Nonlinear Optimization of Vehicle Safety Structures

Nonlinear Optimization of Vehicle Safety Structures

Modeling of Structures Subjected to Large Deformations

1st Edition - December 7, 2015

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  • Authors: Jesper Christensen, Christophe Bastien
  • eBook ISBN: 9780124173095
  • Paperback ISBN: 9780128044247

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Nonlinear Optimization of Vehicle Safety Structures: Modeling of Structures Subjected to Large Deformations provides a cutting-edge overview of the latest optimization methods for vehicle structural design. The book focuses on large deformation structural optimization algorithms and applications, covering the basic principles of modern day topology optimization and comparing the benefits and flaws of different algorithms in use. The complications of non-linear optimization are highlighted, along with the shortcomings of recently proposed algorithms. Using industry relevant case studies, users will how optimization software can be used to address challenging vehicle safety structure problems and how to explore the limitations of the approaches given. The authors draw on research work with the likes of MIRA, Jaguar Land Rover and Tata Motors European Technology Centre as part of multi-million pound European funded research projects, emphasizing the industry applications of recent advances. The book is intended for crash engineers, restraints system engineers and vehicle dynamics engineers, as well as other mechanical, automotive and aerospace engineers, researchers and students with a structural focus.

Key Features

  • Focuses on non-linear, large deformation structural optimization problems relating to vehicle safety
  • Discusses the limitations of different algorithms in use and offers guidance on best practice approaches through the use of relevant case studies
  • Author's present research from the cutting-edge of the industry, including research from leading European automotive companies and organizations
  • Uses industry relevant case studies, allowing users to understand how optimization software can be used to address challenging vehicle safety structure problems and how to explore the limitations of the approaches given


Automotive engineers (esp. crash engineers, restraints system engineers and vehicle dynamics engineers) as well as other mechanical and aerospace engineers, researchers and students with a structural focus.

Table of Contents

    • Dedication
    • Preface
    • Chapter | one: Vehicle Architectures, Structures, and Safety Requirements
      • Abstract
      • 1.1. Introduction
      • 1.2. Legislative requirements
      • 1.3. Occupant injuries
      • 1.4. Typical vehicle architectures and scope for optimization
      • 1.5. Holistic approach to vehicle design
      • 1.6. Conclusions and opportunities
    • Chapter | two: Numerical Techniques for Structural Assessment of Vehicle Architectures
      • Abstract
      • 2.1. Introduction to finite element analysis (FEA)
      • 2.2. Theory of elasticity
      • 2.3. Elements
      • 2.4. Fundamental explicit and implicit finite element analysis
      • 2.5. Nonlinear explicit finite element analysis
      • 2.6. Explicit FEA applied to vehicle safety assessment
      • 2.7. Contacts
      • 2.8. Example convergence study of explicit FEA
    • Chapter | three: Introduction to General Optimization Principles and Methods
      • Abstract
      • 3.1. What is structural optimization?
      • 3.2. How are optimization problems generally solved?
      • 3.3. General optimization methods and principles
      • 3.4. The curse of dimensionality
      • 3.5. Convex programming and optimization
      • 3.6. Gradient-based methods and line search methods
      • 3.7. Additional mathematical optimization methods
      • 3.8. Additional aspects of structural optimization
    • Chapter | four: Introduction to Structural Optimization and Its Potential for Development of Vehicle Safety Structures
      • Abstract
      • 4.1. Topology optimization
      • 4.2. Shape optimization
      • 4.3. Metamodeling
      • 4.4. Point selection methods for metamodeling
      • 4.5. Optimization strategies for metamodel-based optimization
    • Chapter | five: Applications of Linear Optimization to Concept Vehicle Safety Structures
      • Abstract
      • 5.1. Introduction
      • 5.2. Full vehicle structure topology optimization
      • 5.3. From topology optimization to computer-aided design (CAD) model
      • 5.4. Conclusions: applications of linear optimization to concept vehicle safety structures
    • Chapter | six: Complications of Nonlinear Structural Optimization
      • Abstract
      • 6.1. Equivalent static load method
      • 6.2. Initial optimization study
      • 6.3. Revised optimization study
      • 6.4. ESLM versus linear static topology optimization
    • Chapter | seven: Heuristic and Meta-Heuristic Optimization Algorithms
      • Abstract
      • 7.1. Mathematical algorithms
      • 7.2. Heuristic and meta-heuristic algorithms
      • 7.3. Evolutionary algorithms
      • 7.4. Requirements for optimization of structures exposed to large (nonlinear) deformations
      • 7.5. Hybrid cellular automata
      • 7.6. Combinatory optimization problems
      • 7.7. Ant colony optimization
      • 7.8. Stochastic hill climbing
      • 7.9. Tabu search
      • 7.10. Simulated annealing
      • 7.11. Particle swarm optimization
      • 7.12. Neural networks
      • 7.13. General principles
      • 7.14. Entropy
    • Chapter | eight: Definition, Implementation, and Partial Validation of a Nonlinear Topology Optimization Algorithm
      • Abstract
      • 8.1. Algorithm definition
      • 8.2. Algorithm implementation and software development
      • 8.3. Linear topology optimization case studies
      • 8.4. Nonlinear topology optimization case studies
      • 8.5. Conclusion of the potential of BEETS for nonlinear topology optimization
    • Chapter | nine: Applications of Concept Nonlinear Optimization
      • Abstract
      • 9.1. Introduction
      • 9.2. Background of the vehicle optimization study
      • 9.3. Initial vehicle crash performance
      • 9.4. Choosing sampling methods and metamodels
      • 9.5. Design of experiment (DOE) and global sensitivities
      • 9.6. Structural optimization
      • 9.7. Conclusions
    • Chapter | ten: Optimization for Refinement of Vehicle Safety Structures
      • Abstract
      • 10.1. Introduction
      • 10.2. Occupant protection analysis case study
      • 10.3. Pedestrian protection analysis case study
      • 10.4. Conclusions
    • Chapter | eleven: The Future of Structural Optimization and Vehicle Safety
      • Abstract
      • 11.1. Vehicle architectures, structures, and safety requirements
      • 11.2. Numerical techniques for structural assessment of vehicle architectures
      • 11.3. Optimization techniques for nonlinear structural optimization
      • 11.4. Application of nonlinear optimization
      • 11.5. The future of structural optimization in engineering
      • 11.6. Additional aspects of optimization
    • Index

Product details

  • No. of pages: 482
  • Language: English
  • Copyright: © Butterworth-Heinemann 2015
  • Published: December 7, 2015
  • Imprint: Butterworth-Heinemann
  • eBook ISBN: 9780124173095
  • Paperback ISBN: 9780128044247

About the Authors

Jesper Christensen

Jesper Christensen is a Senior Research Fellow at Coventry University, and holds a PhD in Structural Optimisation, an MSc in Design of Mechanical Systems as well as a BSc in Industrial Engineering. Prior to his engineering degrees Jesper completed an apprenticeship as an engine fitter working with large marine propulsion systems. His entire academic career has predominately focused on structural optimisation; with a particular emphasis on topology optimisation. Jesper joined Coventry University in 2010; working on the £29m Low Carbon Vehicle Technology Project (LCVTP), developing topology optimisation algorithms for lightweight vehicle structures. Following the LCVTP his focus turned to the continued development of the Mechanical Engineering MSc course at Coventry University; taking over the course leadership. In this context he primarily focused on aspects such as FE theory and application, strain gauging, metal fatigue and optimisation principles. Jesper’s research activities has continued through a number of PhD students as well as a number of successful project grants, including a £780k Engineering and Physical Sciences Research Council (ESPSRC) research grant focusing on multiphysics simulation and optimisation, as well as a £1.6m grant for industrial based research and development project focusing on development, implementation and optimisation of a Flywheel Energy Storage System (FESS) for commercial bus applications.

Jesper is a Chartered Engineer and a Fellow of the Institute of Mechanical Engineers (IMechE), as well as being a Science, Technology, Engineering and Mathematics (STEM) Ambassador; inspiring children and young adults to take up degrees and careers in STEM related areas.

Affiliations and Expertise

Department of Mechanical and Automotive Engineering, Coventry University, UK

Christophe Bastien

Christophe Bastien is a Principal Lecturer in Engineering Simulations at Coventry University and holds a PhD in vehicle safety and biomechanics. He led the university’s Mechanical and Automotive Engineering MSc courses and taught Finite Element Analysis and crashworthiness simulations. He is also a chartered engineer from the Institute of Mechanical Engineers (IMechE).

Christophe has 13 years’ industrial experience in crashworthiness, testing and computer simulation. During this time, he has successfully led the design, testing and computational analysis of the Jaguar ‘X-Type’ for interior head injuries (FMVSS201), as well as the development and analysis of the first pedestrian deployable pyrotechnic bonnet for the Jaguar ‘XK’. Later on, during his employment at Corus Automotive, he developed further static pedestrian bonnet technologies, as well as engineered, analyzed and tested highway crash barriers for high speed vehicle containment.

He joined Coventry University in 2007 and started his research in vehicle lightweighting optimisation, which included the design work for Jaguar and Land Rover (JLR) in the Premium Lightweight Architecture for Carbon Efficient Seating (PLACES) project, the optimisation of lightweight electric vehicle architectures for the £29m Low Carbon Vehicle Technology Project (LCVTP) and the multi-disciplinary / multiphysics optimisation of Virtual Exhaust Systems (VexPro).

Christophe Bastien is a member of the Coventry University’s Mobility & Transport Research Centre, where he is focusing on Automotive Safety, Lightweighting, Optimisation and Human Trauma Predictions. He holds 19 patents in the field of safety engineering.

Affiliations and Expertise

Department of Mechanical and Automotive Engineering, Coventry University, UK

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