Static and dynamic global stiffness analysis for automotive pre-design
Authors:   , Cavaliere Fabiola 
Published: May 2022

In order to be worldwide competitive, the automotive industry is constantly challenged to produce higher quality vehicles in the shortest time possible and with the minimum costs of production. Most of the problems with new products derive from poor quality design processes, which often leads to undesired issues in a stage where changes are extremely expensive. During the preliminary design phase, designers have to deal with complex parametric problems where material and geometric characteristics of the car components are unknown. Any change in these parameters might signiﬁcantly aﬀect the global behaviour of the car. A target which is very sensitive to small variations of the parameters is the noise and vibration response of the vehicle (NVH study), which strictly depends on its global static and dynamic stiﬀness. In order to ﬁnd the optimal solution, a lot of conﬁgurations exploring all the possible parametric combinations need to be tested. The current state of the art in the automotive design context is still based on standard numerical simulations, which are computationally very expensive when applied to this kind of multidimensional problems. As a consequence, a limited number of conﬁgurations is usually analysed, leading to suboptimal products. An alternative is represented by reduced order method (ROM) techniques, which are based on the idea that the essential behaviour of complex systems can be accurately described by simpliﬁed low-order models.This thesis proposes a novel extension of the proper generalized decomposi-tion (PGD) method to optimize the design process of a car structure with respect to its global static and dynamic stiﬀness properties. In particular, the PGD method is coupled with the inertia relief (IR) technique and the inverse power method (IPM) to solve, respectively, the parametric static and dynamic stiﬀness analysis of an unconstrained car structure and extract its noise and vibrations properties. A main advantage is that, unlike many other ROM methods, the proposed approach does not require any pre-processing phase to collect prior knowledge of the solution. Moreover, the PGD solution is computed with only one oﬄine computation and presents an explicit dependency on the introduced design variables. This allows to compute the solutions at a negligible computational cost and therefore opens the door to fast optimisation studies and real-time visualisations of the results in a pre-deﬁned range of parameters. A novel algebraic approach is also proposed which allows to involve both material and com-plex geometric parameters, such that shape optimisation studies can be performed. In addition, the method is developed in a nonintrusive format, such that an interaction with commercial software is possible, which makes it particularly interesting for industrial applications. Finally, in order to support the designers in the decision-making process, a graphical interface app is developed which allows to visualise in real-time how changes in the design variables aﬀect pre-deﬁned quantities of interest.