1,721,056 research outputs found

    Fast brick-based homogenized limit analysis for in- and out-of-plane loaded periodic masonry panels

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    This paper presents a 3D brick-based model that aims at the derivation of in- and out-of-plane homogenized failure surfaces for masonry. The considered masonry panel is discretized into regular parallelepiped 3D finite elements that are supposed to be rigid; the model here introduced uses a Kirchhoff-Love plate kinematics for the out-of-plane description of the displacement rate field of the elements. A linear programming problem formulated in standard form is scripted into Matlab to derive the in- and out-of-plane homogenized failure surfaces, also enabling the extraction of failure modes for the considered masonry element. The constraints of the linear programming problem come from the combination of an upper bound limit analysis problem and a homogenization-based approach. The proposed model is validated for two separate case studies: a running bond masonry test-window and an English bond masonry test-window. The homogenized failure surfaces resulting from the current model show good correspondence to those presented in three distinct works available in literature. Also, a few relevant failure modes are derived for the two case studies, and they are consistent with the expected deformed shapes at collapse for their related load conditions

    3D homogenized limit analysis of non-periodic multi-leaf masonry walls

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    This paper presents a 3D model aiming at investigating the out-of-plane collapse behavior of multi-leaf non-periodic masonry walls. These structural elements are widely employed in several constructions that are part of the European architectural heritage, but have been seldom addressed in the available literature due to their natural complexity and uniqueness. Specifically, the model here proposed allows a quick assessment of the out-of-plane collapse behavior of multi-leaf walls through the extraction of out-of-plane homogenized failure surfaces, acting as macroscopic failure criteria in bending and torsion. These failure surfaces are obtained after solving a standard-form linear programming problem written into a MATLAB script, which expresses a limit analysis problem pairing the well-established upper bound theorem and a homogenization approach. A twofold numerical application is performed by investigating a rubble masonry three-leaf wall and a quasi-regular three-leaf wall; in the latter case study, the influence of the rate of transversal interconnection between the outer wythes of the wall is also investigated. The results show that the presence of two different masonry bonds in the outer wythes entails some changes in the out-of-plane collapse behavior of the two case studies: namely, the out-of-plane response of the wall both under flexural and torsional actions is increased for the rubble masonry three-leaf wall, whereas it is decreased for the quasi-regular three-leaf wall. Moreover, in the latter case it is once more confirmed that a good transversal interconnection between the outer wythes - usually brought by the presence of transversal bricks – has beneficial effects on its out-of-plane collapse behavior, which are displayed both by the out-of-plane homogenized failure surfaces and deformed shapes at collapse

    Seismic vulnerability of masonry walls through an innovative voxel limit analysis homogenization approach

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    This paper addresses the seismic vulnerability of masonry walls, which is assessed using a homogenization-based limit analysis approach for modelling their out-of-plane behavior. The finite element mesh for the numerical model of the masonry wall or panel under investigation is generated from the actual geometry through a voxel approach: once the in-plane and transversal layout of the wall are identified, one voxel (i.e. 3D pixel) is transformed into a finite element. One stretcher bond masonry test-window is considered in this paper. Its out-of-plane behavior is then assessed by solving a limit analysis problem scripted into a Matlab code, whose formulation is also based on homogenization, evaluating their collapse load multiplier. The post-processing stage consists in the derivation of homogenized out-of-plane failure surfaces for the considered test-window. These are expressed in terms of bending moments, which represent the bending strengths of the test-window; they are then compared to similar homogenized failure surfaces obtained in a previous work for validation. Eventually, the collapse mechanisms for the considered test-window are identified and critically discussed

    3D voxel homogenized limit analysis of single-leaf non-periodic masonry

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    This paper presents an extensive investigation on the out-of-plane collapse behavior of single-leaf non-periodic masonry walls. This is achieved by deriving out-of-plane homogenized failure surfaces from test-windows that are extracted from various location within the same non-periodic masonry wall. The concept of “test-window” is inspired by that of Statistically Equivalent Periodic Unit Cell (SEPUC), which is an evolution of that of Representative Element of Volume (REV), and is needed for successfully applying homogenization to non-periodic masonry. An innovative feature introduced in this paper is the automatic generation of a suitable 3D finite element mesh directly from the sketch of the considered masonry test-window, based on a so-called “voxel strategy” that converts each voxel (the 3D equivalent of a pixel) into a finite element. Moreover, this mesh generating procedure enables the correct representation of the transversal layout of the test-window, and it also contains a coarsening strategy that allows a reduction of the overall number of finite elements in the 3D mesh. For the derivation of the out-of-plane homogenized failure surfaces a linear programming problem is solved, which is based on the upper bound theorem of limit analysis coupled with a homogenization approach. The investigation is performed on six real case studies displaying different degrees of non-periodicity: for the four test-windows of each case study, two out-of-plane homogenized failure surfaces are extracted (flexural and torsional) as well as three relevant deformed modes at collapse. Eventually, the results are critically commented; comparisons are drawn among the case studies, highlighting the influence of each non-periodic masonry bond on the results

    Automated procedure for the creation of finite element mesh: Application to non-periodic historical masonry

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    This paper presents an automated procedure that enables the creation of a finite element mesh directly from the image file representing the rasterized sketch of a generic masonry element. This procedure goes under the name “pixel strategy” if a 2D finite element mesh is needed, where the elements are planar and rectangular; conversely, its extension in the 3D case is named “voxel strategy”, and there the resulting finite elements are solid bricks. The finite element meshes so obtained are then used for extracting homogenized in-plane failure surfaces for historical masonry cells, which display a non-periodic arrangement of units. These surfaces are consistent with the expected results, and their shapes suggest that the behavior of such type of masonry may range between orthotropic (if bed mortar joints are clearly noticeable) and quasi-isotropic (if some units spread over two or more masonry layers)

    Creating a finite element mesh of non-periodic masonry from the measurement of its geometrical characteristics: A novel automated procedure

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    This paper presents an automated procedure that enables the creation of a finite element mesh directly from an image file representing a rasterised sketch of a masonry element. When used to create a 2D mesh with planar and rectangular elements, the procedure is called 'pixel strategy', and the creation of a 3D mesh with elements of solid brick is called 'voxel strategy'. The homogenised in-plane and out-of-plane failure surfaces of historical masonry cells that display a non-periodic arrangement of units can be extracted from the obtained finite element meshes. In our tests, these surfaces were consistent with the expected results, and their shapes suggest that the behavior of this type of masonry may range between orthotropic (if bed mortar joints are clearly noticeable) and quasi-isotropic (if some units spread over two or more masonry layers)

    2D pixel homogenized limit analysis of non-periodic masonry walls

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    This paper presents a novel and straightforward procedure for the derivation of homogenized failure surfaces for non-periodic masonry. The most innovative feature of this procedure is the automatic generation of a convenient finite element mesh directly from the sketch of the considered masonry panel, based on the so-called “pixel strategy” that converts each pixel into an element. An upper bound limit analysis problem coupled with homogenization is then solved by aptly formulating it as a linear programming problem. Another main feature is the implementation of a reduced formulation of such problem (called “master-slave approach”) so that the number of unknown variables is reduced and, consequently, the computational times needed for the extraction of the homogenized failure surfaces are shortened as well. A simple procedure is also implemented for a quick identification of the statistical Representative Element of Volume (or REV) for a non-periodic masonry panel. The REV is the smallest portion of a composite material that includes all the physical and geometrical characteristics needed for its complete description. The reliability of the procedure is tested by investigating six case studies displaying different degrees of non-periodicity, extracting and critically commenting the results obtained in terms of homogenized failure surfaces and failure modes
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