1,721,013 research outputs found
A novel approach to model differential settlements and crack patterns in masonry structures
No full textThe present paper introduces a novel methodology for accurately modelling differential settlements beneath the foundations of masonry structures and the resulting crack patterns. In contrast to standard strategies, which typically impose predefined settlements at the structure's base, the proposed approach directly accounts for the soil–structure interaction by coupling the mechanical responses of masonry and soil. Specifically, the mechanical behaviour of the masonry is accurately modelled using an elastic no-tension approach, while the soil is represented as an elastic half-plane. The solution to the coupled mechanical problem, satisfying both equilibrium and compatibility conditions, is obtained through an iterative optimisation-based procedure. Several 2D numerical applications, considering different geometries and loading conditions, are provided to demonstrate the proposed procedure's effectiveness and performance and highlight its potential
Anisotropic yield behaviour of adobe masonry
No full textEarth is one of the most diffused building materials all over the world. Adobe constructions of different type can be found in large areas belonging to developing countries and in some cases are part of Cultural Heritage. The peculiar material characteristics with particular regard to fragility of the blocks together with the strong anisotropy have been experimentally studied, and numerical analyses have been performed in order to design optimal retrofitting techniques. In general classical constitutive models have been applied in this case. This paper proposes an approach to a constitutive model for this material, developed in the framework of rate independent softening plasticity, involving a yield criterion in which anisotropic friction and cohesion tensors are considered. It turns out to be generally useful for materials characterized by ultimate behaviour which varies according to the direction, such as the adobe masonry. A geometrical representation of the limit domain in the case of plane stress, together with the comparison with results of laboratory tests on adobe masonry is presented and discussed. It is shown that the framework of plasticity with internal variables provides a coherent description of the softening problem to represent the behaviour of adobe masonry
Isolation of freestanding art objects
No full textThe study of the rocking response of statues and in general the objects contained within Museums, is a research topic of great interest, being part of research and policy in the more general field of Cultural Heritage. Although the seismic protection of buildings of historical and cultural significance has been developed in all the last century, the protection of the contained objects, with reference to how they are displayed or stored has been only in the last years a key question. Significant is the case of statues and ceramics placed on pedestals. In particular cases, like the Bronzi of Riace, on purpose isolation systems have been developed, while in general museum exhibitions are not equipped with devices capable of mitigating the oscillations induced by possible earthquakes. This paper focuses the attention on this last problem, i.e. objects that can be considered as rigid bodies simply supported on the main structure, leaving out of account the filter’s effect due to the action of structure on the show-case or pedestal. This problem is the same of a large class of non-structural components, such as mechanical and electrical hospital and laboratory equipment that can lose their functionality because of earthquake motions. The influence of a further rigid body inserted between the moving base and the statue is examined in this paper. A preliminary sensitivity analysis is made on order to obtain the optimal friction coefficient to be created in these last surfaces inserte
Seismic behaviour of structures with plastic shear effects
Full text linkNon-linear dynamics is generally recognized as the most reliable method to carry out analyses of structures subjected to earthquake actions. In general non-linear dynamics requires a great level of expertise, as well as cost and time necessary for calculation. The lack of suitable computational techniques has induced seismic analyses involving two classes of simplified procedures: modal approximations and constitutive and structural models with sufficient accuracy and low numerical complexities. The dynamic response of building structures subjected to seismic loads has been often examined using the single-degree-of-freedom model, that provides a good estimation of the fundamental response mode, which is normally responsible for overall structural failure. A SDOF analysis can give a preliminary assessment for a protective structure, even in cases in which the constitutive models are somewhat more complex.
The rigid-plastic cantilever beam can be in fact a simple structural scheme to clarify the behaviour of more complex structures and to verify the accuracy of the numerical methods in a non-linear dynamic analysis. In general, significant differences exist between a complete building and uniform beams, nevertheless the continuum model provide useful results. This paper presents a general treatment to develop approximate solutions for rigid-plastic response of structures subjected to base harmonic pulse, that has been shown in literature as an appropriate approach to the seismic analysis. A numerical procedure has been on purpose developed, taking into account two different approaches: a step-by-step solution of the general non linear dynamic problem and the evaluation due to a modal approximate response, satisfying both kinematical admissibility requirements and boundary conditions. An estimation of the error due to the second approach is given. In order to assess the reliability of the approximate procedure it is shown that the approximation does not depend on the forcing accelerogram
A direct technique for the homogenization of periodic beam-like structures by transfer matrix eigen-analysis
No full textTo homogenize lattice beam-like structures, a direct approach based on the matrix eigen- and principal vectors of the state transfer matrix is proposed and discussed. The Timoshenko couple-stress beam is the equivalent continuum medium adopted in the homogenization process. The girders unit cell transmits two kinds of bending moments: the first is generated by the couple of the axial forces acting on the section nodes, the other one is due to the moments directly applied at the node sections by the adjacent cells. This latter moment is modelled as the resultant of couple-stress. The main advantage of the method consists in to operate directly on the sub-partitions of the unit cell stiffness matrix. Closed form solutions for the transmission principal vectors of the Pratt and X-braced girders are also attained and employed to calculate the stiffnesses of the related equivalent beams. Unit cells having more complex geometries are analysed numerically. As a result, the principal vector problem is always reduced to the inversion of a well-conditioned (3×3) matrix employing the direct approach. Hence, no ill-conditioning problems, affecting all the known transfer methods, are present in the proposed method. Finally, comparing the predictions of the homogenized models with the finite element (f.e.) results of a series of girder, a validation of the homogenization method is performed
Parametric design of purely compressed shells
No full textWithin the frame of parametric design, in the present work we focus on a very special objective, namely parametrically generating families of purely compressed shells. A similar task can be pursued by adopting for the equilibrium analysis the so-called Thrust Network Analysis for which the shell structure is condensed into a network of bars. Here instead, we adopt a continuum approach, namely the so-called Membrane Equilibrium Analysis. With this continuum approach, a purely compressed membrane equilibrium solution is searched by solving a scalar second-order partial differential equation representing the transverse equilibrium equation of the membrane. The shell is compressed if the membrane surface is contained within the volume of the shell and if the stress potential is concave. For a given shell, the main difficulty is represented by the fulfillment of the concavity constraint for the stress potential. In the present study, this difficulty is overcome by assigning families of convenient concave stress potentials and considering the shape as the unknown. By considering stress potentials or boundary data controlled by a few parameters, such variable parameters can be manipulated in order to alter the end result. Other methods tackling the stress function with the help of a computer, exist in the literature, but the main contribution of the present paper is the shape analysis of compression-only shells with the help of finite element apparatus. A few illustrative examples are presented to demonstrate the method
Rigid block models for masonry structures
No full textMasonry structural modelling needs of a completely different methodology from the ones adopted for ductile structures. In fact, the concepts of strength, stiffness and elastic stability, fundamental for the latter structures, play a marginal role in masonry mechanics. In this respect, Heyman’s theory, gives a modern turn to the old methods of masonry design, adopting a set of very simple and clear mechanical hypotheses. In these papers, the basic ingredients of a new method based on unilateral equilibrium and rigid block kinematics, which may allow the implementation of Heyman’s model for masonry on a computer, is introduced. In particular a simple method based on energy minimisation, with the possibility of combining the effects of loads and settlements on real masonry structures, is developed
A continuous energy-based numerical approach to predict fracture mechanisms in masonry structures: CDF method
No full textIn the present paper, we propose the Continuous Displacement for Fracture (CDF) method, a continuous energy-based numerical approach to find mechanisms and crack patterns exhibited by 2D masonry structures subjected to given loads and settlements. The structure is modelled through the normal, rigid, no-tension material, and the equilibrium problem is solved as the minimum of the total potential energy (TPE). With the CDF method the solution is sought in the space of continuous functions. The CDF performances are compared and illustrated against the PRD approach that finds the TPE minimum in the space of small, piecewise-rigid displacements. The CDF method is displacement-based approach, allowing for a direct control of the effects of foundation settlements. Some problems are proposed to benchmark the methodology against both PRD and analytical solutions to also clearly illustrate its peculiarities. Finally, its use and potentials are benchmarked and compared on a case study. CDF provides results in good agreement with both the PRD approach and another more sophisticated model. The main outcome is that, although more computationally cumbersome, CDF is mesh independent and perfectly captures a clear subdivision of the structural domain into macro-regions behaving as rigid or quasi-rigid bodies
Parametric design of purely compressed shells
No full textWithin the frame of parametric design, in the present work we focus on a very special objective, namely parametrically generating families of purely compressed shells. A similar task can be pursued by adopting for the equilibrium analysis the so-called Thrust Network Analysis for which the shell structure is condensed into a network of bars. Here instead, we adopt a continuum approach, namely the so-called Membrane Equilibrium Analysis. With this continuum approach, a purely compressed membrane equilibrium solution is searched by solving a scalar second-order partial differential equation representing the transverse equilibrium equation of the membrane. The shell is compressed if the membrane surface is contained within the volume of the shell and if the stress potential is concave. For a given shell, the main difficulty is represented by the fulfillment of the concavity constraint for the stress potential. In the present study, this difficulty is overcome by assigning families of convenient concave stress potentials and considering the shape as the unknown. By considering stress potentials or boundary data controlled by a few parameters, such variable parameters can be manipulated in order to alter the end result. Other methods tackling the stress function with the help of a computer, exist in the literature, but the main contribution of the present paper is the shape analysis of compression-only shells with the help of finite element apparatus. A few illustrative examples are presented to demonstrate the method
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