A time-domain method to solve transient elastic wave propagation in a multilayer medium with a hybrid spectral-finite element space approximation

International audienceThis paper introduces a new numerical hybrid method to simulate transient wave propagation in a multilayer semi-infinite medium, which can be fluid or solid, subjected to given transient loads. The medium is constituted of a finite number of unbounded layers with finite thicknesses. The method has a low numerical cost and is relatively straightforward to implement, as opposed to most available numerical techniques devoted to similar problems. The proposed method is based on a time-domain formulation associated with a 2D-space Fourier transform for the variables associated with the two infinite dimensions and uses a finite element approximation in the direction perpendicular to the layers. An illustration of the method is given for an elasto-acoustic wave propagation problem: a three-layer medium constituted of an elastic layer sandwiched between two acoustic fluid layers and excited by an acoustic line source located in one fluid layer

A Non-Parametric Approach for Uncertainty Quantification in Elastodynamics

Matrix variate distributions are are used to quantify uncertainty in the mass, stiffness and damping matrices. The proposed approach is based on the so called Wishart random matrices. The probability density function of the system matri-ces are derived using the maximum entropy method. It is assumed that the mean of the system matrices are known. A new optimal Wishart distribution is pro-posed to model the random system matrices. The optimal Wishart distribution is such that the mean of the matrix and its inverse produce minimum deviations from their deterministic values. The method proposed here gives a simple non-parametric approach for uncertainty quantification and propagation for complex aerospace structural systems. The new method is illustrated using two examples. Nomenclature D(ω) dynamic stiffness matrix F symbol for the inverse of a system matrix, F ≡ {M−1,C−1,K−1} f(t) forcing vector G symbol for a system matrix, G ≡ {M,C,K} H(ω) frequency response function (FRF) matrix In identity matrix of dimension n M, C and K mass, damping and stiffness matrices respectively On,m null matrix of dimension n×m q(t) response vector Γn (a) multivariate gamma function ν order of the inverse-moment constraint ω excitation frequency m,Ψ scalar and matrix parameters of the inverted Wishart distribution n number of degrees of freedom p,Σ scalar and matrix parameters of the Wishart distribution Conventions (•)T matrix transposition C space of complex numbers R space of real numbers R n space n × n real positive definite matrices Rn,m space n×m real matrice

Association of follow-up infarct volume with functional outcome in acute ischemic stroke: a pooled analysis of seven randomized trials.

BACKGROUND: Follow-up infarct volume (FIV) has been recommended as an early indicator of treatment efficacy in patients with acute ischemic stroke. Questions remain about the optimal imaging approach for FIV measurement. OBJECTIVE: To examine the association of FIV with 90-day modified Rankin Scale (mRS) score and investigate its dependency on acquisition time and modality. METHODS: Data of seven trials were pooled. FIV was assessed on follow-up (12 hours to 2 weeks) CT or MRI. Infarct location was defined as laterality and involvement of the Alberta Stroke Program Early CT Score regions. Relative quality and strength of multivariable regression models of the association between FIV and functional outcome were assessed. Dependency of imaging modality and acquisition time (≤48 hours vs >48 hours) was evaluated. RESULTS: Of 1665 included patients, 83% were imaged with CT. Median FIV was 41 mL (IQR 14-120). A large FIV was associated with worse functional outcome (OR=0.88(95% CI 0.87 to 0.89) per 10 mL) in adjusted analysis. A model including FIV, location, and hemorrhage type best predicted mRS score. FIV of ≥133 mL was highly specific for unfavorable outcome. FIV was equally strongly associated with mRS score for assessment on CT and MRI, even though large differences in volume were present (48 mL (IQR 15-131) vs 22 mL (IQR 8-71), respectively). Associations of both early and late FIV assessments with outcome were similar in strength (ρ=0.60(95% CI 0.56 to 0.64) and ρ=0.55(95% CI 0.50 to 0.60), respectively). CONCLUSIONS: In patients with an acute ischemic stroke due to a proximal intracranial occlusion of the anterior circulation, FIV is a strong independent predictor of functional outcome and can be assessed before 48 hours, oneither CT or MRI

Dynamic substructuring in the medium-frequency range

International audienceThere are several methods in linear dynamic substructuring for numerical simulation of complex structures in the low-frequency range, that is, in the modal range. For instance, the Craig-Bampton method is a very efficient and popular method. Such a method, based on the use of the first normal structural modes of each undamped substructure with fixed coupling interface, leads to small-sized reduced matrix models. In the medium-frequency range, that is, in the nonmodal range, and for complex structures, a large number of normal structural modes should be computed with finite element models having a very large number of degrees of freedom. Such an approach is not really efficient and, generally, cannot be carried out. We present a new approach in dynamic substructuring for numerical calculation of complex structures in the medium-frequency range. This approach is still based on the use of the Craig-Bampton decomposition of the admissible displacement field, but the reduced matrix model of each substructure with fixed coupling interface is not constructed using the normal structural modes of each undamped substructure but instead using the eigenfunctions associated with the first highest eigenvalues of the mechanical energy operator relative to the medium-frequency band for each damped substructure with fixed coupling interface. The method and numerical example are presented

Dynamic substructuring in the medium-frequency range

International audienceThere are several methods in dynamic substructuring for numerical simulation of complex structures in the low-frequency range, that is to say in the modal range. For instance, the Craig-Bampton method is a very efficient and popular method in linear structural dynamics. Such a method is based on the use of the first structural modes of each substructure with fixed coupling interface. In the medium-frequency range, i.e. in the non-modal range, and for complex structures, a large number of structural modes should be computed with finite element models having a very large number of degrees of freedom. Such an approach would not be efficient at all and generally, cannot be carried out. In this paper, we present a new approach in dynamic substructuring for numerical calculation of complex structures in the medium-frequency range. This approach is still based on the use of the Craig-Bampton decomposition of the admissible displacement field but the reduced matrix model of each substructure with fixed coupling interface, which is not constructed using the structural modes, is constructed using the first eigenfunctions of the mechanical energy operator of the substructure with fixed coupling interface related to the medium-frequency band. The method and a numerical example is presented

Dynamique stochastique non linéaire de deux systèmes dynamiques incertains couplés

National audienceThis paper deals with. a reduction method of models composed of a linear behaviour subsystem which has a high number of eigenmodes in the range of analysis and of a nonlinear behaviour subsystem. Each subsystem has model uncertainties and data uncertainties. Those uncertainties are taken into account using the usual parametric probabilistic approach and the non parametric probabilistic approach. We present a numerical example constituted of a simple system owning all the properties of the systems we are interested in and which validates the proposed methodology