00 Finite To Infinite ....Sa.nj.ee.v.V Bedekar San-jay 5 Deshpande Anand NThite ..First Edition -Nitin 5 Gokhale -San jay 5 Deshpande -Sanjeev V Bedekar -Anand N Thite Finite To Infinite, Pune vPublished by: Finite To Infinite 686, Budhwar Peth, Shivganga Chambers, Near PrabhatTalkies Pune -411002. Maharashtra, India. Tel: 0091 -20 -24454981 Mobile: 0091-9423571952 E-mail: finite@vsnl.com Website: www.finitetoinfinite.com Copyrights @2008 by FiniteToInfinite Allrights strictly reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted 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 of this book are vested solely with the publisher. First Printing: January 2008 Images sourced from AltairCalendar 2005, 2006, 2007 and 2008 are copyright of Altair Engineering, India and have been used with prior consent. Commercial software names, company names, other product trademarks, registered trademark logos are the properties of their respective owners. Price: Rs. 650/-Disclaimer: Everyefforts have been made to keep the book free from technicalas wellas other mistakes. However, publishers and authors will not be responsible for loss,damage in any formand consequences arisingdirectlyor indirectlyfrom the use of this book. Our Bankers: Bankof Maharashtra, Shaniwar Peth Branch, Pune Printed at: KJoshi &Co.,1745/2, Sadashiv Peth, Near Bhikardas MarutiTemple, Pune -30 Cover Designed by: Mooon Design Studio Composed by: Shailesh Bhingare viPreface -DrPeterFischer Finite Element Analysis... a complicated mathematical theory for computer specialists; ... or an indispensable tool for all-day industrial product development? Finite Element Analysis... a myth which allows to solve most of the worlds technical problems; ... or an analysis method which produces just results that ':.. have to be checked by further testing ...7" All 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 all. These equation systems can then be solved by any numerical and computer aided technique. The method of Finite Elements was developed at perfectly right times: growing computer capacities, growing human skills and industry demands for ever faster and cost effective product development made it a synonym for high-tech engineering and nearly unlimited possibilities of the technical community. In this context, the name "Finite Element Analysis" is nowadays commonly used for a wide range of computation techniques in engineering practice. viiThis book summarizes the most important techniques of current Finite Element applications. It is dedicated to the needs of practising engineers and provides clearly structured, well understandable information for managers, design &test engineers, students and all interested technicians. Basing on demonstrative examples the fundamental theory is summarized. The focus is to explain 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 successful projects 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 will provide appreciation between various disciplines working together in engineering projects. But I wish, that this book will be also a seed for better understanding between all people working for common objectives of our lives, societies and cultures, our world and our spirits. -Dr Peter Fischer Managing Director DTECH STEYR -Dynamics & Technology Services GmbH Austria viiiFo rewa rd -Mr Ashok R Sona/kar I have great pleasure and feel honored in sharing my thoughts with the readers through this preface, because of following reasons -1) This is a unique book of its kind in the sense it is combining many years of actual hands on experience with adequate coverage of theoretical treatment. 2) I personally know the authors Nitin Gokhale, Sanjeev Bedekar, Sanjay Deshpande and Dr Anand Thite. We have worked together in research and development for some years and I had many occasions to discuss the problems related with Finite Element Analysis. 3) This book is going to be a standard reference for the CAE(Computer Aided Engineering) engineers for many years to come. When we started the CAE DEPARTMENT in our company in 1995 (we were all new to this technique), arranged for intensive training of a specially selected group of highly talented young engineers. The training was imparted by many experts of international repute and also by university and liT professors. The authors were in this group. The group showed outstanding results which surprised even the teachers. Very quickly they could grasp the fundamental concepts, get a deep insight and develop a feel of FEA (which is very essential for one to be really competent). They had enough confidence to take a plunge in this very new field (it was not even known widely in India in those days) by starting their own company solely to provide this technology service and training to engineering industry globally. They have not looked back since. It is this feel and the sixth sense which they have sincerely attempted to pass on to the serious students through many examples, thumb rules, empirical rules ete. These are generally regarded as professional secrets which most ixexperts are not willing to share. This is that knowledge which (in the true Indian style) the disciples learn at the feet of their 'GURU' From this point of view also, I 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 all available technical literature on FEAbut alsoassimilating it and putting it to test by taking newer and newer (more and more formidable) challenges. They must certainly have faltered many a times. Failures come only to those who are courageous enough to venture in to new lands. They have learnt a lot from each and every mistake and sprang back with double the energy and enthusiasm to achieve and conquer even more exalted heights. They have very sincerely documented these mistakes and 'the lessons learnt' and included in this book for the benefit of devoted students. This -in my opinion-one of the most valuable feature of this book which sets it apart from most other books on the subject. This is not only a book which adds to your knowledge and makes you aware of new technology but it is also a practical guide which tells you about the nuts and bolts of this technique and tells you which mistakes you should guard against what are the tricks of this trade and where are the pitfalls. I wish a most enriching learning experience to all those who want to take a dip in this 'Gyan kund' (source of knowledge). -Ashok RSona/kar R & D Head (Retired) Mahindra &Mahindra Ltd. FES -Tractor Division xWhy the book has been written ... FEAis 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. Often professionals realize that they are 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 book shelves... Authors of this book are from liT's & IIScand after joining the industry realized gap between university education & the practical FEA. Over the years they learned it via interaction with experts from international community, sharing experience with each other and hard route of trial & error method. The basic aim of this book is to share the knowledge and practices used in the industry with experienced and in particular beginners so as to reduce the learning curve and avoid reinvention of the cycle. Emphasis is on simple language, practical usage, minimum mathematics & no pre-requisites. All 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 Dee. 21, 2007 xiAcknowledgement Thanks to the teachers Thanks to co-authors for their contributions CFD Non-linear analysis Crash Analysis Thermal Analysis NVH Experimental Validation and Data acquisition Thanks for image contribution Special Thanks Thanks to softwares companies Altair Engineering UGS FEMFAT Thanks to colleagues and students Thanks to family members Thanks for painstaking DTPefforts Thanks for Cover Design &Book Layout Thanks to printer Thanks to our bank Helmut Dannbauer, Dr Peter Fischer, Dr P Seshu, Dr Vijay Ukadgaonkar, Dr S KMaiti Sanjay S Deshpande Sanjay S Deshpande, Chaman Lal Sahu Sanjay S Deshpande, Rajesh S Koli Sanjeev VBedekar Dr Anand NThite Prashant R Pawar, Dr Anand NThite Altair Engineering, Apollo Tyres Ltd., ARAI, Ashok Leyland, Bajaj Auto Ltd., BHEL, Bharat Forge Ltd., DOW India, Emerson Climate Technologies, Engineering Center Steyr, Lear Corporation, L&T Ltd. (Switch Gear Div.), Maruti Udyog Ltd., Mahindra &Mahindra Ltd. (Tractor Div.), Mahindra &Mahindra Ltd. (Automotive Sector), Piaggio Vehicle Ltd., Tata Motors Ltd., Tata Johnson Controls Automotive Ltd., TVS Motor Company Ltd. Rajneesh Shinde, Nelson Dias, A. R.Sonalkar Nitin Kshirsagar, S. R. Marathe M. R. Saraf, VijayVPatharkar Rohit Sadalge, AmalrajTatapudi, Jagdish Tahalyani, Sujatha KG Nawdeep Puranik, KaushikChoudhuri AxelWerkhausen, Eberhard Dutzler Mandar Kulkarni,Tushar Akolkar,Sachin Mate, Manoj Gothe, BalajiRajmane, Shakti Chavan, Jitendra Pawar, Sachin Dani, Nitin Karhade, DS Bhalerao, Prasanna Shanbhag, Parag Shimpi, Prashant Khedkar, C.L.Patel, AjaySohani, Swapnil Wadkar, Rahul Pardesi, Santosh Belure, Jitendra Chaugule, Shrikant Sheodey Parents and specially to brother Sandeep Shailesh Bhingare Mooon Design Studio 'K.Joshi &Co:, AnilJoshi and team MKDeval,P S Bagade, SSDeo Bankof Maharashtra, Shaniwar Peth Branch xii Thanks to all who have helped directly or indirectlyContents 1. Introduction to FiniteElement Analysis 1.1 Methods Solve any Engineering Problem 1.2 Procedure for Solving any Analytical or Numerical Problem 1.3 Brief Introduction to Different Numerical Methods 1.4 What is DOF 1.5 Why do we Carry Out Meshing, What is FEM 1.6 Advantages of FEA 1.7 Design Cycles 1.8 Absolute vs. Relative Design 1.91s FEAa Replacement for Costly and Time Consuming Testing 2. Past, Present and Future of FEA 2.1 History of Finite Element Method 2.2 Present 2.3 Theoretical Finite 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) 3.1 Linear Static Analysis 3.2 Non Linear Analysis 3.3 Dynamic Analysis 3.4 Linear Buckling Analysis 3.5 Thermal Analysis 3.6 Fatigue analysis 3.7 Optimization 3.8 Computational Fluid Dynamics 3.9 Crash Analysis 3.10 Noise Vibration and Harshness, NVH 4. Basics of Statics and Strength of Materials 4.1 What is Stress 4.2 Types of Stress 4.3 Types of Forces 4.4 Types of Moments 4.5 Uniaxial Stress 4.6 Bi-axial Stress 4.7 Tri-axial Stress 4.8 What is "I"Area Moment of Inertia and "J"Polar Moment of Inertia 5. Introduction to Meshing 5.1 Why do We Carry Out Meshing 5.2 Types of Elements 5.3 How to Decide Element Type 5.4 Can We Solve Same Problem Using 1-d, 2-d, 3-d Elements 5.5 How to Decide Element Length 5.6 How to Start Meshing 5.7 Meshing Techniques 5.8 Meshing in Critical Areas 5.9 Mesh Display Options 6. 1-DMeshing 6.1 When to Use 1-d Elements 6.2 Stiffness Matrix Derivation 6.3 Stiffness Matrix-Assembly of Two Rod Elements 6.4 Beam Element 6.5 Special Features of Beam Elements 7. 2-DMeshing 7.1 When to Use 2-d Elements 7.2 Family of 2-d Elements 7.3 Thin Shell Elements 7.4 Effect of Mesh Density in the Critical Region 7.5 Effect of Biasing in the Critical Region 7.6 Symmetric Boundary Conditions 7.7 Different Element Type Options for Shell Meshing 7.8 Geometry Associative Mesh 7.9 Quality Checks 7.10 Other Checks for 2-d Meshing 7.11 How Not to Mesh . .... ... xiii8. 3-DMeshing 8.1 When to Use 3-d Elements 8.2 DOFs for Solid Elements 8.3 Tetra Meshing Techniques 8.4 Quality Checks for Tetra Meshing 8.S Other Checks for Tetra Meshing 8.6 Brick Meshing 8.7 Brick Mesh Quality Checks 8.8 Other Checks for Brick Meshing 8.9 How Not to Mesh 9. Special Elementsand SpecialTechniques 9.1 Connection of Solid Elements with Beams and Shells 9.2 Linear to Parabolic and Brick to Tetra Connection 9.3 Hybrid Meshing (Hex-Pyram-Tetra) 9.4 GAP Element 9.5 Mass Element 9.6 Spring and Damper Element 9.7 Rigid & Constraint Elements 9.8 Simple Linear Static Analysis Techniques to Simulate Contact 10. Weld, Bolt, Bearing and Shrink Fit Simulation 10.1 Welding Simulation 10.2 How to Model Spot Weld 10.3 How to Model Arc Weld 10.4 Practical Considerations for Welded Joints 10.5 Bolted Joint 10.6 Bearing Simulation 10.7 Shrink Fit Simulation 11. Material Properties and Boundary Conditions 11.1 E,G &u 11.2 Material Classification 11.3 Material Properties 11.4 Boundary Conditions 11.5 How to Apply Constraints 11.6 Symmetry 12. Linear Static Analysis 12.1 Definition 12.2 While Starting any Finite Element Analysis Project 12.3 How to Check Mesh Model Submitted by a Vendor or Colleague 12.4 Design Modifications Based on Linear Static Analysis: A Case Study 12.5 Linear Static Solvers 12.6 Solution Restart Method 12.7 h-element vs. p-element 12.8 Sub-modeling 12.9 Linear Buckling Analysis 13. Non Linear Analysis 13.1 Introduction 13.2 Comparison of Linear and Nonlinear FEA 13.3 Types of Nonlinearity 13.4 Stress-Strain Measures for Nonlinear Analysis 13.5 Solution Techniques for Nonlinear Analysis 13.6 Issues Related to the Convergence of Newton Raphson Method 13.7 Essential Steps to Start with Nonlinear FEA 13.8 A General Procedure for Nonlinear Static Analysis Project 13.9 Exercise Problem 14. Dynamic Analysis 14.1 Why Dynamic Analysis 14.2 Static Analysis vs. Dynamic Analysis 14.3 Definitions 14.4What is Difference Between Time Domain and Frequency Domain 14.5 Types of loading 14.6 Simple Harmonic Motion 14.7 Free Vibration 14.8 Free -Free Run 14.9 How to Avoid Resonance 14.10 Damping Consideration 14.11 Forced Vibration 14.12 Single DOF System, Frequency Response Analysis 14.13 Single DOFSystem, Transient Response Analysis 14.14 Dynamic Analysis Solvers 14.15 Two DOFSystem, Frequency Response Analysis Base Excitation 14.16 Bracket, Transient Response Analysis (Short Duration Force) 14.17 What is PSD(Power Spectral Density) 15. Thermal Analysis 15.1 Introduction 15.2 Conduction HeatTransfer 15.3 Steady State Conduction 15.4 Unsteady State Conduction 15.5 Convection Heat Transfer 15.6 Forced Convection (Internal Flow) 15.7 Forced Convection (External Flow) 15.8 Meshing forThermal Analysis 15.9 Free/Natural Convection 15.10 Radiation Heat Transfer 15.11 Practical Application ofThermal Analysis 16. Computational Fluid Dynamics 16.1 What is CFD 16.2 Various levels of Approximations in Fluid Dynamics 16.3 Equilibrium Equations for a Fluid 16.4 The Physics of the Navier Stokes Equations 16.5 Conservation Form of Fluid Flow Equations 16.6 Integral Form of the Conservation laws 16.7 Model Equations for Convection and Diffusion: Their Mathematical and Physical Aspects 16.8 Numerical Schemes for a Model Convection Equation 16.9 Numerical Schemes for a Standard Diffusion Equation 16.10 Explicit and Implicit Numerical Schemes 16.11 Different Types of xiv III ......III IIICodes Used for CFD Calculations 16.12 DifferentTypes of Grids Used for CFD 16.13 Difference Between Meshes Used in Computational Structural Mechanics and Computational Fluid Dynamics 16.14 Strengths and Weaknesses of CFD Against Experimental Fluid Dynamics or Wind Tunnel Testing 16.15 CFD Project Tracking Sheet 16.16 Typical Applications of Computational Fluid Dynamics in Various Industries 17. Fatigue Analysis 17.1 Why Fatigue Analysis 17.2 Static, Dynamic and Fatigue Analysis Comparison 17.3 What is Fatigue 17.4 History of Fatigue 17.5 Definitions 17.6 Various Approaches in Fatigue Analysis 17.7 Stress Life Approach 17.8 Strain Life Approach 17.9 Fracture Mechanics Approach 17.10 CycleCounting 17.11 Multi-AxialFatigue 17.12 Welding Analysis 17.13 CAE(Fatigue) and Test Data Correlation 18. CrashAnalysis 18.1 Introduction 18.2 What do We solve in Structural Crash Worthiness 18.3 Transient Dynamics Solution Methodology 18.4 Increasing the speed of Explicit Methods for Quasi Static Simulation 18.5 Comparison of Explicit vs. Implicit Methods 18.6 Typical Issues in Contact Analysis 18.7 Some Aspects of Shell Element Technology 18.8 Contact Impact Algorithms 18.9 Full Dynamic /Impact vs. Quasi Static Simulations 18.10 Lagrangian and Eulerian Codes 18.11 Effect of Process and Residual Stress on Crash Analysis 18.12 Typical Application of Crash Worthiness Simulations in Various Industries 19. NVHAnalysis 19.1 Introduction to NVHConcepts 19.2 Frequency Range of FE Dynamic Analysis 19.3 FEA for Structural Dynamics 19.4 FEAfor Acoustics 19.5 Model Validation 19.6 Model Updating 19.7 Design Modification 19.8 Vibration and Noise Control 20. Post Processing Techniques 20.1 How to Validate &Check Accuracy of the Result 20.2 How to View Results 20.3 Average and Unaverage Stresses 20.4 Special Tricks for Post Processing 20.5 Interpretation of Results and Design Modifications 20.6 CAE Reports 21. Experimental Validation and Data Acquisition 21.1 Strain Gauge 21.2 Photo-elasticity 21.3 Load Cells 21.4 Torque Sensors Torque Transducers 21.5 How to Collect Force vs. Time Data (Dynamic Test) 21.6 How to Measure Acceleration 21.7 How to Measure Fatigue Life 21.8 How to Measure Natural Frequency 22. Common Mistakes and Errors 23. Preparation for Interview Abbreviations Appendix III III III 1.1I III .. xv