The wave finite element method has been developed for waveguides and periodic structures with advantages in the calculation time. However, this method cannot be applied easily if the structure is subjected to complex or density loads and this is the aim of this article. Based on the finite element method, the dynamic equation of one period of the structure is rewritten to obtain a relation between the responses (DOF and nodal loads) on the left and right boundaries. This relation presents an additive term which links to the loads applying on the period. Then, by using WFE technique, we can compute the wave mode of the period and the wave decomposition. Because of the periodicity, we can also obtain a relation between the response and the left and right ends of the structure. Afterwards, the response of the structure is calculated by using the wave decomposition to apply in the dynamic stiffness matrix (DSM) approach or the wave analysis (WA). For the DMS approach, this technique shows that the external loads have no contribution to the global matrix but they lead to a equivalent force in the dynamic equation. Meanwhile, the external loads create waves propagating to the left and right of the structure in the WA approach.

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The wave finite element (WFE) method is now an established numerical method for obtaining the structural response of periodic structures. From a model of a substructure obtained from any finite element software, it allows to get dispersion curves and responses of finite periodic structures with a low calculation cost. Here, we consider some recent improvements of the method. First of all, the original WFE is often formulated with some point loads on the structure, but we show that it is possible to extend this to the consideration of general loads as pressure waves or moving loads for which external loads are applied on each substructure. Second, the classical WFE deals with structures in the frequency domain. It would be interesting to consider the analysis of periodic structures in the time domain, for instance to deal with blast loads. We present here one possibility to do so by computing absorbing boundary conditions in the time domain. By considering supplementary variables at the boundary, a new formulation can be obtained and a classical equation with extended mass, damping and stiffness matrices can be formulated in the time domain and solved by classical algorithms like the Newmark scheme. COMPDYN 2021 8 th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering M. Papadrakakis, M. Fragiadakis (eds.

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La pollution de l’air reste un problème environnemental majeur. Malgré les efforts importants réalisés pour limiter cette pollution, les niveaux de polluants présents dans l’atmosphère restent encore problématiques pour la santé, notamment en Asie et en Afrique. Si l’état des connaissances a considérablement progressé au cours des dernières décennies dans les domaines de la physico-chimie de l’atmosphère, de la toxicologie et de l’épidémiologie, d’importants verrous scientifiques subsistent. Notre capacité à relier sources de pollution et leurs impacts doit être améliorée pour mettre en œuvre des solutions plus efficaces. Cela passe par une meilleure estimation de l’exposition individuelle, mais aussi par une meilleure connaissance des pathologies et des mécanismes associés. Cette problématique nécessite non seulement de mettre en œuvre des approches transdisciplinaires entre acteurs académiques, mais aussi de développer des approches intégrant les institutionnels, les partenaires socio-économiques, les collectivités et, plus directement, les citoyens.