Design and Analysis of Composite Structures for Automotive Applications Automotive Series Advanced Battery Management Technologies for Electric Vehicles Rui Xiong, Weixiang Shen Noise and Vibration Control in Automotive Bodies Jian Pang Automotive Power Transmission Systems Yi Zhang, Chris Mi High Speed Off-Road Vehicles: Suspensions, Tracks, Wheels and Dynamics Bruce Maclaurin Hybrid Electric Vehicles: Principles and Applications with Practical Perspectives, 2nd Edition Chris Mi, M. Abul Masrur Hybrid Electric Vehicle System Modeling and Control, 2nd Edition Wei Liu Thermal Management of Electric Vehicle Battery Systems Ibrahim Dincer, Halil S. Hamut, Nader Javani Automotive Aerodynamics Joseph Katz The Global Automotive Industry Paul Nieuwenhuis, Peter Wells Vehicle Dynamics Martin Meywerk Modelling, Simulation and Control of Two-Wheeled Vehicles Mara Tanelli, Matteo Corno, Sergio Saveresi Vehicle Gearbox Noise and Vibration: Measurement, Signal Analysis, Signal Pro- cessing and Noise Reduction Measures Jiri Tuma Modeling and Control of Engines and Drivelines Lars Eriksson, Lars Nielsen Advanced Composite Materials for Automotive Applications: Structural Integrity and Crashworthiness Ahmed Elmarakbi Guide to Load Analysis for Durability in Vehicle Engineering P. Speckert Design and Analysis of Composite Structures for Automotive Applications Chassis and Drivetrain Vladimir Kobelev Department of Natural Sciences, University of Siegen, Germany This edition first published 2019 © 2019 John Wiley and Sons Ltd All rights reserved.
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Title: Design and analysis of composite structures for automotive applications : chassis and drivetrain / Vladimir Kobelev, Department of Natural Sciences, University of Siegen, Germany. Description: First edition. | Hoboken, NJ : Wiley, 2019. | Series: Automotive series | Includes bibliographical references and index.
| Identifiers: LCCN 2019005286 (print) | LCCN 2019011866 (ebook) | ISBN 9781119513841 (Adobe PDF) | ISBN 9781119513865 (ePub) | ISBN 9781119513858 (hardback) Subjects: LCSH: Automobiles–Chassis. | Automobiles–Power trains. | Automobiles–Design and construction. Classification: LCC TL255 (ebook) | LCC TL255 .2/4–dc23 LC record available at https://lccn.gov/2019005286 Cover Design: Wiley Cover Images: © Vladimir Kobelev, Background: © solarseven/ShuWerstock Set in 10/12pt WarnockPro by SPi Global, Chennai, India Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY 10 9 8 7 6 5 4 3 2 1 v Contents Foreword xiii Series Preface xv List of Symbols and Abbreviations xvii Introduction xxiii About the Companion Website xxxv 1 Elastic Anisotropic Behavior of Composite Materials 1 1.1 Anisotropic Elasticity of Composite Materials 1 1.1 Fourth Rank Tensor Notation of Hooke’s Law 1 1.2 Voigt’s Matrix Notation of Hooke’s Law 2 1.3 Kelvin’s Matrix Notation of Hooke’s Law 5 1.2 Unidirectional Fiber Bundle 7 1.1 Components of a Unidirectional Fiber Bundle 7 1.2 Elastic Properties of a Unidirectional Fiber Bundle 7 1.3 Effective Elastic Constants of Unidirectional Composites 8 1.3 Rotational Transformations of Material Laws, Stress and Strain 10 1.1 Rotation of Fourth Rank Elasticity Tensors 11 1.2 Rotation of Elasticity Matrices in Voigt’s Notation 11 1.3 Rotation of Elasticity Matrices in Kelvin’s Notation 13 1.4 Elasticity Matrices for Laminated Plates 14 1.1 Voigt’s Matrix Notation for Anisotropic Plates 14 1.2 Rotation of Matrices in Voigt’s Notation 15 1.3 Kelvin’s Matrix Notation for Anisotropic Plates 15 1.4 Rotation of Matrices in Kelvin’s Notation 16 1.5 Coupling Effects of Anisotropic Laminates 17 1.1 Orthotropic Laminate Without Coupling 17 1.2 Anisotropic Laminate Without Coupling 17 1.3 Anisotropic Laminate With Coupling 17 1.4 Coupling Effects in Laminated Thin-Walled Sections 18 1.6 Conclusions 18 References 19 2 Phenomenological Failure Criteria of Composites 21 2.1 Phenomenological Failure Criteria 21 2.1 Criteria for Static Failure Behavior 21 2.2 Stress Failure Criteria for Isotropic Homogenous Materials 21 2.3 Phenomenological Failure Criteria for Composites 22 vi Contents 2.4 Phenomenological Criteria Without Stress Coupling 23 2.1 Criterion of Maximum Averaged Stresses 23 2.2 Criterion of Maximum Averaged Strains 24 2.5 Phenomenological Criteria with Stress Coupling 24 2.1 Mises–Hill Anisotropic Failure Criterion 24 2.2 Pressure-Sensitive Mises–Hill Anisotropic Failure Criterion 26 2.3 Tensor-Polynomial Failure Criterion 27 2.4 Tsai–Wu Criterion 30 2.5 Assessment of Coefficients in Tensor-Polynomial Criteria 30 2.2 Differentiating Criteria 33 2.1 Fiber and Intermediate Break Criteria 33 2.2 Hashin Strength Criterion 33 2.3 Physically Based Failure Criteria 35 2.4 Rotational Transformation of Anisotropic Failure Criteria 37 2.5 Conclusions 40 References 40 3 Micromechanical Failure Criteria of Composites 45 3.1 Pullout of Fibers from the Elastic-Plastic Matrix 45 3.1 Axial Tension of Fiber and Matrix 45 3.2 Shear Stresses in Matrix Cylinders 51 3.3 Coupled Elongation of Fibers and Matrix 53 3.4 Failures in Matrix and Fibers 54 3.1 Equations for Mean Axial Displacements of Fibers and Matrix 54 3.2 Solutions of Equations for Mean Axial Displacements of Fibers and Matrix 56 3.5 Rupture of Matrix and Pullout of Fibers from Crack Edges in a Matrix 57 3.2 Plastic Sliding on the Fiber Surface (Case II) 58 3.6 Rupture of Fibers, Matrix Joints and Crack Edges 59 3.2 Crack Bridging in Elastic-Plastic Unidirectional Composites 60 3.1 Crack Bridging in Unidirectional Fiber-Reinforced Composites 60 3.2 Matrix Crack Growth 61 3.3 Fiber Crack Growth 62 3.4 Penny-Shaped Crack 65 3.1 Crack in a Transversal-Isotropic Medium 65 3.2 Mechanisms of the Fracture Process 66 3.3 Crack Bridging in an Orthotropic Body With Disk Crack 66 3.4 Solution to an Axially Symmetric Crack Problem 68 3.5 Plane Crack Problem 72 3.1 Equations of the Plane Crack Problem 72 3.2 Solution to the Plane Crack Problem 74 3.3 Debonding of Fibers in Unidirectional Composites 75 Contents vii 3.1 Axial Deformation of Unidirectional Fiber Composites 75 3.2 Stresses in Unidirectional Composite in Cases of Ideal Debonding or Adhesion 79 3.1 Equations of an Axially Loaded Unidirectional Compound Medium (A) 79 3.3 Stresses in a Unidirectional Composite in a Case of Partial Debonding 84 3.1 Partial Radial Load on the Fiber Surface 84 3.2 Partial Radial Load on the Matrix Cavity Surface 84 3.3 Partial Debonding With Central Adhesion Region (D) 85 3.4 Partial Debonding With Central Debonding Region (E) 88 3.5 Semi-Infinite Debonding With Central Debonding Region (F) 89 3.4 Contact Problem for a Finite Adhesion Region 89 3.5 Debonding of a Semi-Infinite Adhesion Region 93 3.6 Debonding of Fibers from a Matrix Under Cyclic Deformation 95 3.4 Conclusions 98 References 98 4 Optimization Principles for Structural Elements Made of Composites 105 4.1 Stiffness Optimization of Anisotropic Structural Elements 105 4.3 Optimal Solutions in Anti-Plane Elasticity 109 4.4 Optimal Solutions in Plane Elasticity 109 4.2 Optimization of Strength and Loading Capacity of Anisotropic Elements 110 4.3 Optimal Solutions in Anti-Plane Elasticity 114 4.4 Optimal Solutions in Plane Elasticity 114 4.3 Optimization of Accumulated Elastic Energy in Flexible Anisotropic Elements 116 4.3 Optimal Solutions in Anti-Plane Elasticity 118 4.4 Optimal Solutions in Plane Elasticity 119 4.4 Optimal Anisotropy in a Twisted Rod 119 4.5 Optimal Anisotropy of Bending Console 122 4.6 Optimization of Plates in Bending 123 4.7 Conclusions 125 References 125 5 Optimization of Composite Driveshaft 129 5.1 Torsion of Anisotropic Shafts With Solid Cross-Sections 129 5.2 Thin-Walled Anisotropic Driveshaft with Closed Profile 132 5.1 Geometry of Cross-Section 132 viii Contents 5.2 Main Kinematic Hypothesis 133 5.3 Deformation of a Composite Thin-Walled Rod 135 5.1 Equations of Deformation of a Anisotropic Thin-Walled Rod 135 5.2 Ideally Free End 138 5.3 Boundary Conditions of the Intermediate Type 140 5.3 Governing Equations in Special Cases of Symmetry 140 5.2 Constant Elastic Properties Along the Arc of a Cross-Section 140 5.4 Symmetry of Section 140 5.4 Buckling of Composite Driveshafts Under a Twist Moment 141 5.1 Greenhill’s Buckling of Driveshafts 141 5.2 Optimal Shape of the Solid Cross-Section for Driveshaft 143 5.3 Hollow Circular and Triangular Cross-Sections 144 5.5 Patents for Composite Driveshafts 146 5.6 Conclusions 150 References 150 6 Dynamics of a Vehicle with Rigid Structural Elements of Chassis 155 6.1 Classification of Wheel Suspensions 155 6.1 Common Designs of Suspensions 155 6.2 Types of Twist-Beam Axles 156 6.3 Kinematics of Wheel Suspensions 157 6.2 Fundamental Models in Vehicle Dynamics 159 6.1 Basic Variables of Vehicle Dynamics 159 6.2 Coordinate Systems of Vehicle and Local Coordinate Systems 161 6.1 Earth-Fixed Coordinate System 161 6.2 Vehicle-Fixed Coordinate System 162 6.3 Horizontal Coordinate System 162 6.4 Wheel Coordinate System 162 6.3 Angle Definitions 162 6.4 Components of Force and Moments in Car Dynamics 163 6.5 Degrees of Freedom of a Vehicle 163 6.3 Forces Between Tires and Road 167 6.2 Side Slip Curve and Lateral Force Properties 168 6.4 Dynamic Equations of a Single-Track Model 170 6.1 Hypotheses of a Single-Track Model 170 6.2 Moments and Forces in a Single-Track Model 171 6.3 Balance of Forces and Moments in a Single-Track Model 173 6.1 Necessary Steer Angle for Steady Cornering 174 6.2 Yaw Gain Factor and Steer Angle Gradient 175 6.3 Classification of Self-Steering Behavior 176 6.5 Non-Steady Cornering 179 6.1 Equations of Non-Stationary Cornering 179 Contents ix 6.2 Oscillatory Behavior of Vehicle During Non-Steady Cornering 180 6.6 Anti-Roll Bars Made of Composite Materials 181 6.5 Conclusions 182 References 182 7 Dynamics of a Vehicle With Flexible, Anisotropic Structural Elements of Chassis 183 7.1 Effects of Body and Chassis Elasticity on Vehicle Dynamics 183 7.1 Influence of Body Stiffness on Vehicle Dynamics 183 7.2 Lateral Dynamics of Vehicles With Stiff Rear Axles 184 7.3 Induced Effects on Wheel Orientation and Positioning of Vehicles with Flexible Rear Axle 185 7.2 Self-Steering Behavior of a Vehicle With Coupling of Bending and Torsion 188 7.1 Countersteering for Vehicles with Twist-Beam Axles 188 7.