Nonlinear Optimization of Vehicle Safety Structures

Modeling of Structures Subjected to Large Deformations

Jesper Christensen,Christophe Bastien

• Publisher: Butterworth-Heinemann
• Year: 2015
• ISBN:
  9780124173095
• Topic: Mathematics
• Subtopic: Optimization
• Index: Mathematics

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.

• 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

Chapter | three

Introduction to General Optimization Principles and Methods

Abstract

The purpose of this chapter is to provide an introduction to optimization techniques in general, starting with the “simple” question, “what is structural optimization”? How is a general optimization problem typically defined and how is it solved?

Following this the reader will be introduced to various optimization principles and techniques gradually increasing in complexity. This includes aspects such as the curse of dimensionality, convex programming and optimization, the Simplex method, sequential linear programming, gradient-based methods, and line search methods. These all include detailed examples including process flowcharts and MatLab examples. Following these other mathematical optimization methods/tools such as Lagrangian multipliers, the Karush–Kuhn Tucker optimality criteria, and trust regions are presented. The final section of this chapter deals with a wider variety of structural optimization, such as design space and design volumes, uniqueness of solutions, design sensitivity and robustness, multiobjective, multidisciplinary, and multiphysics optimization.

Keywords

structural optimization

line search methods

gradient-based optimization

sequential linear programming

MatLab example

convex optimization

the curse of dimensionality

Karush–Kuhn tucker

trust region

Lagrangian multipliers

Chapter outline

3.1 What is Structural Optimization? 107

3.2 How are Optimization Problems Generally Solved? 108

3.3 General Optimization Methods and Principles 111

3.4 The Curse of Dimensionality 113

3.5 Convex Programming and Optimization 115

3.6 Gradient-Based Methods and Line Search Methods 132

3.7 Additional Mathematical Optimization Methods 161

3.8 Additional Aspects of Structural Optimization 163

References 168

The first two chapters of this book were aimed at introducing the reader to fundamental aspects of vehicle structures as well as finite element (FE) theory and finite element analysis (FEA), with an emphasis on vehicle safety structures. The purpose of this chapter is to introduce the reader to some of the general mathematical optimization principles, techniques, and methods, giving the reader an overall understanding of what constitutes ...