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1 practical finite element analysis firrt edition

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r practical finite element analysic nitin s gokhale sanjay s deshpande sanjeev v bedekar -anandn thite finitetoinfinire pune -

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pubiished by finiteto infinite 686 budhwar peth shivganga chambers near prabhattalkies pune 411002 maharashtra india tek 0091 20 24454981 mobile:0091 9423571952 e-mail finite@vsnl.com website www.finitetoinfinite.com copyrights 0 2008 by finiteto lnfinite all rights strictiy reserved no part of this publication may be reproduced stored in a retrieval system or transniitted in any form or by any means electronic mechanical photocopying recording or otherwise without the prior written permission from finite to infinite isbn 978-81-906195-0-9 the export rights ofthis bookarevested solely with the publisher first printing january 2008 iniages sourced from altaircalendar 2005,2006,2007 and 2008 are copyright of aitair engineering lndia and have been used with prior consent commercial software nanies company names other product trademarks registered trademark logos are the properties of their respective owners price us 6501 disclaimer every efforts have been made to keep the book free from technical as well as other mistakes however publishers and authors will not be responsible for loss damage in any form and consequences arising directly or indirectly from the use of this book our bankers bank of maharashtra shaniwar peth branch pune prlnted at k joshi co 1745/2 sadashiv peth near bhikardas maruti temple pune 30 cover designed by mooon design studio composed by shailesh bhingare

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drpeterfischer mikmyral a complicated mathematical theory for camputer specialists indispensable toolfor 011-day industrialproduct development finite element analysis a myth which allows to solve most of the warlds technical problems or an analysis method which produces just results that l have to be checked by further testing al1 the answers may be correct however none of the answers really describes finite element analysis properly originally finite elements were developed to approximate continuous structures by discrete equation systems that s al these equation systems can then be solved by any numericaland computeraided technique the method of finite elements was developed at perfectly right times growing computercapacities,growing human skills andindustry demands for ever faster and cost effective product development made it a synonym for high-tech engineering andnearly unlimitedpassibilities of the technical community in this context thename finiteelementana1ysis is nowadays cammonly used fora wide range ofcomputation techniques in engineering practice or an

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this book summarizes the most important techniques of current finite element applications it is dedicoted to the needs of practising engineers and provides clearly structured well understandable information for managers design test engineers students and al1 interested technicians basing on demonstrative exarnples the fundamen ta1theory is summarized the focus is to exploin those principles which have most important affects on the practical work for understanding and for interpreting the results most valuable are the guidelines tips tricks and checklists which result from long term experiences and many successfulprojects of the authors the book aims to understand finite element analysis as a computational engineering tool and to share the knowledge and experiences in this field it willprovide appreciation between various disciplines working togetherin engineeringprojects but 1wish that this book will be also a seedfor better understanding between al1 people working for common objectives of our lives societies and cultures our world and our spirits -dr peter fischer manoging director dtech steyr dynamics technology services gmbh austria

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foreward 1 have great pleosure and feel honored in sharing my thoughts with the readers through thisprefoce because of following reosons 1 this is o unique book of its kind in the sense it is combining many years of actual hands on experience with adequate coverage of theoreticol treatment 2 1 personolly know the authors nitin gokhale sonjeev bedekar sanjay deshpande and dr anond thite we have worked together in reseorch and development for some years and 1had many occasions to discuss the problems related with finite elementanalysis 3 this book is going to be a standard reference for the cae cornputer aided engineeringengineers for many years to corne when westarted the caedepartmentnourcomponyin 1995 wewereall new to this technique arranged for intensive training of a speciallyselected group of highly tolented young engineers the training was imparted by many experts of international repute and also by university ond iit professors the authors were in this group the group showedoutstanding results which surprisedeven the teachers very quickly they couldgrosp the fundomentalconcepts get a deep insight and develop o feelof fea which is very essentiol for one to be really competent they hod enough confidence to take a plunge in this very new field fit was noteven known widelyinlndioin thosedaysbystarting theirowncompany solely to provide this technology service and training to engineering industry globally they have not looked bocksince itis this feelond thesixth sense which theyhavesincerely attempted topass on to the serious students through many examples thumb rules empiricol rules etc theseore generally regarded as professional secrets which most

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experts are not willing to shore this is that knowledge which in the true lndian style the disciples learn at the feet of their guru from this point of view also 1 feel this is a rare book written with a true and sincere desire to spread knowledge in the last few years not only have they been relentlessly devouring al1 available technicalliteratureon fea but alsoassimilating itandputting it to test by taking newer ondnewer more and more formidable challenges jhey must certainlyhave falteredmany a times foilures come only to those who are courageous enough to venture in to new lands they have leornt a lot from eoch andevery mistake andsprang back with double the energy and enthusiasm to achieve and conquer even more exalted heights jhey have very sincerelydocumented these mistakes and the lessons learnt and included in this book for the benefit of devoted students this -in my opinion one of the rnost valuoble feature of this book which sets it apart from rnost other books on the subject this is not anly a book which odds to your knowledge and makes you aware of new technology but it is also apracticalguide which tells you about the nuts and bolts of this technique and tells you which mistakes you should guard against whot are the tricks of this trade and where ore thepitfalls 1wish a most enriching learning experience to al1 those who want to take a dip in this gyan kund source of knowledge ashok r sonalkar r d head retired mahindra &mahindra ltd fe5 tracfardivision

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why the book has been written fea is gaining popularity day by day and is a sought after dream career for mechanical engineers enthusiastic engineers and managers who want to refresh or update the knowledge on fea are encountered with volumes of published books oftenprofessionalsrealize that they ore not in touch with theoretical concepts as being pre-requisite and find it too mathematical and hi-fi many a times these books just end up being decoration in their bookshelves authorsofthis bookarefromiit s&iiscandafterjoining theindustryrealized gop between university education the pmctical fea over the years they learned it via interaction with experts from international community sharing experience with each other and hard route of trial errormethod the basic aim of this book is to share the knowledge andpractices used in the industry with experienced and in particular beginners so as to reduce thelearning cuweandavoidreinvention of the cycle emphasis is an simple language practical usage minimum mathematics n o pre-requisites.al1 basic concepts of engineering are included as and where it is required it is hoped that this book would be helpful to beginners experienced users managers group leaders and as additional reading material for university courses nitin 5 gokhale dec.21,2007

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acknowledgement thanks t o the teachers thanks toco-authors for their contributions cfd non-linear analysis crash anaiysis thermal anaiysis nvh experimentalvalidation and data acquisition thanks for image contribution heimut dannbauer dr peter fischer dr p seshu drvijay ukadgaonkar dr s k maiti sanjay s deshpande sanjay s deshpande chanian lal sahu sanjay s deshpande rajesh s koli sanjeevv bedekar dr anand n thite prashant r pawar dr anand nthite altair engineering apollotyres ltd arai ashok leyland bajaj auto ltd bhel bharat forge ltd dow india emerson ciimatetechnoiogies engineering center steyr lear corporation l&t ltd switchgear div maruti udyog ltd mahindra mahindra ltd tractor div mahindra mahindra ltd automotive sector piaggio vehicle ltd tata motors ltd tata johnson controis automotive ltd tv5 motor company ltd r a p e r lsninde he son l h s a r 5oiialkar i n liii krnirraoar 5 k ma~atlic m r saraf gjay patharkar thanks t o softwares companies aitair engineering ugs femfat thanks t o colleagues and students 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 branch thanks t o al1who have helped directly or indirectly thanks tofamily members thanks for painstaking dtp efforts thanksfor cover design booklayout thanks t o printer thanks toour bank

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rn 1 contents introduction to finite element analysis 1.1 methods solve any engineering problem 1.2 procedure for solving any analytical or numerical problem 1.3 brief introduction ta different numerical methods 1.4 what e dof e 1.5 why dawecarty0ut merhing what is ffm 1.6advantagesoff a 1.7 cerigncycler 1.8 absolute vs relalivedesign 1.9 ir fea a k~placcmrnt costly and timeconsuming terring foi 2 fast present and future of fea 2.1 history of finite element method 2.2 present 2.3 theoretical flnite element analysis 2.4 software based fem 2 5 practical applications of fea 2.6 failure analysis 2.7 future of fea 3 types of analyses brief introduction 31 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 vibration and harshness nvh 4 basics of statics and 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 introduction to meshing 5.1 why do we carry out meshing 5.2types of elements 5.3 how to decide element type 5a can w solve same problem using 1-d 2-d 3-d elemems 5.5 how to decide element e 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 rdd elements 6.4 beam element 6.5 speciaifeatures of beam elements 7 2-d meshing 7.1 when to use 2-d elements 7.2 family of 2 d elements 7.3thin shell elements 7.4 effect ofmesh density inthecriticairegion 7.5 effectof biaslngin thecritical region 7.6symmetrlc baundary conditions 7.7 different elementtype options for shell meshing 7.8 geometry associative mesh 7 9 quality checks 7.10 other checks for 2-d meshing 7.1 1 how not ta mesh xiil

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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 rrkk mrshquality chccir 8.8other checks for bi:ckmeshing 8.9 how nol tomeih 9 special elements and specialtechniques 9.1 connection of solid elements with bearns and sheilr 9.2 llnear 10 parabolic and brick to tetra connection 9.3 hybrid meshing [hex-pyram-tetra 9.4 gap element 9.5 masr eiement 9.6 spring and damper eiement 9.7 rigid constraint elements 9.8 simple linear static analysis techniques i o simulatecontact 10 weld bolt bearing and shrink fit simuiatlon 10.1 weiding simulation 10.2 how to 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 10.7shrink fit 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 finite element 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 caie study 12.5 linear static salverr 12.6 solution restart method 12.7 h-element vs p-element 128sub-modellng 129linwr buckling analysir 13 non linear analysis 13.1 introdcction 13.2 cun~pdriron linwr and nonlnca fea 13.3 types of nonlineariiy of anaiysis 13.5 so.utiontechniquer foi non inrar 13.4 stress strain measures for noniinea analysis 13.6 issues rrlated totheconverqenceof newton raphson method 13.7 errentiol steps i o start with nonlinear fea 13.8 i enera procedure for nonlinear static analysis l project 13.9 exercise problem 14 dynamicanalysis 14.1 why dynarnic analysis 14.2 static analysis vs dynarnic analysis 14.3 definitlonr 14.4 what is difference betweentirne domainand frequency domain 14.5 types of 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 freauencv remonse analmis 14.13 sinde dof svstern transient resoonse analvsis 14.14 ~ynainic ~nalysis solvers 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 power spectral density 15 thermal analysis 15.1 introduction 15.2conductionheattransfer 15.3steadvstateconduction is.4unsteadv state conduction 15.5 convection heat transfer 15.6 forced convection interna1 flow 15.7 forced convection external flow 15.8 meshing forthermal analysis 15.9 freeinaturai convection 15.10 radiation heat transfer 15.11 practical application ofniermal analysis 16 computatlonal fluld dynamics 16.1 what 1 cfd 162various levels of approximationsin fluid dynamics 16.3 equilibrium s equations fora fiuid 16.4the physrs of the navter stokes equations 16.5conservation farm of fluld flow equations 16.6 lntegrai form of the conservation laws 16.7 model equations for convection and diffusion their mathematical and physicai aspects 16.8 numericalschemesfor a model convection equation 16.9 numerical schemes forastandard diffusion equation 16.10 explicit and implicit numerical schemes 16 11 dffferenttypes of xiv

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codes ured farcfd caicuiationi 16.12 differenttypes ofgridsused for cfd 16.13 difference between me~hes used in comoutational stmctural mechanics and cornoutational fluld dynamics 16 14 strrngths and wraknrsws of crd agalnst exp~i~mrntai fiuid dynamks or win0 tunnrl terting 16.15 cfd projert irackiny sheer 16.16 typicdl applications of computationalfluid dynamics in various lndusbies 17 fatigue analysis 17.1 why fatigue analysis 17.2 static dynamicandfatigue analysis comparison 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 andtest data correlation 18 crash analysis 18.1 introduction 18.2 what do w v inp structural ciarh worthincrs 18.3 transmt p 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 eulerian codes 18.1 1 elkt of procerr and resldual stress on crash analyiis 18.12 typicdl application of crash worthlness slniuiations invarious industries 19 nvh analysis 19.1 introduction to nvh concepts 19.2 frequency range of f dynamfc analysir 19.3 fea e for structural dynamics 19.4 fea for acoustics 19.5 modelvalidation 19.6 modei updating 19.7 design modification 14.8vibration and noise connoi 20 post proces i ntechniques g 20 1 iow to vddate &checkarcuracy uf tne herult 20.2 haw toview herults 20.3 average and unaveiagestresses 20.4 speclaltrlckr for pori processing 20.5 lnterpretationof results and derign modifications 20.6cae reportr 21 experimental validation a n d data acquisition 21.1 straingauge 21.2 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 measure fatigue i.ik 21.8 how 10 mrasure nawral freqiiency 22 common mistakesand errors 23 preparation for interview abbreviations appendix

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