Jesper Christensen

Effects of roof crush loading scenario upon body in white using topology optimisation

This paper investigates the effects of variations in modelling of roof crush loading scenarios upon topology and mass of a body in white (BIW) for a hybrid electric vehicle (HEV). These variations incorporated the proposed changes to the Federal Motor Vehicle Safety Standards (FMVSS) 216 standard. The base model used for the investigation in this paper was based upon a series of optimisation studies. The overall purpose was to minimise the BIW mass of an HEV subjected to multiple crash scenarios including high-speed front impact, offset deformable barrier (ODB), side impact, pole impact, high-speed rear impact and low-speed rear impact in addition to a roof crush scenario. For the purpose of achieving this goal, finite element (FE) topology optimisation was employed. Owing to the limitations of present-day FE optimisation software, all models utilised linear static load cases. In addition, all models made use of inertia relief (IR) boundary conditions. With the above approach, the BIW topology was investigated.

Buckling considerations and cross-sectional geometry development for topology optimised body in white

This paper will investigate how current state-of-the-art structural optimisation algorithms, with an emphasis on topology optimisation, can be used to rapidly develop lightweight body in white (BIW) concept designs, based on a computer aided design envelope. The optimisation models included in the paper will primarily focus on crashworthiness and roof crush scenarios as specified in the Federal Motor Vehicle Safety Standards (FMVSS) 216 standard. This paper is a continuation of a previously published paper, which investigated the potential effects of recently proposed changes to FMVSS 216 upon BIW mass and architecture using topology optimisation. The paper will investigate the possibilities of including buckling considerations of roof members directly into current state-of-the-art topology optimisation algorithms. This paper will also demonstrate the potential for developing a detailed BIW design including cross-sectional properties based on a styling envelope.

Optimization for Refinement of Vehicle Safety Structures

This purpose of this chapter is to demonstrate how vehicle safety structures can be optimized with an emphasis on occupant and pedestrian safety. This chapter focuses on size and variable optimization as opposed to topology optimization which has been the emphasis in the preceding chapters. The chapter will investigate means of optimizing a restraint system in the context of a frontal crash scenario by considering restraint system parameters. In the pedestrian scenario, the chapter will focus on the emerging technology of deployable bonnets and will investigate methods of optimizing the associated pyrotechnic lifting system.

Complications of Nonlinear Structural Optimization

This chapter focuses on some of the main issues relating to nonlinear optimization with an emphasis on topology optimization. This is specifically done by comparing and reviewing the equivalent static load method (ESLM) which is based on the VDM-SIMP approach presented in Chapter 4; ESLM was, however, explicitly developed for nonlinear topology optimization. ESLM has been successfully used for many topology optimization applications; the case studies of this chapter are, however, intended to expose the shortcomings of this approach, thereby also exposing many of the central issues relating to any finite element-based nonlinear topology optimization algorithm. These include, but are not limited to, parameter sensitivity, boundary condition modeling, scalability, as well as robustness and sensitivity studies in general. This chapter concludes with a direct comparison of linear static VDM-SIMP to ESLM, including further review of the case studies presented in Chapter 5 (Applications of Linear Optimization to Concept Vehicle Safety Structures).

Numerical Techniques for Structural Assessment of Vehicle Architectures

This chapter addresses three main aspects: introduction to the finite element method (FEM), advanced finite element analysis (FEA), and the application of FEM/FEA to vehicle structures with an emphasis on large deformation/nonlinear and dynamic analysis. The first sections of the chapter are intended to act as a refresher of the basics of FEM, briefly outlining the fundamental equations and principles. The following sections of the chapter are aimed at providing an overview of more complex FEA problems, such as nonlinear and/or dynamic analysis, as often required in connection with vehicle safety structures. The purpose of the final sections of this chapter is to unite Chapter 1 and the initial sections of this chapter into an overview of how FEM/FEA is used for vehicle structural design and analysis, including postprocessing of results, and will form the basis for the remaining chapters of this book.

Heuristic and Meta-Heuristic Optimization Algorithms

The purpose of this chapter is to review a broad range of optimization principles, techniques, and algorithms collectively referred to as heuristic or meta-heuristic. As the demand for nonlinear optimization with high levels of component and system detail techniques increases so do the benefits of potential tradeoff between precision and computing speed, which is often attempted through the use of “nature” inspired techniques or heuristic optimization. Although the majority of techniques presented and discussed in this chapter have not generally been applied to structural optimization problems, some are readily available in commercial FE packages. This chapter focuses on the potential of developing each individual technique for nonlinear (topology) optimization; this includes reflecting on results from the previous chapters. This chapter also covers some general principles that are not directly optimization related but should be considered in the context of developing nonlinear optimization algorithms and techniques.

Applications of Concept Nonlinear Optimization

The purpose of this chapter is to refine the results of the case study conducted in Chapter 5 . Which were obtained using a combination of commercial and “tailor made” software, and defined the main vehicle safety cell as well as the front crash structure. A study is presented and focuses on the detail tuning of the main vehicle body structure when subjected to multiple impact scenarios comprising three safety loadcases (frontal, side, and pole impacts) and one torsional rigidity durability loadcase. The study will consider panel sizing and local material grade optimization. Using detailed finite element models of a vehicle, this chapter will propose a step-by-step time-efficient method which reduces the number of variables while achieving a structural performance meeting prespecified design objectives.

Introduction to General Optimization Principles and Methods

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?

Introduction to Structural Optimization and Its Potential for Development of Vehicle Safety Structures

The purpose of this chapter is to present specific structural optimization techniques. This is an extension of Chapter 3, which presented general optimization techniques. This chapter firstly addresses topology optimization including aspects such as relaxation, the checkerboard effect, the variable density method (VDM), the solid isotropic material with penalization (SIMP) interpolation schema, the sum of reciprocal values (SRV) constraint, design sensitivity analysis (DSA), and homogenization-based optimization (HBO). The chapter then focuses on three main methods for shape optimization: the Lagrangian approach, the Eulerian approach, and morphing.

Vehicle Architectures, Structures, and Safety Requirements

The purpose of this chapter is to outline the general principles of vehicle safety structure design and engineering. This chapter will cover aspects such as draft design, load path generation, material selection, legislative requirements, manufacturing methodologies, and constraints, as well as occupant and pedestrian safety considerations. A brief overview of a “normal” design cycle of a “typical” vehicle structure from a holistic viewpoint will be given. The following sections will then heavily focus on the specific aspects that the mechanical/automotive/safety engineers will have to address during the subsequent phases of the design cycle.