A numerical model for non-linear dynamic analysis of slender masonry structures

A numerical model is presented to enable performing non-linear dynamic analysis of slender masonry structures and elements, such as towers and columns or masonry walls in out-of-plane flexure. Such structures are represented via a continuous one-dimensional model. The main mechanical characteristics of the material in all sections along the height of such structures are taken into account by means of a non-linear elastic constitutive law formulated in terms of generalized stress and strain, under the assumption that the material has no resistance to tension and limited compressive strength. The relations defined herein for the general case of hollow rectangular cross-sections are also aimed at enabling study of towers, bell-towers and similar slender structures.     

A computational model for the limit analysis of three-dimensional masonry structures

This paper extends previous work on the limit analysis of ductile frames and plane masonry arches to the limit analysis of three-dimensional masonry structures. A lower-bound approach is developed which can handle three-dimensional collapse mechanisms involving any combination of sliding, twisting and hingeing at the block interfaces. A computer program for determining the collapse load of such structures is used to study (a) the equilibrium limits of a block with four contact points resting on an inclined plane and (b) the collapse of a semicircular arch of four blocks. The paper also describes experimental and computational work on a radially symmetric model dome of 380 blocks subject to foundation settlement.

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Sommario Il presentre contributo estende al campo delle structture tridimensionali in muratura un precedente lavoro sull'analisi limite di telai duttili ed archi in muratura piani. Si e' sviluppato un approccio statico che analizza meccanismi di collasso tridimensionale ottenuti per combinazione dei meccanismi semplici di scorrimento e rotazione nel piano e fuori dal piano delle superfici di interfaccia tra i blocchi. Si descrivono (a) i limiti di equilibrio di un blocco con 4 punti di contatto su base inclinata, (b) le condizioni di collasso di un arco semicircolare costituito da quattro blocchi, applicando un programma di calcolo redatto per l'analisi e la definizione del carico di collasso di tali strutture. La terza parte dell'articolo presenta il lavoro sperimentale e di calcolo sviluppato su un modello di cupola a simmetria radiale costituita da 380 blocchi soggetta a cedimenti fondali.

     

A reduction model for eigensolutions of damped viscoelastic sandwich structures

The aim of this paper is to develop a reduction method to determine the modal characteristics of viscoelastic sandwich structures. The method is based on the high order Newton algorithm and reduction techniques. Numerical tests have been performed in the case of sandwich beams and cylindrical shells. The comparison of the results obtained by the reduction method with those given by direct simulation shows both a good agreement and a significant reduction in computational cost.     

Duplex model for homogenized elastic-viscoplastic behavior of plate-fin structures at high temperatures

In this study, a duplex model is developed as a constitutive model for the homogenized elastic-viscoplastic behavior of a class of plate-fin structures operating at high temperatures. This model consists of plate and fin layers, which are individually ruled by different macro-constitutive models. An anisotropic, compressible power-law equation that was derived in a recent study by the present authors is used to describe the homogenized viscoplastic behavior of the fin layer. On the other hand, an isotropic, incompressible power-law equation is used as the macro-constitutive equation of the plate layer. The duplex model developed is applied to an ultra-fine plate-fin structure made of Hastelloy X. It is shown that the duplex model is more successful under multiaxial loading than the corresponding simplex model in which plates and fins are non-separately homogenized.     

A simple meso-macro model based on SQP for the non-linear analysis of masonry double curvature structures

A 3D model for the evaluation of the non-linear behavior of masonry double curvature structures is presented. In the model, the heterogeneous assemblage of blocks is substituted with a macroscopically equivalent homogeneous non-linear material. At the meso-scale, a curved running bond representative element of volume (REV) constituted by a central block interconnected with its six neighbors is discretized through of a few six-noded rigid wedge elements and rectangular interfaces. Non linearity is concentrated exclusively on joints reduced to interface, exhibiting a frictional behavior with limited tensile and compressive strength with softening. The macroscopic homogenous masonry behavior is then evaluated on the REV imposing separately increasing internal actions (in-plane membrane actions, meridian and parallel bending, torsion and out-of-plane shear). This simplified approach allows to estimate heuristically the macroscopic stress–strain behavior of masonry at the meso-scale. The non-linear behavior so obtained is then implemented at a structural level in a novel FE non-linear code, relying on an assemblage of rigid infinitely resistant six-noded wedge elements and non-linear interfaces, exhibiting deterioration of the mechanical properties.Several numerical examples are analyzed, consisting of two different typologies of masonry arches (a parabolic vault and an arch in a so-called “skew” disposition), a ribbed cross vault, a hemispherical dome and a cloister vault. To fully assess numerical results, additional non-linear FE analyses are presented. In particular, a simplified model is proposed, which relies in performing at a structural level a preliminary limit analysis – which allows to identify the failure mechanism – and subsequently in modeling masonry through elastic elements and non-linear interfaces placed only in correspondence or near the failure mechanism provided by limit analysis. Simulations performed through an equivalent macroscopic material with orthotropic behavior and possible softening are also presented, along with existing experimental evidences (where available), in order to have a full insight into the capabilities and limitations of the approach proposed.     

A micro-mechanical model for the homogenisation of masonry

Masonry is a composite material made of units (brick, blocks, etc.) and mortar. For periodic arrangements of the units, the homogenisation techniques represent a powerful tool for structural analysis. The main problem pending is the errors introduced in the homogenisation process when large difference in stiffness are expected for the two components. This issue is obvious in the case of non-linear analysis, where the tangent stiffness of one component or the tangent stiffness of the two components tends to zero with increasing inelastic behaviour.The paper itself does not concentrate on the issue of non-linear homogenisation. But as the accuracy of the model is assessed for an increasing ratio between the stiffness of the two components, the benefits of adopting the proposed method for non-linear analysis are demonstrated. Therefore, the proposed model represents a major step in the application of homogenisation techniques for masonry structures.The micro-mechanical model presented has been derived from the actual deformations of the basic cell and includes additional internal deformation modes, with regard to the standard two-step homogenisation procedure. These mechanisms, which result from the staggered alignment of the units in the composite, are of capital importance for the global response. For the proposed model, it is shown that, up to a stiffness ratio of one thousand, the maximum error in the calculation of the homogenised Young's moduli is lower than five percent. It is also shown that the anisotropic failure surface obtained from the homogenised model seems to represent well experimental results available in the literature.     

Repair of masonry structures

Besides the traditional repair techniques of craftsmen for masonry structures, engineering methods and procedures such as grouting and reinforcing of old masonry are available. These technical measures can help to save the monumental value of historically important buildings more effectively than the procedure of dismantling and rebuilding; and, as a rule, they are distinctly less costly. Nevertheless, too much technical aid can destroy what is meant to be preserved. For that reason the investigations described in this paper on both improvement and development of engineer-like repair techniques have been focused on the goal of minimizing interventions and modern additions as far as possible.

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Sommario In alternativa alle tecniche tradizionali usate dagli artigiani e dai capomastri per la riparazione delle strutture murarie, sono oggi ampiamente sperimentate ed applicate alcune tecniche e metodi di ingegneria strutturale quale le iniezioni e l'inserimento di elementi resistenti a trazione. Interventi di questio tipo possono aiutare a preservare il valore storico e monumentale di edifici antichi, in maniera piu' filologica rispetto al metodo dello smantellamento e ricostruzione con nuovi elementi dello stesso materiale; e, di regola, hanno costi piu' contenuti. Ciononostante, l'uso indiscriminato di tali tecniche puo' finire per distruggere cio' che si aveva intenzione di conservare. Per tale motivo gli studi descritti nel presente contributo, sul miglioramento e sviluppo di tecniche di intervento strutturale, applicano la filosofia del minimo disturbo possible.

     

A linear viscoelastic model for solid polyethylene

Stress relaxation tests have been carried out on a blue, pipe grade PE 80 medium density polyethylene (BP Chemicals), to provide thermo-viscoelastic rheology for use in calculating thermal stresses in pipe production. Stresses up to 4 MPa were used, with strains up to about 2%, in tests at temperatures from 23° to 90°C. Within this range a linear viscoelastic model was applicable, provided the initial ramp strain rate was less than 7×10^–5 s^–1. The stress relaxation data was fitted directly by a model incorporating an elastic response to volumetric strains, and a generalised linear solid model, consisting of two Maxwell elements and a purely elastic element in parallel, for deviatoric strains. Arrhenius type temperature dependence of relaxation times and shear moduli is found, and within experimental accuracy the temperature dependence of all these model parameters is the same. As a consequence, and provided that the duration of the strain ramp is sufficiently short relative to relaxation times, the model leads to time-temperature superposition of the relaxation moduli, using the same shift factor on both the response magnitude and time axes.     

基于各向异性损伤本构模型的砌体结构抗震分析

进一步完善了应力张量的线性变换方法,并将其应用于砌体材料本构模型的开发。在整体式有限元模型中,因不区分砌块和砂浆而将其视为匀质的连续材料,难以用受拉和受压两个损伤变量准确描述灰缝的II型滑移破坏。为解决这一问题,提出应再引入一个针对II型滑移破坏的损伤变量。基于以上研究工作,对砌体结构的振动台试验进行了模拟。模拟结果进一步验证了本文提出的弹塑性损伤本构模型的有效性,以及在进行结构非线性分析方面的优越性。由于本文提出的本构模型能够较为真实地描述砌体墙的破坏模式,因此使用该模型进行结构非线性分析,除了能够获取结构的位移和应力等反应外,还能较为准确地实时提供结构中的损伤分布状态信息,找出结构的薄弱部位,并据此合理地设计结构或进行相应的结构修复。     

A multi-scale enriched model for the analysis of masonry panels

A multi-scale model for the structural analysis of the in-plane response of masonry panels, characterized by periodic arrangement of bricks and mortar, is presented. The model is based on the use of two scales: at the macroscopic level the Cosserat micropolar continuum is adopted, while at the microscopic scale the classical Cauchy medium is employed. A nonlinear constitutive law is introduced at the microscopic level, which includes damage, friction, crushing and unilateral contact effects for the mortar joints. The nonlinear homogenization is performed employing the Transformation Field Analysis (TFA) technique, properly extended to the macroscopic Cosserat continuum. A numerical procedure is developed and implemented in a Finite Element (FE) code in order to analyze some interesting structural problems. In particular, four numerical applications are presented: the first one analyzes the response of the masonry Representative Volume Element (RVE) subjected to a cyclic loading history; in the other three applications, a comparison between the numerically evaluated response and the micromechanical or experimental one is performed for some masonry panels.     

砌体结构长脉宽爆炸荷载损伤等级评估方法

随着百千吨级当量爆炸工业事故的频繁发生,建筑结构的损伤评估和抗爆安全性更受到关注。目前,构件级的评估方法相对成熟,而大当量冲击波作用下的建筑结构整体毁伤评估依旧是个开放性问题。本文中,面向结构级的毁伤评估,提出了一种新的评估方法?构件损伤加权。该方法以承重构件损伤程度为基础,通过基于应变能的构件权系数加权,进而评估结构级损伤破坏程度。为了验证评估方法的有效性,以典型砌体结构为例,利用自主研发的冲击波结构毁伤模拟有限元程序,开展了百毫秒脉宽爆炸冲击波荷载下结构动力学响应数值模拟。根据数值模拟结果,结合构件损伤加权的评估方法,获取砌体结构损伤等级与冲击波超压的关系。预测的超压值的相对误差为?16.9%～26.2%,验证了评估方法的有效性。该评估方法为获取砌体结构的超压-冲量曲线提供了可行的途径,可为结构的抗爆安全设计提供参考。     

A non-linear viscoelastic model for ceramics at high temperatures

High-temperature mechanical behavior of ceramics is characterized by non-linear rate dependent responses, asymmetric behavior in tension and compression, and nucleation and coalescence of voids leading to rupture. Moreover, rupture experiments show considerable scatter or randomness in fatigue lives of nominally equal specimens. To capture the non-linear, asymmetric time-dependent behavior, a new non-linear viscoelastic model is proposed. Non-linearity and asymmetry are introduced in the volumetric component. To model the random formation and coalescence of voids, each element is assigned a failure strain sampled from a lognormal distribution. An element is deleted when its volumetric strain exceeds its failure strain. Temporal increases in strains produce a sequential loss of elements (a model for void nucleation and growth), which in turn leads to failure. Non-linear viscoelastic model parameters are determined from uniaxial tensile and compressive creep experiments on silicon nitride. The model is then used to predict the deformation of four-point bending and ball-on-ring specimens. Simulation is used to predict statistical moments of rupture lives. Numerical simulation results compare well with results of four-point bending experiments.     

关于黏弹性材料的广义Maxwell模型

采用流变力学分析黏弹性材料的流变特性时,常要用到广义Maxwell模型 表达的应力松弛模量. 而从试验中获得的应力松弛模量,其表达式常为 Kohlrausch-William-Watts function(KWW函数)形式. 通过把KWW函数和广义Maxwell模型的拟合问题转化为两 矩阵相等的求解问题后,又把两矩阵的相等等价于两矩阵差值向量的一阶范数为无穷小的问 题,并通过引入广义逆矩阵,求得两矩阵差值向量的一阶范数的最小值,最后以一阶范数的 最小值为目标函数,松弛时间为约束条件,利用单纯形法对两矩阵差值向量的一阶范数的最 小值优化,从而提出了一种针对黏弹材料的KWW函数与广义Maxwell模型转换的计算方法. 借助于MATLAB软件,实现了对黏弹材料的广义Maxwell模型的拟合.     

A “constrained-chain” network model for viscoelastic fluids

A specific case of the general “constrained-chain” strain-dependent integral viscoelastic model is evaluated with steady simple shear data, stress growth and relaxation data, and steady elongational viscosity data. The model is qualitatively correct and quantitatively reasonable in its predictions and, on balance, compares favourably with strain-dependent, strain-rate-dependent, and stress-dependent models from the current literature. Specific model comparisons are made to demonstrate the effect of the “constrained-chain” or finite extensibility feature of the model.     

A model for the nonisothermal behavior of viscoelastic media

Summary A new constitutive model is derived for the viscoelastic behavior of polymers under non-isothermal loading. The model extends the concept of adaptive links (entanglements) between polymeric molecules to thermoviscoelastic media. By using experimental data for Nylon-6 and polyisobutylene in the vicinity of the glass-transition temperature, we find parameters of the model and study their dependence on temperature. The model is employed for the numerical analysis of the material response to time-periodic loads under isothermal conditions and to time-varying loads under heating. The results of numerical simulation demonstrate fair agreement with experimental data. Accepted for publication 23 May 1996     

A model for the thermorheological behavior of viscoelastic fluids

Using a power-law ansatz for the temperature dependence of the shear modulus on the level of internal variables, the thermorheological behavior is modeled for viscoelastic fluids of a special group of rheological constitutive equations (rate-type models). The model parameter introduced characterizes thermoelastic contributions. The relation between the model parameter and the physical quantities appearing in deformation processes is discussed. Based on the chosen temperature dependence of the shear modulus, thermodynamically consistent equations like the nonlinear rheological constitutive equation and the temperature equation are derived. The special cases of entirely entropy and energy elastic fluids are also considered. The thermorheological behavior (exo-, - or endothermal processes) of a viscoelastic fluid in a stress-growth experiment followed by relaxation is analyzed with respect to the model parameter.     

Second-gradient homogenized model for wave propagation in heterogeneous periodic media

The paper is focused on a homogenization procedure for the analysis of wave propagation in materials with periodic microstructure. By a reformulation of the variational-asymptotic homogenization technique recently proposed by Bacigalupo and Gambarotta (2012a), a second-gradient continuum model is derived, which provides a sufficiently accurate approximation of the lowest (acoustic) branch of the dispersion curves obtained by the Floquet–Bloch theory and may be a useful tool for the wave propagation analysis in bounded domains. The multi-scale kinematics is described through micro-fluctuation functions of the displacement field, which are derived by the solution of a recurrent sequence of cell BVPs and obtained as the superposition of a static and dynamic contribution. The latters are proportional to the even powers of the phase velocity and consequently the micro-fluctuation functions also depend on the direction of propagation. Therefore, both the higher order elastic moduli and the inertial terms result to depend by the dynamic correctors. This approach is applied to the study of wave propagation in layered bi-materials with orthotropic phases, having an axis of orthotropy parallel to the direction of layering, in which case, the overall elastic and inertial constants can be determined analytically. The reliability of the proposed procedure is analysed by comparing the obtained dispersion functions with those derived by the Floquet–Bloch theory.