Robust design of spot welds in automotive structures : a decisionmaking methodology

International audienceAutomotive structures include thousands of spot welds whose design must allow the assembled vehicle to satisfy a wide variety of performance constraints including static, dynamic and crash criteria. The objective of a standard optimization strategy is to reduce the number of spot welds as much as possible while satisfying all the design objectives. However, a classical optimization of the spot weld distribution using an exhaustive search approach is simply not feasible due to the very high order of the design space and the subsequently prohibitive calculation costs. Moreover, even if this calculation could be done, the result would not necessarily be very informative with respect to the design robustness to manufacturing uncertainties (location of welds and defective welds) and to the degradation of spot welds due to fatigue effects over the lifetime of the vehicle. In this paper, a decision-making methodology is presented which allows some aspects of the robustness issues to beintegrated into the spot weld design process. The starting point is a given distribution of spot welds on the structure, which is based on both engineering know-how and preliminary critical numerical results, in particular criteria such as crash behavior. An over-populated spot weld distribution is then built in order to satisfy the remaining design criteria, such as static torsion angle and modal behavior. Then, an efficient optimization procedure based on energy considerations is used to eliminate redundant spot welds while preserving as far as possible the nominal structural behavior. The resulting sub-optimal solution is then used to provide a decision indicator for defining effective quality control procedures (e.g. visual post-assembly inspection of a small number of critical spot welds) as well as designing redundancy into critical zones. The final part of the paper is related to comparing the robustness of competing designs. Some decision-making indicators are presented to help the analyst to plan robust resistance spot welds designs along with quality controls in order to insure a specified level of structural performance. All examples are presented on a full body-in-white structure (one million dofs and thousands spot welds)

Robust optimization and quality control in spot welded structures

International audienceThe performance characteristics (i.e., static, dynamic, crash, etc.) of a spot welded structure are strongly influenced by the number and the locations of the resistance spot welds. The design problem requires the number and locations of spot welds to be optimized so as to obtain reasonable trade-offs between manufacturing costs and structural performances. An optimization procedure is proposed which iterativelyadds and removes spot welds in order to correct for approximations made in the iterative process. Moreover, a robustness indicator is formulated that allows to analyze the impact of the number of defective or broken spot welds on the system performance. This indicator provides a useful decision making tool for deciding both how many spot welds should be inspected following assembly as well as pointing to a small number of critical spot welds that should be reinforced. The proposed methodology will be illustrated on a full body-in-white structure

Robust design of spacecraft structures under lack of knowledge

International audienceIn robust design, lacks of knowledge are rarely taken into account explicitly, but this is the case in the RRDO-IG. This paper summarises the ongoing developments and perspectives for the use of the RRDO-IG methodology in a spatial industrial context, where non-linearities have to be treated. After shortly describing the RRDO-IG methodology and the actual encountered problems, we will construct an improvement strategy based on a state of the art in metamodelisation and failure probability computation

Stochastic Model Updating with Uncertainty Quantification: An Overview and Tutorial

This paper presents an overview of the theoretic framework of stochastic model updating, including critical aspects of model parameterisation, sensitivity analysis, surrogate modelling, test-analysis correlation, parameter calibration, etc. Special attention is paid to uncertainty analysis, which extends model updating from the deterministic domain to the stochastic domain. This extension is significantly promoted by uncertainty quantification metrics, no longer describing the model parameters as unknown-but-fixed constants but random variables with uncertain distributions, i.e. imprecise probabilities. As a result, the stochastic model updating no longer aims at a single model prediction with maximum fidelity to a single experiment, but rather a reduced uncertainty space of the simulation enveloping the complete scatter of multiple experiment data. Quantification of such an imprecise probability requires a dedicated uncertainty propagation process to investigate how the uncertainty space of the input is propagated via the model to the uncertainty space of the output. The two key aspects, forward uncertainty propagation and inverse parameter calibration, along with key techniques such as P-box propagation, statistical distance-based metrics, Markov chain Monte Carlo sampling, and Bayesian updating, are elaborated in this tutorial. The overall technical framework is demonstrated by solving the NASA Multidisciplinary UQ Challenge 2014, with the purpose of encouraging the readers to reproduce the result following this tutorial. The second practical demonstration is performed on a newly designed benchmark testbed, where a series of lab-scale aeroplane models are manufactured with varying geometry sizes, following pre-defined probabilistic distributions, and tested in terms of their natural frequencies and model shapes. Such a measurement database contains naturally not only measurement errors but also, more importantly, controllable uncertainties from the pre-defined distributions of the structure geometry. Finally, open questions are discussed to fulfil the motivation of this tutorial in providing researchers, especially beginners, with further directions on stochastic model updating with uncertainty treatment perspectives

Sensitivity analysis and control of a cantilever beam by mean of a shunted piezoelectric patch

International audienceIn this paper, a sensitivity analysis of a beam controlled with a shunted piezoelectric patch is presented. A negative capacitance controller is implemented and a study of stability and performance is performed. Besides, the effects of the technological aspects such as the variability in the material properties or in the position of the piezoelectric patch is evaluated through a finite element simulatio

Robust model calibration of a wind turbine with load uncertainties

International audienceThe goal of this work is to explore a model calibration strategy for an industrial problem consisting in a MW class geared wind turbine power train subjected to uncertain loads. Lack of knowledge is commonplace in this kind of engineering system and a realistic model calibration cannot be performed without taking into account this type of uncertainty. The question at stake in this study is how to perform a more robust model of a dynamic system given that the excitations are poorly known. The uncertainty in the latter will be represented with an info-gap model. This methodology is illustrated on a Megawat class wind turbine power train torsional model

Sensitivity analysis and optimization of sheet steel thickness for vibroacoustic behavior of enclosures

International audienceIn automotive applications, one of the keys to ensure weight reduction is the optimization of the sheet steel thickness. This paper presents a non-exhaustive list of sensitivity analysis methods (local, global and energy-based) allowing to determine which thicknesses could be reduced. The first results of an adaptive optimization procedure allowing reduction of the thicknesses under design constraints are also illustrated for the modal behaviour of an academic structure representing a simplified cab coupled with an acoustic cavity

Robust expansion of experimental mode shapes under epistemic uncertainties

International audienceImportant variations in response behaviors of power plant generators are observed in a population of nominally identica installations due to numerous and significant sources of variability. As a result, it proves to be extremely difficult to implement a predictive and reliable physics-based model. The present study attempts to leverage an existing non validated numerical model to reconstruct information on unobserved degrees of freedom based on the results of modal tests. An expansion method is proposed based on the concept of the constitutive relation error (CRE). This method leads to minimization of an energy-based functional that takes into account both errors in the model and in the test data. Due to lack of knowledge, commonplace in this kind of complex system, the expansion will be presented in the framework of robust approach. More precisely, the first objective of this article is to assess the robustness of the mode shape expansion in presence of large epistemic uncertainties that are represented as info-gap models. Secondly, a strategy will be presented to maximize the robustness of the expansion by appropriately selecting the model decision variables for a given horizon of uncertainty. The proposed methodology is illustrated on simple academic test cases