Predicting aircraft dynamics and vibration loads at components' interfaces is a key task for ensuring a robust design and development of the product. Usually, whereas in the case of isolate components the dynamic behavior can be predicted quite accurately, when several components are assembled through discontinuous junctions the predictiveness of a model decreases. The junctions, whose mechanical properties are seldom well characterized experimentally, often introduce nonlinearities in the loads' path. Additionally, their behavior is intrinsically uncertain and as a consequence, the dynamic response of the connected structures becomes stochastic. We propose a sample-based approach which aims to cope with both aspects, nonlinearities and uncertainties, and can be split in two main tasks. First, the computational cost of each deterministic simulation is minimized considering that the global nonlinear behavior depends on localized sources of nonlinearities at the interfaces. Second, the uncertainties are propagated through the model by a non-intrusive method based on Sobol's low discrepancy design. Attention is paid to the global sensitivity indices, which are estimated by creating a meta-model based on Polynomial Chaos Expansion. An industrial application considering an aircraft component whose dynamic behavior is affected by uncertain free-plays at its interfaces is presented.
The calibration of any sophisticated model, and in particular a constitutive relation, is a complex problem that has a direct impact in the cost of generating experimental data and the accuracy of its prediction capacity. In this work, we address this common situation using a two-stage procedure. In order to evaluate the sensitivity of the model to its parameters, the first step in our approach consists of formulating a meta-model and employing it to identify the most relevant parameters. In the second step, a Bayesian calibration is performed on the most influential parameters of the model in order to obtain an optimal mean value and its associated uncertainty. We claim that this strategy is very efficient for a wide range of applications and can guide the design of experiments, thus reducing test campaigns and computational costs. Moreover, the use of Gaussian processes together with Bayesian calibration effectively combines the information coming from experiments and numerical simulations. The framework described is applied to the calibration of three widely employed material constitutive relations for metals under high strain rates and temperatures, namely, the Johnson–Cook, Zerilli–Armstrong, and Arrhenius models.
Nonintrusive methods are now established in the engineering community as a pragmatic approach for the uncertainty quantification (UQ) and global sensitivity analysis (GSA) of complex models. However, especially for computationally expensive models, both types of analyses can only be completed by employing surrogates that replace the original models and are considerably less expensive. This work studies the construction of accurate and predictive meta‐models for their use in both UQ and GSA, and their application to complex problems in nonlinear mechanics. In particular, meta‐models based on radial functions are examined and enhanced with anisotropic metrics for improved predictiveness and cost effectiveness. Three numerical examples illustrate the performance of the proposed methodology.
The focus of this work is to present, from a practical point of view, a methodology able to tune the dynamic behaviour of complex assembled structures in frequency domain and optimizing the parameters, in terms of stiffness and damping, of lumped elements at junction points among structural components. Performing sensitivity studies through evaluating the impact of a set of modifications in the dynamic behaviour of complex structures by means of running several FEM models, requires significant computational effort and even if it is accepted, it is often not able to fit the experimental data adequately. In this context, the Direct Structural Dynamic Modification Method is defined as the procedure which permits one to evaluate the impact of a set of changes on the structural dynamic behaviour, without the need to continuously rerun the FEM Model. The Inverse SDM problem aims to identify in the framework of physical compatible sets of modifications, the most appropriate in order to fit the desired dynamic behaviour. In this study the ISDM problem is completed in order to be implemented efficiently in MATLAB and is applied to fit the analytical Frequency Response Functions (FRFs) with the experimental results. The full aircraft model and the Ground Vibration Test of the A340-600 are considered in order to test the power of the method when applied to a real and complex structure. From the results it can be seen that the parameters of the lumped elements at the interfaces among components are efficiently optimized in order to improve the dynamic response of the structure. The physical understanding of junction behaviour permits appropriate definition of the constraints of the optimization problem and to get a global minimum of the objective function. The results are shown in terms of FRFs and in terms of global FRF indicators
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