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This manuscript presents a simplified approach to adhesive joints calculation. Aviation and space rocket engineering constructions joints deals with coaxial cylindrical pipes that can be connected by adhesive with advantages in terms of tightness, aerodynamic efficiency, manufacturability, low weight. Glue joints are, therefore, considered and simplified in this article by the analytical calculation of the shape functions for a macro-element applied to the Volkersen’s theory. The mathematical solution makes possible to calculate the explicit form of the stiffness matrix of the macro-element. The analysis proposed shows the perfect matching of the solution for a single element under classical mechanical loads.

International audience; In the context of increasing the strength-to-mass ratio of lightweight structures, the adhesively bonded joining technology appears to be an attractive solution. Nevertheless, the adhesive bonding method is important when the structural integrity of joints has to be ensured. In the literature, the cohesive zone models (CZMs) are shown to be able to predict both the static and fatigue strengths of adhesively bonded joints. The strength prediction is dependent on material laws and associated material parameters, characterizing the bondline behaviour mainly under pure mode I, mode II and mixed-mode I/II. The characterization methods are thus crucial. This paper aims at assessing the capabilities to identify the parameters of a particular CZM for both the inverse method, based on the energy balance associated with the path independent J-integral, and of a direct method described in this present work. The particular CZM has a classical shape based on the definition of a bilinear law for each of both pure modes, associated with pure mode interaction energy laws for initiation and propagation under mixed-mode I/II. The methodology used in this paper is based on a numerical test campaign only, involving the macro-element (ME) technique. A new approach for the fast formulation and implementation of ME modelling of two bonded beams is described.

The demand for designing lightweight structures without any loss of strength or stiffness has conducted many engineers and researchers to seek for alternative joining methods. In this context, adhesive bonding may appear as an attractive joining method. However the interest of adhesive bonding remains while the structural integrity of the joint is ensured. According to recent literature the Cohesive Zone Model (CZM) appears as a suitable approach able to predict both static and fatigue strength of adhesively bonded joints. This approach of the fracture process of adhesive layers is based on the modeling of the adhesive mechanical behavior through a set of adhesive cohesive properties in either mode I, mode II or mixed-mode I/II. The strength prediction of adhesively bonded joints is then highly dependent on the CZM parameters. The methods used to experimentally characterize them are thus essential. A new methodology, termed direct method, is presented and tested. It is based on the measurement of displacement field of bonded adherends at the crack tip of classical specimens allowing for the loading of the adhesive layer in pure mode I, pure mode II and mixed-mode I/II. The tested adhesive is a methacrylate–based two-component adhesive paste found under the reference SAF30 MIB manufactured by AEC Polymers (ARKEMA group). The adherends are in aluminium 6060. It is shown that it is possible to characterize the cohesive properties of the adhesive layer using the direct method. The numerical tests involve both adherends and adhesive nonlinearities. Nevertheless, the presented experimental implementation passes by the development of a dedicated data pre-processing to interpret the experimental measurements, highlighting the significance of the choice of the measurement means linked to the design of specimen.

The seismic performance assessment of historical masonry structures is still a complex issue in civil engineering. This paper investigates the seismic response of seven masonry churches, which are located in the province of Ferrara (Northern Italy) and suffered extensive damage during the 2012 Emilia earthquake. Different field surveys, which were conducted after the earthquake to collect information on typical damage patterns, provided a preliminary knowledge of utmost importance for developing detailed FE models of the churches and for better understanding the results of advanced numerical simulations. First, modal analyses were performed to have a preliminary insight into the dynamic behavior of the churches. Then, non-linear dynamic analyses with different peak ground accelerations were carried out in order to obtain the damage distribution in the churches and to identify the most vulnerable macro-elements. The results highlighted the influence of morphological and geometrical characteristics on the seismic behavior of the different macro-elements composing the churches.

Many reinforced concrete buildings have been built with masonry infill walls for architectural needs without considering their mechanical contribution. However, ignoring the structural influence of infills may lead to significant inaccuracies in the prediction of the actual seismic capabilities of the structure. Aiming at providing numerical tools suitable for engineering practice, simplified methodologies for predicting the nonlinear seismic behaviour of infilled frame structures (IFS) have been proposed, mostly considering the contribution of the infill as an equivalent diagonal strut element. In this paper, an alternative plane macro-element approach for the seismic assessment of IFS is proposed, validated and applied to a benchmark prototype building. The model validation is focused on recent experimental and numerical results that investigate the influence of non-structural infills, also in the presence of different openings layouts. As a benchmark investigation, a multi-storey plane frame prototype, for which the results of pseudo-dynamic tests are available, is investigated and compared to the results obtained by using a commonly adopted single-strut model. The merits and drawbacks of the considered numerical approaches are highlighted., info:eu-repo/semantics/publishedVersion

A macro-element to simulate the in- and out-of-plane response of masonry structures is proposed.The approach is based on a three-dimensional discrete element and requires a low computational cost.The performance is assessed by means of nonlinear static analyses on a historical masonry church. Recent earthquakes have demonstrated the high vulnerability of cultural heritage buildings, whose seismic assessment and rehabilitation constitute an important issue in seismic regions around the world. The high nonlinear behaviour of masonry material requires ad hoc refined finite element numerical models, whose complexity and computational cost are generally unsuitable for practical applications. For these reasons many authors proposed simplified numerical strategies to be used in engineering practice. However, most of these alternative methods are oversimplified since based on the assumption of in plane behaviour of masonry walls.In this paper a discrete-modelling approach for the simulation of both the in plane and out of-plane response of masonry structures is proposed. The method is applied to a basilica plan church, which has been partially investigated in the literature. The results show the capability of the proposed discrete element approach to simulate the nonlinear response of monumental structures also in those cases in which the 'in' and the 'out' of plane response cannot be decoupled, as it happens for many structural layouts typical of churches, ancient palaces and several other monumental structures.

The stability of velocity and pressure mixed approximations of the Stokes problem is studied, when different finite element (FE) spaces for each component of the velocity field are considered. Using the macro-element technique of Stenberg, analytical results are obtained for some new combinations of FE with globally continuous and piecewise linear pressure. These new combinations are introduced with the idea of reducing the number of degrees of freedom in some of the velocity components. Although the resulting FE are not stable in general, we show their stability in a wide family of meshes (uniformly unstructured meshes). Moreover, this method can be extended to any mesh family whenever a post-processing be performed in order to convert it in an unstructured mesh. Some 2D and 3D numerical simulations are provided to agree with the previous analysis.

International audience; Bolting technologies have been commonly used to assemble structural members in order to carry loads. However, the main drawback of these joints is the local reduction of the strength-to-stress ratio. Compared to the bolted joints, adhesive bonding technology allows for the increase of static and fatigue strength while reducing the weight. The Finite Element (FE) method is able to address the stress analysis of bonded joints. Nevertheless, analyses based on FE models are computationally expensive. Therefore, it is profitable to develop new simplified approaches enabling extensive parametric studies. A semi-analytical technique was developed to model the joints based on the formulation of 4-node special elements, termed macro-elements, which is able to simulate an entire bonded overlap at low computational costs. In this paper, a multilayered bonded-bars and a multilayered bonded-beams macro-elements are derived from bonded-bar and bonded-beam macro-elements. 1D-bar and 1D-beam simplified stress analyses of such multilayered joints are presented in order to predict the adhesive stress distributions along the overlap. For validation purpose, the results obtained by the simplified 1D-bar and 1D-beam model are compared with the results predicted by 1D-FE models. Good agreements are shown. Finally, the parametric studies are performed in order to understand the mechanical behavior of multilayered adhesively bonded structures. This presented simplified stress analysis can be used to deduce the sizing guidelines as a consequence of these parametric studies.

This paper investigates the seismic response of ten tuff masonry churches with basilica plan, which are located in Southern Italy, through advanced numerical simulations. The comparative study highlights considerable analogies and differences in the seismic response of the various churches in terms of damage distribution, energy density dissipated by tensile damage and maximum normalised displacements. The extensive set of numerical simulations performed shows that the geometrical characteristics of the different macro-elements are the main parameters influencing the seismic performance of the churches. A fundamental role is also played by the interactions of the different macro-elements with the adjacent structural parts. Recurrent damage concentrations and relevant out-of-plane deformations are observed for the most vulnerable macro-elements. The results obtained in this work, considering a representative sample of case studies, can be used to draw general conclusions about the seismic vulnerability of masonry churches with basilica plan at a territorial scale.

This is the post-print version of the final paper published in Engineering Structures. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2012 Elsevier B.V. Seismic behaviour of steel–concrete composite high-rise buildings, composed of external steel frames (SFs) and internal concrete tube (CT), with rectangular plan is investigated in this paper. A macro-element based model is established for seismic analysis of composite high-rise buildings aiming at predicting their global responses under earthquakes. By employing this macro-element based model, natural frequencies and vibration modes, storey and inter-storey drifts, overturning moments and storey shear forces of composite structures, induced by earthquakes, are able to be obtained with much less computation time and cost compared with using micro-element based analytical models. To validate its efficiency and reliability, the macro-element based model is employed to analyse a 1/20 scaled-down model of a 25-storey steel–concrete composite high-rise building subjected to simulated earthquakes with various intensities through a shaking table. Natural frequencies and storey drifts of the model structure are obtained from numerical analyses and compared with those from shaking table test results. It has been found that the calculated dynamic responses of the composite model structure subjected to minor, basic, major and super strong earthquakes agree reasonably well with those obtained from experiments, suggesting that the proposed macro-element based model is appropriate for inelastic time-history analyse for global responses of steel–concrete composite high-rise structures subjected to earthquakes with satisfactory precision and reliability. This research thus provides a practical model for elastic and inelastic deformation check of high-rise composite buildings under earthquakes. Ministry of Science and Technology of China

On the basis of the boundary integral equation method, in its symmetric formulation, the frictionless unilateral contact between two elastic bodies has been studied. A boundary discretization by boundary elements leads to an algebraic formulation in the form of a linear complementarity problem. In this paper the process of contact or detachment is obtained through a step by step analysis by using generalized (weighted) quantities as the check elements: the detachment or the contact phenomenon may happen when the weighted traction or the weighted displacement is greater than the weighted cohesion or weighted minimum reference gap, respectively. The applications are performed by using the Karnak.sGbem program made by some of the authors of this paper.

The structural analysis involves the definition of the model and selection of the analysis type. The model should represent the stiffness, the mass, and the loads of the structure. The structures can be represented using simplified models, such as the lumped mass models, and advanced models resorting the finite element method (FEM) and discrete element method (DEM). Depending on the characteristics of the structure, different types of analysis can be used such as limit analysis, linear and nonlinear static analysis, and linear and nonlinear dynamic analysis. Unreinforced masonry structures present low tensile strength, and the linear analyses seem to not be adequate for assessing their structural behavior. On the other hand, the static and dynamic nonlinear analyses are complex, since they involve large time computational requirements and advanced knowledge of the practitioner. The nonlinear analysis requires advanced knowledge on the material properties, analysis tools, and interpretation of results. The limit analysis with macro-blocks can be assumed as a more practical method in the estimation of maximum load capacity of structure. Furthermore, the limit analysis requires a reduced number of parameters, which is an advantage for the assessment of ancient and historical masonry structures, due to the difficulty in obtaining reliable data. The observation of the damage in masonry buildings caused by earthquakes in the past has been shown that the masonry structures can be discretized into several macro-blocks and interfaces. The macro-blocks are portions of a structure with similar material properties and structural behavior, to which the mechanical properties of the material can be assigned or, by simplification, they can be assumed to be infinitely rigid. The interfaces in a macro-modelling represent, in general, the cracks associated to the failure mechanisms. However, in a micro-modelling strategy applied to masonry, in which the units and the joints are individually considered, the interfaces simulate the behavior of the joints. Furthermore, different criteria for the strength parameters of macro-blocks and interfaces can be considered. The limit analysis (Fig. 1) with macro-blocks is a simplified and powerful structural analysis tool to evaluate the ultimate capacity of masonry structures by static models, involving the equilibrium of the macro-blocks through the limit analysis basic concepts.

A research project on the deformation capacity of unreinforced masonry structures is underway at the Institute of Structural Engineering of ETH Zurich. The development of the basic building blocks for the displacement-based design of unreinforced masonry structures is the objective of the present research project, which should be seen as a first step in an initiative to investigate the limits of the deformation capacity of unreinforced masonry walls. This paper presents a summary review of previous experimental and analytical studies on the deformation capacity of unreinforced masonry walls subjected to in-plane loading. This review is the first phase of the aforementioned research program. A summary of 71 shear tests on unreinforced masonry walls is presented in the form of a database, along with the statistical analysis and discussion of the tests results. Furthermore, three different computational approaches for structural masonry, i.e. micro-modelling, macro-modelling and macro-element discretization, are discussed, and a review of macro-elements for the in-plane response of unreinforced masonry walls is presented. The reviewed models are discussed and a set of conclusions is given. Special attention is devoted to the deformation capacity parameter throughout the paper. Finally, the paper shows the limitations of our current state of knowledge of the deformation capacity of structural masonry. ISSN:2008-3556 ISSN:2008-6695

Dans le cadre de la technologie d'assemblage par collage, l'évaluation des propriétés interfaciales est essentielle afin de déterminer la réponse globale de l'assemblage collé. En ce qui concerne la caractérisation mécanique des assemblages collés, une grande gamme de tests est largement utilisée pour déterminer les propriétés des adhésifs (rupture cohésive) et peu de tests sont disponibles afin d’évaluer les propriétés interfaciales entre les adhésifs et les substrats (rupture adhésive). Ainsi, parmi les tests de caractérisation d’une rupture adhésive, le test de flexion trois points peut être appliqué afin d’examiner les interactions entre l'adhésif et le substrat. Néanmoins, une comparaison directe de l’adhérence entre ce test et d’autres essais n’est pas possible, en raison des répartitions des contrainte et de modes de sollicitations différents. Une solution pratique pour résoudre ce problème consiste à l’application d’un critère couplé contrainte-énergétique (CC) puisque les propriétés d'interface sont indépendantes de l'épaisseur du substrat et/ou adhésif. Ces travaux de thèse proposent une méthode originale d'exploitation des essais de flexion trois points pour déterminer les propriétés interfaciales. Cette méthode est basée sur le critère couplé alimenté par une modélisation simplifiée par macro-éléments de l'essai..De plus, le comportement global du test de flexion trois points a été établi en termes d’adhérence, de taux de restitution d’énergie incrémentale et de contrainte critique. La thèse vise à faire un premier lien entre les propriétés interfaciales du système polyépoxy-aluminium et les propriétés cohésives de l’adhésif. Ainsi, cette thèse peut être vue comme un premier pas vers la capacité à prédire la rupture interfaciale dans le cadre d'un test de flexion trois points. En conclusion, l'apparition d'une rupture adhésive ou cohésive et la propagation de rupture instable ou stable des assemblages collés ont été triées et classées en fonction des propriétés d'interface. In the frame of the adhesive bonding technology, the assessment of interfacial properties has an essential role in determining the adhesive joints' global responses. Various surface preparations are available for each type of metallic substrate. There are plenty of tests widely used for mechanical characterization to determine the adhesive properties and few tests to assess interfacial properties. For such a case, a specific three-point bending test can be applied to examine the interactions between adhesive and substrate. On the other hand, a direct comparison of the critical force is not always possible because of geometrical incompatibility. A practical solution for the last issue is applying a coupled stress-energy criterion (CC) to asses the adhesive-to-substrate interface, and therefore, the mechanical properties of the interface are no more dependent on the geometry considered. In the present works, the interfacial properties between an aluminum alloy 2024-T3 and the adhesive DGEBA/DETA™ under many preparation conditions were determined using the CC and the macro-element technique.As a result, the three-point bending test's overall behavior is established in terms of interface strength (adherence), such as incremental energy release rate and critical stress. The Thesis aims to propose a preliminary correlation of an epoxy-aluminum system and the cohesive properties of such an adhesive. Thus, the Thesis can be read as the first work towards the ability to predict the interface failure in the frame of three-point bending test using different geometries. In conclusion, the occurrence of an adhesive or cohesive failure and the unstable or a stable failure propagation of the adhesively bonded system are sorted and classified as a function of interface properties.