Struct Multidisc Optim (2013) 48:367–378 DOI 10.1007/s00158-013-0903-z RESEARCH PAPER Shape optimisation for crashworthiness followed by a robustness analysis with respect to shape variables Example of a front rail Stephan Hunkeler · Fabian Duddeck · Milan Rayamajhi · Hans Zimmer Received: 15 March 2012 / Revised: 8 January 2013 / Accepted: 1 February 2013 / Published online: 1 March 2013 © Springer-Verlag Berlin Heidelberg 2013 Abstract This paper presents the results of a study on shape optimisation for crashworthiness design of passenger cars based on the software SFE CONCEPT. In contrast to classi- cal morphing approaches, SFE CONCEPT allows for larger geometrical modifications via an implicit parameterisation technique. This is advantageous in particular in the early design phases where different design alternatives are inves- tigated and the optimal and robust geometry needs to be identified. As a first example, the front rail of a standard passenger car is optimised here. This is – as one of the main parts of the body in white – an appropriate example for exploration of optimisation methods. The performance of a classical optimisation approach is analysed and com- plemented by a robustness analysis where uncertainties in shape parameters are considered. Keywords Crashworthiness · Shape optimisation · Parametric design · Shape uncertainties · Robustness analysis S. Hunkeler () · M. Rayamajhi School of Engineering and Materials Sciences, Queen Mary University of London, Mile End Road, E1 4NS, London, UK e-mail: s.hunkeler@qmul.ac.uk F. Duddeck Technische Universit¨ at M¨ unchen, Arcisstrasse 21, 80333 M¨ unchen, Germany H. Zimmer SFE GmbH, Voltastrasse 5, 13355 Berlin, Germany 1 Introduction Over the last few years, the main challenge in automo- tive industry has been to lower CO 2 emissions. Thus, there has been a lot of interest in electric and hybrid vehicles or internal combustion engines with reduced fuel consump- tion. Nevertheless, one can argue that the easiest way to achieve energy savings is to reduce the mass of vehi- cles. Hence, lightweight structural design is currently one of the most important topics in automotive research. For example, multi-material mix or new manufacturing and assembling techniques are promising areas. Nevertheless, one of the main approaches for lightweight design lies in optimising the structure of the car body, using different materials, dedicated metal sheet thicknesses and, especially, varying the topology and shape of components and the overall structure. Because of the complexity and variabil- ity of these structures, this is not an easy task and requires well designed software and optimisation strategies. In addi- tion, optimisation needs to assess different performance functionalities (dynamic behaviour, NVH, CFD, crash- worthiness...), which often need to be arbitrated between each others using multi-disciplinary optimisation methods (Duddeck 2008). 1.1 Optimisation for crashworthiness design Optimisation for crashworthiness design is an application field of structural optimisation. It can be divided into three, well-discussed, sub-categories: sizing optimisation, shape optimisation and topology optimisation. So far, most studies intending to optimise structural design for crashworthiness have been limited to the field of sizing optimisation (Redhe et al. 2004; Will et al. 2006;