Ewald methods for inverse power-law interactions in tridimensional and quasi-two dimensional systems

In this paper, we derive the Ewald method for inverse power-law interactions in quasi-two dimensional systems. The derivation is done by using two different analytical methods. The first uses the Parry's limit, that considers the Ewald methods for quasi-two dimensional systems as a limit of the Ewald methods for tridimensional systems, the second uses Poisson-Jacobi identities for lattice sums. Taking into account the equivalence of both derivations, we obtain a new analytical Fourier transform intregral involving incomplete gamma function. Energies of the generalized restrictive primitive model of electrolytes ($\eta$-RPM) and of the generalized one component plasma model ($\eta$-OCP) are given for the tridimensional, quasi-two dimensional and monolayers systems. Few numerical results, using Monte-Carlo simulations, for $\eta$-RPM and $\eta$-OCP monolayers systems are reported.Comment: to be published in Journal of Physics A: Mathematical and Theoretical (19 pages, 2 figures and 3 tables

Seismic vulnerability of RC structures: Assessment before and after FRP retrofitting (case study)

In structural engineering, seismic assessment of existing structures is a crucial issue to provide adapted decisions in a vulnerability reduction context. Amongst the widely range of technical solutions for structural upgrading, external reinforcement by Fiber Reinforced Polymer (FRP) is an interesting tool. Nevertheless, the use of FRP as a retrofitting method is limited, one of the reasons being the lack of predictive numerical tools allowing the vulnerability assessment. Based on a case-study, this paper presents a simplified modeling strategy to assess the seismic vulnerability of an existing reinforced concrete building before and after FRP retrofitting. More specifically, the structure is simulated using multifiber beam elements, the model is validated with in-situ ambient vibrations records and a simplified method to consider FRP retrofitting is proposed. Non linear dynamic analysis studies are performed using a synthetic earthquake signal according to the Eurocode 8. Finally, local indicators, based on the European Macroseismic Scale (EMS 98), are adopted to quantify the damage level in the structure, before and after its FRP retrofitting.Keywords: earthquake; vulnerability; retrofitting; FRP; concrete; multifiber beam

Nonlocal damage based failure models, extraction of crack opening and transition to fracture

International audienceDamage models are capable to represent initiation and somehow crack propagation in a continuum framework. Thus crack openings are not explicitly described. However for concrete structures durability analysis, crack opening through transfer properties is a key issue. Therefore, in this contribution we present a new approach that is able from a continuum modelling to locate a crack from internal variable field and then to estimate crack opening along its path. Results compared to experimental measures for a three point bending test are in a good agreement with an error lower than 10% for widely opened crack (40μm)

Damage model for FRP-confined concrete columns under cyclic loading

International audienceIn structural engineering, seismic vulnerability reduction of existing structures is a crucial issue. External reinforcement with fiber-reinforced polymer (FRP) holds interest in achieving this aim. Its use as a retrofitting method is limited, however, for a number of reasons, including the lack of numerical tools for predicting cyclic loading. This paper presents a simplified stress-strain model suitable for monotonic and cycling loading capable of predicting the FRP's effect on reinforced-concrete columns. The model was inspired by two well-known concrete constitutive laws: one based on damage mechanics (La Borderie's concrete-damage model, 1991); the other on extensive experimental studies (Eid and Paultre's confined-concrete model, 2008). Validation is provided using experimental results on reinforced concrete columns subjected to axial and flexural cyclic loading. The proposed approach also deals with steel-bar rupture, considering low-cycle fatigue effects. All the simulations were conducted with multifiber Timoshenko beam elements

Stress-strain model for FRP-confined concrete columns under cyclic and seismic loading

In structural engineering, seismic vulnerability reduction of existing structures is a crucial issue. External reinforcement with fiber-reinforced polymer (FRP) holds interest in achieving this aim. Its use as a retrofitting method is limited, however, for a number of reasons, including the lack of numerical tools for predicting cyclic loading. This paper presents a simplified stress-strain model suitable for monotonic and cycling loading capable of predicting the FRP's effect on reinforced-concrete col umns. The model is inspired by two well-known concrete constitutive laws: one based on damage mechanics (La Borderie's concrete-damage model, 1991); the other on extensive experimental studies (Eid & Paultre's confined-concrete model, 2008). Validation is provided using experimental results on reinforced concrete columns subjected to axial and flexural cyclic loading. All the simulations were conducted with multifiber Timoshenko beam elements

Seismic vulnerability reduction: numerical modeling of FRP reinforcement using multifiber beams elements

This paper presents a simplified modeling strategy for reproducing the behavior of beam-column structures reinforced with Polymer Reinforced Fibers (FRP). A 1D concrete constitutive model has been recently proposed, suitable for both monotonic and cycling loadings. The model is inspired on two well-known concrete laws, one based on damage mechanics theory (La Borderie concrete damage model) and one based on experimental studies (Eid & Paultre's confined concrete model). Spatial discretization is done using multifiber Timoshenko beam elements. Validation of the strategy is provided using two case studies: a retrofitted bridge pier and a vulnerability analysis on an existing building

Yukawa potentials in systems with partial periodic boundary conditions I : Ewald sums for quasi-two dimensional systems

Yukawa potentials are often used as effective potentials for systems as colloids, plasmas, etc. When the Debye screening length is large, the Yukawa potential tends to the non-screened Coulomb potential ; in this small screening limit, or Coulomb limit, the potential is long ranged. As it is well known in computer simulation, a simple truncation of the long ranged potential and the minimum image convention are insufficient to obtain accurate numerical data on systems. The Ewald method for bulk systems, i.e. with periodic boundary conditions in all three directions of the space, has already been derived for Yukawa potential [cf. Y., Rosenfeld, {\it Mol. Phys.}, \bm{88}, 1357, (1996) and G., Salin and J.-M., Caillol, {\it J. Chem. Phys.}, \bm{113}, 10459, (2000)], but for systems with partial periodic boundary conditions, the Ewald sums have only recently been obtained [M., Mazars, {\it J. Chem. Phys.}, {\bf 126}, 056101 (2007)]. In this paper, we provide a closed derivation of the Ewald sums for Yukawa potentials in systems with periodic boundary conditions in only two directions and for any value of the Debye length. A special attention is paid to the Coulomb limit and its relation with the electroneutrality of systems.Comment: 40 pages, 5 figures and 4 table

Fault detection and isolation filter design for systems subject to polytopic uncertainties

This paper considers the robust fault detection and isolation (FDI) problem for linear time-invariant dynamic systems subject to faults, disturbances and polytopic uncertainties. We employ an observer-based FDI filter to generate a residual signal. We propose a cost function that penalizes a weighted combination of the deviation of the fault to residual dynamics from a given fault isolation reference model, as well as the effects of disturbances and uncertainties on the residual, using the Hinfin norm as a measure. The proposed cost function thus captures the requirements of fault detection and isolation and disturbance rejection in the presence of polytopic uncertainties. We derive necessary and sufficient conditions for the existence of an FDI filter that achieves the design specifications. This condition takes the form of easily implementable linear matrix inequality (LMI) optimization problem

Retrofitting reinforced concrete structures with FRP: Numerical simulations using multifiber beam elements

In structural engineering, seismic vulnerability reduction of existing structures is a crucial issue. External reinforcement by Polymer Reinforced Fibers (FRP) is an interesting tool in order to fulfill this aim. However, the use of FRP reinforcement as a retrofitting method is limited, one of the reasons being the lack of predicting numerical tools for cyclic loading. This paper presents a method to predict the behavior of beam-column structures considering the FRP reinforcement effect. It describes the construction of a 1D concrete constitutive model suitable for monotonic and cycling loadings. The model is inspired on two well-known concrete models, the first one based on the damage mechanics theory (La Borderie concrete damage model), and the second one based on experimental studies (Eid & Paultre's confined concrete model). Validation of the approach is done using experimental results on reinforced concrete beam and columns submitted to axial and flexural cyclic loading. The proposed method deals also with steel bar rupture considering low cycle fatigue effects. All the simulations are done using multifiber Timoshenko beam elements

Analyse et Réduction de la Vulnérabilité Sismique d'une Structure Existante en Béton Armé : Renforcement par TFC

La réduction de la vulnérabilité sismique des structures existantes est un enjeu majeur. Le renforcement d'éléments par Tissus de Fibres de Carbone (TFC) offre une réponse intéressante à cette problématique. Ces travaux proposent une stratégie simplifiée de modélisation non linéaire permettant de prédire le comportement d'une structure en béton armé renforcée par TFC. Celle-ci est fondée sur l'utilisation d'éléments finis poutres multifibres ainsi que de modèles d'endommagement et de plasticité. Le confortement d'éléments en flexion et le confinement des poteaux sont étudiés. Plus spécifiquement une loi constitutive cyclique pour béton confiné est proposée. Cette loi est fondée sur deux modèles, le premier basé sur la théorie de l'endommagement et le second sur une série d'études expérimentales. Cette approche est validée à travers deux cas d'études : une pile de pont renforcée et une analyse de vulnérabilité d'un ouvrage sous sollicitations statiques (poussée progressive) et dynamiques