Static and dynamic global stiffness analysis for automotive pre-design

Fabiola Cavaliere

Díez Mejía, Pedro Zlotnik, S.

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 decomposition (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 complex 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.

The presented method has been successfully developed and tested on a simplified case of study during the PhD program. The industrial partner, SEA T S.A., actively contributed to define the industrial problem and showed constant enthusiasm and interest towards the obtained results. As a confirmation of the success of this work, on last July 2022 the industrial partner gave me the chance to join the company as a new employee in order to scale up the method to real applications and include it in the current SEA T workflow. The project is in a "Proof of Concept" stage. From a methodology point of view, the application of the method to real vehicle models is straightforward and we plan to obtain preliminary results within the next six months.

Automotive Industry; Quality Vehicles; Production Costs; Quality Design Processes; Preliminary Design Phase; Complex Parametric Problems; Material Characteristics; Geometric Characteristics; Car Components; Global Car Behaviour; Noise and Vibration Response (NVH Study); Global Static Stiffness; Global Dynamic Stiffness; Optimal Solution; Parametric Combinations; Numerical Simulations; Computationally Expensive; Multidimensional Problems; Suboptimal Products; Reduced Order Method (ROM) Techniques; Simplified Low-Order Models; Proper Generalized Decomposition (PGD) Method; Optimize Design Process; Car Structure; Inertia Relief (IR) Technique; Inverse Power Method (IPM); Parametric Static Stiffness Analysis; Parametric Dynamic Stiffness Analysis; Unconstrained Car Structure; Noise and Vibrations Properties; No Pre-processing Phase; Prior Knowledge of Solution; One Offline Computation; Explicit Dependency; Design Variables; Negligible Computational Cost; Fast Optimisation Studies; Real-time Visualisations; Pre-defined Parameter Range; Novel Algebraic Approach; Material Parameters; Complex Geometric Parameters; Shape Optimisation Studies; Nonintrusive Format; Commercial Software Interaction; Industrial Applications; Graphical Interface App; Decision-Making Process; Quantities of Interest.