Optimisation study of a vehicle bumper subsystem with fuzzy parameters

In a mechanical product development process, during the different virtual design stages, performance attributes are optimised and reliability, robustness and safety are evaluated. As computer simulations are given a more central role in the decision-making process, physical trustworthiness of the numerical modelling process becomes crucial. The credibility of the virtual modelling process can be increased by introducing model parametric non-determinism into the numerical simulations. Model parametric non-determinism represents different model parameters such as material properties, geometrical tolerances that carry some physical variation (variabilities) or represent some information deficiency (uncertainties). The application of the fuzzy finite element method in early design stage enables the analyst to assess the effect of different model uncertainties on the product performance. Moreover the combined application of the fuzzy Finite Element (FE) concept with optimisation leads to an optimised product for which the performance is guaranteed in the presence of uncertainties. Such uncertainties can arise from the not yet known production process that affects the geometry in terms of tolerances, or such uncertainties can be accounted for material imperfections that occur in the real physical product. This paper deals with the design and optimisation for crashworthiness of a vehicle bumper subsystem, which is a key scenario for vehicle component design. Passive safety has a central attention during a vehicle development process. Bumper systems are important in the energy management of vehicles during a low-speed vehicle impact, and also have major impact on pedestrian safety. The automotive manufacturers and suppliers have to find optimal design solutions for such subsystems that comply with the conflicting requirements of the regulatory bodies regarding functional performance (safety and repairability) and regarding the environmental impact (mass). Manufacturers and suppliers address the complex design problems by means of virtual modelling and simulation procedures that enable optimising the performance of such subsystems as early as possible in the design timeline. For the bumper design challenge, an integrated methodology for multi-attribute design engineering of mechanical structures is set up. The integrated process captures the various tasks that are usually performed manually, this way facilitating the automated design iterations for optimisation. Subsequently, an optimisation process is applied that takes the effect of parametric uncertainties into account, such that the system level of failure possibility is acceptable. This optimisation process is referred to as possibility-based design optimisation and integrates the fuzzy FE analysis applied for the uncertainty treatment in crash simulations. This process is the counterpart of the reliability-based design optimisation used in a probabilistic context with statistically defined parameters (variabilities).