Product designers worldwide are confronted with highly competitive though conflicting demands to deliver more complex products with increased quality in ever shorter development cycles. Since optimizing design performance with purely test-based approaches is no longer an option, nowadays numerical simulation methods are widely used to model, assess and improve the product design based on virtual prototypes. The use of the Finite Element (FE) method is widely established for the virtual prototyping phase.
An FE analysis yields a single deterministic prediction of the model performance for one set of model parameters, without taking into account the variability in geometric and material properties and manufacturing processes. With a single FE analysis, the effect of the variability on the performance is thus not assessed. A traditional solution is to apply safety factors on the system parameters, but this typically leads to oversized, too heavy structures.
A more promising approach is to include variability (also known as aleatory uncertainty) in the mechanical simulation to guarantee the robustness and reliability of the design. The outcome of the analysis consists of a probabilistic model of the structural performance (e.g. stresses, strains, fatigue life etc.), given the variability in the material properties and geometrical parameters, including operating environment and manufacturing tolerances.
This probabilistic model can then be used in a reliability-based design optimization (RBDO) procedure to improve the design of the structural component or system, while guaranteeing the reliability of the nominal design. These reliability analysis and RBDO strategies make use of limit state approximations as well as of sampling procedures, thus enabling the analyst to balance the accuracy and the computational effort required to extract the necessary information on safety and performance stability.
This paper gives an overview of reliability-based design in automotive and aerospace engineering. Reliability analysis and a reliability-based design optimization framework can deal with variability. As these methods typically require a substantial number of deterministic design iterations, a number of enabling technologies can be adopted to alleviate the computational burden, such as the automation and parallelization of the workflow, the application of design of experiments and response surface methodology to speed up design iterations, and other methodologies that are highlighted in this paper.
Automotive and aerospace application cases are presented to underline the benefits and feasibility of this reliability-based design paradigm. In particular, special focus will be given to manufacturing variability for steel structures. Examples will be given on how to integrate stochastic modeling with durability predictions of aerospace and automotive components. In addition, it is shown how the stochastic modeling framework can be applied also to automotive crash simulations.
