A sample-based approach to estimate the dynamic loads of components with nonlinear uncertain interfaces

Abstract

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.

Arbitrary polynomial chaos expansion method for uncertainty quantification and global sensitivity analysis in structural dynamics

“…wide range of applications [31][32][33][34][35][36][37], since it maintains great capability in modeling highly complex systems with a relatively low computational cost. PCE is a surrogate model to represent the probabilistic response as a series expansion of orthogonal polynomials of the input random variables.…”

“…The Lagrangian multipliers  can be determined by using the constraint conditions given in Eq. (36). It becomes the solution of multiple nonlinear equations below…”

Anisotropic meta‐models for computationally expensive simulations in nonlinear mechanics

“…Their use is becoming widespread and they are making possible the numerical exploration of complex industrial applications. 4,9 The former methods are constructed by projecting states and distributed parameters on a low-dimensional subspace, and, in some way, are still physics-based models. Common techniques to reduce the complexity of the large model are based on eigenfunctions, proper orthogonal decomposition (POD), and Krylov subspaces.…”

“…These surrogates can be broadly categorized into two nonexclusive families: reduction‐based and regression‐based models. Their use is becoming widespread and they are making possible the numerical exploration of complex industrial applications . The former methods are constructed by projecting states and distributed parameters on a low‐dimensional subspace, and, in some way, are still physics‐based models.…”

Uncertainty Quantification and Global Sensitivity Analysis in Computational Mechanics

“…All the models, from the coarser to more refined, contain choices which can compromise their reliability and predictiveness [10,11]. For example, there can be unquantified errors associated with the linear or non-linear behavior of a system, in the damping model [12], in the model of structural interfaces among components [13,14].…”