundqualityand radiation a t a certain distance from the car is important.Commonlvusedsofîwores: Sysnoise, LMS -Virtual Lab, Matlab etc.

I Ba,sicsot Statics and Strength ot Materials'4.1 What k %res?Stress - Interna1resistanceto external force. ln simple words it is defined as - force per unit area(O=FIA). Mathematicallystress at a point is defined asLim O =FlnAAA-f OStress is a surface or area based property. It could be determined at any point by assumingAA +0.SI units of stress is Nlm2.But it results in very small numerical figure & hence Nlmm2 (or Mpa,Mega Pascal) is more popular among CAE engineers.Consider a freely lying pen on table. Lift the pen and hold it in your hand softly. As per thedefinition of stress, force has been applied also there i s area or volume of the object.What do you feel, will there beany stress i n the pen?Please think about the answer and do not hurry to turn the page.