Rigid Block Model Research Articles

Big data approach for the simultaneous determination of the topology and end-effector location of a planar linkage mechanism

Although significant advances have been made in mechanism synthesis to find a mechanism generating a desired motion at its end-effector, no available synthesis methods can determine the topology of a mechanism and its end-effector location simultaneously. It is generally difficult to pre-determine the location of the end-effector relative to the input drive link because the mechanism synthesis may fail if the end-effector location is incorrectly selected. Therefore, the simultaneous determination of the mechanism topology and its end-effector location can be critically useful to advance automated mechanism synthesis. Motivated by this, we propose a neural network-based big data approach to achieve the simultaneous determination. To implement a big data approach which requires a training dataset consisting of diverse mechanisms of different topologies, we propose the use of a spring-connected rigid block model as a unified means to be able to represent diverse mechanisms. The big data approach is followed by gradient-based shape optimization to determine the detailed dimensions of the mechanism synthesized by the approach. The effectiveness and validity of the proposed method are checked with various mechanism synthesis problems.

Large displacement analysis of dry-joint masonry arches subject to inclined support movements

In this paper, the structural response of a segmental dry-joint masonry arch subjected to increasing support displacements was investigated. The arch behaviour was analysed in the framework of large displacements using finite element (FE) and rigid block (RB) models, both based on a micro-modelling strategy. Once the two modelling approaches were validated against experimental results from literature, nonlinear analyses were carried out considering different configurations of support displacements (i.e. vertical, horizontal and inclined). The effect of the displacement direction on the arch response was evaluated in terms of initial hinge position, collapse mechanism, support reaction-displacements curves as well as ultimate displacement capacity. The sensitivity of the results to the number of voussoirs was also investigated. The good agreement between the results from the two models allowed to draw new conclusions about the response of segmental masonry arches to inclined support displacements in the large displacement regime. A limit displacement domain computed as a function of the direction of the support displacements is also proposed.

Numerical and Experimental Response of Free-Standing Art Objects Subjected to Ground Motion

ABSTRACT Earthquakes may damage buildings, but they also induce uplift and overturn the content of a building that, in the case of museums, can lead to the irreparable loss of art objects. In many cases, these objects, subjected to seismic actions, can be modeled considering the nonlinear dynamics of rigid blocks. This paper is focused on the seismic behavior of statues, which generally present a quite complex geometry, and are mostly characterized by a pronounced unsymmetrical response under seismic excitations. The proposed study, involving both numerical analyses and experimental tests, is applied to the masterpiece Venere Landolina of the Paolo Orsi museum (Syracuse, Italy). Analytical simulations are conducted according to a novel rigid block model accounting for asymmetric behavior and contact impairments. The experimental campaign is conducted on a scaled physical prototype, built according to a highly detailed digital model obtained by 3D survey. The numerical and experimental campaign is conducted with reference to compatible seismic ground motions, conveniently scaled to cope with scale effects. The results are finally correlated and discussed, showing the potential of the proposed approach for modeling artwork in seismic conditions and the reliability of a combined experimental and numerical strategy to assess the seismic safety of statues.

A rigid block model with no-tension elastic contacts for displacement-based assessment of historic masonry structures subjected to settlements

This paper deals with the vulnerability assessment of historic masonry structures subjected to settlements using rigid block modelling. A 2-D rigid block model with unilateral elastic contacts and finite friction is developed for the evaluation of the displacement capacity in the large displacement regime by push-down analysis. A variational formulation of the rigid block model is adopted, which relies on associative behavior for displacement rates. Under this assumption, the equation systems governing the behavior of the rigid block model can be uncoupled into two equivalent force and displacement-based problems, thus reducing computational costs. The numerical model was validated against the results of an ad-hoc experimental campaign on small scale tuff panels and against the tests on a small-scale masonry façade subjected to moving supports, from the literature. Applications of the proposed modelling approach are presented to the assessment of a full scale, monumental masonry façade. Following classic force-displacement methods that are used in the case of seismic actions, capacity curves are proposed for the damage assessment induced by settlements. Those state the relation between the base reaction at the moving supports and the displacement of a control point, which is obtained from the push-down analysis. Finally, comparisons with empirical assessment methods from the literature are presented.

Topology Optimization of Linkage Mechanisms Simultaneously Considering Both Kinematic and Compliance Characteristics

Abstract Studies on the topology optimization of linkage mechanisms have thus far focused mainly on mechanism synthesis considering only kinematic characteristics describing a desired path or motion. Here, we propose a new topology optimization method that synthesizes a linkage mechanism considering both kinematic and compliance (K&C) characteristics simultaneously, as compliance characteristics can also significantly affect the linkage mechanism performance; compliance characteristics dictate how elastic components, such as bushings in a vehicle suspension, are deformed by external forces. To achieve our objective, we use the spring-connected rigid block model (SBM) developed earlier for mechanism synthesis considering only kinematic characteristics, but we make it suitable for the simultaneous consideration of K&C characteristics during mechanism synthesis by making its zero-length springs multifunctional. Variable stiffness springs were used to identify the mechanism kinematic configuration only, but now in the proposed approach, they serve to determine not only the mechanism kinematic configuration but also the compliance element distribution. In particular, the ground-anchoring springs used to anchor a linkage mechanism to the ground are functionalized to simulate actual bushings and to identify the desired linkage kinematic chain. After the proposed formulation and numerical implementation are presented, case studies are considered. In particular, the effectiveness of the proposed method is demonstrated with a simplified two-dimensional vehicle suspension design problem.

SEISMIC VULNERABILITY ASSESSMENT OF THE TRIUMPHAL ARCH OF CARACALLA IN VOLUBILIS (MOROCCO): PAST EVENTS AND PROVISIONS FOR THE FUTURE

Abstract. The triumphal arch of Caracalla in the Roman archaeological site of Volubilis dates back to 216 AD. It was built in a strategic position at the intersection of the main roads leading to the Forum, the decumanus maximus to the east and the roads from Porte à trios baies to the west, that almost certainly was the main gate to the city. The current arrangement of the monument is the result of a restoration intervention carried out in the 1930s by French restorers. Some ancient photos witness that the monument was just a ruin in 1915, when Chatelain carried out the former archaeological excavations and, as a consequence, that it was totally rebuilt. In fact, the monument suffered wide damages provoked by the 1755 Lisbon earthquake, that affected also Morocco, which almost completely destroyed it. By means of the drawings made by the travelers Henry Boyde and John Windus, that retraced the monument thirty years before the earthquake, the original configuration of the monument can be observed and the timeline of events can be reconstructed. In this paper, the timeline of the seismic events that affected the triumphal arch is reconstructed and investigated by means of a structural analysis based on a rigid-block model. Finally, with the purpose of preventing future damage, the seismic vulnerability level of the construction is assessed with reference to its current configuration.

Force-Based Seismic Evaluation of Retrofitting Interventions of Historic Masonry Castles by 3D Rigid Block Limit Analysis

This paper deals with the force-based assessment of collapse mechanisms and strengthening interventions of the historic masonry castle “Bussi sul Tirino” (Abruzzi, Italy) using rigid block limit analysis (RBLA). The structure, which is a fortified palace dating back to the 11th century, has experienced severe earthquakes over the centuries and was hit once again in 2009 by the L’Aquila earthquake. Based on the historical analysis and the results of in situ investigations, a spatial rigid block model of an entire structural unit was generated using the in-house software LiABlock_3D. The software is a MATLAB® based tool for three-dimensional RBLA, which provides as outputs collapse failure modes and collapse load multipliers. In addition, a specific routine was developed for the purpose of the study to compute the participating mass ratio and the spectral acceleration that activated the failure mechanisms. The results of the numerical analysis were used to address three different retrofitting interventions, based on the use of connection elements and ties that, according to the minimum intervention principle, progressively enhanced the seismic capacity. Comparisons in terms of seismic safety indices are finally provided in order to give a quantitative measure of the effectiveness of the adopted retrofitting strategies.

Influence of spatial variability of soil strength parameters on probabilistic seismic slope displacement hazard analysis

Permanent sliding displacement analysis is commonly used to evaluate the seismic performance of slopes. Specifically, the fully probabilistic seismic slope displacement hazard analysis (PSSDHA) has attracted increasing attention recently, since it appropriately accounts for various sources of uncertainties associated with the estimation of sliding displacement. Within this analysis, the uncertainty of soil strength parameters (e.g., effective cohesion c′ and effective internal friction angle ϕ′) is commonly quantified by a logic-tree method, in which the spatial variability of c′ and ϕ′ is simply ignored. This study aims at proposing an extended PSSDHA framework by rigorously accounting for the spatial variability of c′ and ϕ′, and then investigating its influence on the resultant slope displacement hazard curves based on the Newmark rigid-block model. Two different approaches, namely an analytical-based and a simulation-based method, are proposed separately. The results of the analytical-based method are found to be consistent with those obtained by the simulation-based one. It is also shown that the displacement hazard would be underestimated if the spatial variability of c′ and ϕ′ is ignored; such underestimation is more significant for slopes with soil parameters exhibiting weak c′-ϕ′ correlation and strong spatial variability. Besides, it suggests that the proper configuration of logic-tree framework plays an important role in developing displacement hazard curves, and a relatively large range of discrete strength values is recommended to better account for the effect of the spatial variability of soil strength parameters.

Delimiting the eastern extent of the Altyn Tagh Fault: Insights from structural analyses of seismic reflection profiles

AbstractThe Altyn Tagh Fault (ATF) serves as a key continental‐scale controlling structural element of the Tibetan Plateau. However, its eastward extent remains controversial. Here we use high‐resolution seismic reflection profiles to investigate the subsurface structures of the easternmost ATF and use these to delimit the easternmost extent of the fault. The structural analyses show an eastward geometric change from transpressional positive flower structures to compressional thrusts, with transpression‐induced shortening magnitudes decreasing eastwards from a maximum of ~5.3 km to being absent. Stratigraphic controls indicate that the deformation took place over the last ~<1.2 Ma. Our wider findings lead us to: (a) reject the suggestion that the ATF previously extended beyond the Kuantan Shan‐Hei Shan to link with the Alxa‐East Mongolia Fault; and (b) propose that the rigid block model used to describe the Tibetan Plateau crust is not consistent with the extent and structural details of the easternmost ATF.

Refined Rigid Block Model for In‐Plane Loaded Masonry

In this work, a refined rigid block model is proposed for studying the in‐plane behavior of regular masonry. The rigid block model is based on an existing discrete/rigid model with rigid blocks and elastoplastic interfaces that already proven its effectiveness in representing masonry behavior in linear and nonlinear fields. In this case, the proposed model is improved by assuming rigid quadrilateral elements connected by one‐dimensional nonlinear interfaces, which are adopted both to represent mortar (or dry) joints between the blocks and also to represent inner potential cracks into the blocks. Furthermore, the softening behavior of interfaces in tension and shear is taken into account. Several numerical tests are performed by considering masonry panels with regular texture subjected to compression and shear. Particular attention is given to the collapse mechanisms and the pushover curves obtained numerically and compared with existing numerical and laboratory results. Furthermore, the numerical tests aim to evaluate the applicability limits of the proposed model with respect to existing results.

The prediction of collapse mechanisms for masonry structures affected by ground movements using Rigid Block Limit Analysis

Masonry structures belonged to the Cultural Heritage suffered severe damages in the last decays due to the action of the settlement-induced ground movements. The researchers have been developing numerical tools for the vulnerability analysis and assessment of masonry structures subjected to settlements. Continuous, discrete and rigid block models were proposed in literature. The analysis of both local or global failure modes due to settlement is a still debated topic, involving several questions related to the modelling techniques and to the investigation of the parameters which affect the masonry behaviour against foundation movements. In this framework, the paper focuses on a numerical approach for the settlement analysis based on the rigid block limit analysis. The Italian Code (NTC 2018) also suggests linear kinematic approach for the seismic-induced collapse mechanisms analysis. In such a formulation, the structure is modelled as a collection of polyhedral rigid blocks assuming frictional contact interfaces with infinite compressive strength and zero tensile strength and neglecting the mortar contribution. Originally formulated for the in-plane and out-of-plane mechanisms analysis, the numerical formulation was recently improved in order to analyze blocky-structures subjected to uniform settlement.Numerical case study of a monumental masonry church façade subjected to uniform settlement at the base was presented in this paper aiming at testing the numerical procedure. The results were discussed to evaluate the software capability and accuracy in the settlement-induced collapse mechanisms prediction.

In-plane and out-of-plane seismic vulnerability assessment of an ancient colonnade in the archaeological site of Pompeii (Italy)

The paper presents the results of an investigation carried out about the construction technique, the mechanical behaviour and the seismic response of some selected masonry remains in the archaeological site of Pompeii. In particular, the portion of the ancient colonnade dating back to the 1st century BC and located to the east of the civil forum of Pompeii is studied. Since this colonnade is a classic example of a rigid-block structure, its seismic vulnerability level is assessed performing a rigid-block model through the computer program BrickWORK, a tool developed by the authors. In-plane and out-of-plane non-linear analyses are carried out, considering both the horizontal uniform and the linear lateral load pattern to simulate the actions of an earthquake. In each analyzed case, the vulnerability level is assessed by detecting the collapse mechanism and the spectral acceleration of activation. Collapse mechanisms are detected by the program and graphically shown through its visual user interface. Furthermore, the influence of the joint inclination on the mechanical response of the structure is investigated considering various inclination angles of the joints between the stones of the lintel.

Rigid block and finite element analysis of settlement-induced failure mechanisms in historic masonry wall panels

The paper is related to the assessment of collapse mechanisms of historic masonry structures suffering settlements induced by ground movements. Two numerical strategies are adopted in order to study the influence of the settled zone on the cracking of masonry buildings: a discrete rigid block model and a continuous homogenized model. The first approach provides an estimate of the collapse load and failure pattern of masonry based on the lower bound theorem of limit analysis. The second approach is formulated in the framework of multi-surface plasticity and implemented in a FE code for the path-following non-linear analysis of masonry wall described as continuous anisotropic plate. Several settlement configurations, of masonry walls under moving ground support are investigated and the corresponding failure patterns resulting from the analysis are obtained resulting in local or global failure modes. The results of the two modeling formulations are compared and discussed in order to highlight the features of the two different approaches in the prediction of settlement-induced damage.

Structural analysis of masonry vaulted staircases through rigid block limit analysis

This paper investigates the structural behaviour of masonry vaulted staircases and the efficacy of different modelling strategies for the assessment of their structural safety. In particular, the present study focuses on the structural analysis of the masonry vaulted stairs of the medieval Santa Maria delle Vigne bell tower in Genoa (Italy), dating back from XVI to XVII Century. Both a limit analysis tool and a static incremental analysis using a finite element model are adopted. The limit analysis problem is formulated for a rigid block model using an iterative solution procedure to take into account crushing failure. Results indicate that crushing failure is crucial in capturing the response of this structural typology.

Activity of crustal faults and the Xolapa sliver motion in Guerrero\u2013Oaxaca forearc of Mexico, from seismic data

Oblique convergent margins often host forearc slivers separated by the subduction interface and a trench parallel strike-slip fault system in the overriding plate. Mexican oblique subduction setting led to the formation of a forearc sliver and accomodation of part of the slip at the bounding system of strike-slip faults. The Xolapa sliver is, on average, a sim 105-km-wide crustal block located along the coast of Guerrero and Oaxaca states of Mexico, and is limited by a sim 650-km-long La Venta-Chacalapa fault zone. Two types of datasets, local catalog and Global CMT compilation, are used to estimate the motion of the Xolapa sliver using the rigid block model that describes the phenomenon of slip partitioning. According to the results obtained from local and Global CMT catalogs for selected subduction thrust earthquakes, the forearc sliver moves southeastwards with respect to the fixed North America plate at the rate of 10 ± 1 mm/year and 5.6 ± 0.8 mm/year, respectively. These velocities in general agree with the values obtained from long-term GPS observations (5–6 mm/year). The origin of the inconsistency between local and teleseismic estimates is attributed to a difference in the double couple focal mechanism parameters for two types of datasets. Convergence obliquity changes from 10.42{^circ } and the rate of 58 mm/year to 13.29{^circ } at the rate of 68 mm/year along the Guerrero and Oaxaca coast increasing from northwest to southeast; therefore, the Xolapa sliver is supposed to be stretched. However, the slip vector azimuths of thrust subduction earthquakes tend to approach plate convergence vectors southeastwards along the coast; so, we assume that this may produce the forearc block compression.

Simultaneous Shape and Topology Optimization of Planar Linkage Mechanisms Based on the Spring-Connected Rigid Block Model

Abstract Using the topology optimization can be an effective means of synthesizing planar rigid-body linkage mechanisms to generate desired motion, as it does not require a baseline mechanism for a specific topology. While most earlier studies were mainly concerned with the formulation and implementation of topology optimization-based synthesis in a fixed grid, this study aims to realize the simultaneous shape and topology optimization of planar linkage mechanisms using a low-resolution spring-connected rigid block model. Here, we demonstrate the effectiveness of simultaneous optimization over a higher-resolution fixed-grid rigid block-based topology optimization process. When shape optimization to change the block shapes is combined with topology optimization to synthesize the mechanism, the use of low-resolution discretized models improves the computation efficiency considerably and helps to yield compact mechanisms with less complexity, making them more amenable to fabrication. After verifying the effectiveness of the simultaneous shape and topology optimization process with several benchmark problems, we apply the method to synthesize a mechanism which guides a planar version of a human's gait trajectory.

Numerical Assessment of Cracks on a Freestanding Masonry Minaret

ABSTRACT The Minaret of the Sheikh Mutahhar Mosque was constructed in the beginning of sixteenth century. It is located in Diyarbakır, a city with moderate seismicity in Turkey. Although it has survived for five centuries, the tower is seemingly vulnerable to ground movements, because the minaret body simply stands freely on four cylindrical stone columns. A description of this special structure is provided. In recent years significant cracks have developed in two of the main lintels at the base of the minaret. The square cross-section minaret may be used as an ersatz, large-size seismograph, to examine the possible upper limits of seismic action that must have affected it without leading to overturning and stressed it beyond its strength to develop the observed cracks. Seismic response of the minaret is investigated through a numerical model generated using an explicit finite element code. The frictional contact behavior between stone units is included in the model and used to estimate the inherent damping. The 3D nonlinear finite element model results are compared with results of rocking rigid block model. It appears that the amplitude of the ground motion at the site did not exceed 0.15 g during the 500 years life span of the minaret.

Seismic performance and design approach for friction dissipative foundations

The seismic actions transmitted to a structure can be limited by inserting a frictional system between the foundation and the underlying soil. This allows a controlled sliding when the seismic forces reach a given critical value, that should be chosen to provide a desired seismic performance of the structure. Although this type of dissipative foundation has recently been adopted for the towers of two long-span bridges, its design still requires the development of a clear and robust design approach. In this view, the present paper studies the response of dissipative foundations, developing a generalised non-dimensional formulation that can be useful for design. The dynamic response of the foundation is analysed using a Newmark rigid block model, that is modified to account for the multi-directionality of the ground motion and to include a simplified description of the dynamic response of the superstructure. The main factors affecting the dynamic response of the dissipative system are highlighted through an extensive parametric study, leading to the definition of an optimised design approach of the dissipative foundation.

Displacement/velocity‐based control of a liquid spring—MR damper for vertical isolation

Seismic isolation is an effective technique used to mitigate effects of shaking and helps to achieve higher seismic performance. Recent researches have suggested that vertical excitation has significant effects on structures behavior during earthquake. In this study, three-dimensional (3D) isolation is proposed that combines an elastomeric bearing to resist horizontal ground shaking in series with a bilinear liquid spring (BLS)–controllable magnetorheological fluid damper (CMRD) to resist vertical shaking. A numerical model of a simplified rigid 2D block was developed to predict BLS-CMRD response under earthquake loading. The response of the BLS-CMRDs was simulated through a combination of nonlinear stiffness and viscous and hysteretic (semi-active) damping. A Disp/Vel-based control strategy was proposed that adjusts the input current according to the instantaneous vector combination of feedback displacement and velocity of the damper. Two variations of the control strategy were explored. First, with linear current variation, the current is activated when a threshold lower bound vector magnitude is reached, and maximum current is applied when threshold upper bound magnitude is exceeded. Second, the simplified ON–OFF strategy uses single threshold vector magnitude that triggers the maximum current to turn on when the instantaneous vector magnitude exceeds the threshold, and turn off otherwise. Results show that for ground motions that exceed the design level, Disp/Vel-based Control is effective to moderate the level of energy dissipation, keep the device vertical displacement within the design stroke limit, and attenuate vertical acceleration below PGA. In addition, Disp/Vel-based control reduces all responses relative to the well-known clipped optimal strategy used for structural control.

Collapse mechanism analysis of historic masonry structures subjected to lateral loads: A comparison between continuous and discrete models

The aim of this paper is to show to what extent a simple constitutive model can adequately describe the collapse mechanisms of historic masonry structures under horizontal seismic loads. Referring to block masonry, the paper presents the formulation and the numerical implementation of a constitutive relationship for modeling masonry structures regarded at a macroscopic scale as homogenized anisotropic continuum. The macroscopic model is shown to retain memory of the mechanical characteristics of the joints and of the shape of the blocks. The overall mechanical properties display anisotropy and singularities in the yield surface, arising from the discrete nature of the block structure and the geometrical arrangement of the units. The model is formulated in the framework of multi-surface plasticity. It is implemented in a FE code by means of a minimization algorithm directly derived from the Haar-Karman principle.A sensitivity analysis to mechanical and geometrical parameters was carried out to show the influence on the predicted response of small-scale wall components from the literature. The model is then used for the analysis of a numerical case study which is representative of a masonry church subjected to horizontal seismic action.The result of the model will be compared with those obtained by a rigid block model (RBM) of the same small-scale masonry prototypes and of the church building. In the paper, the results of the two models are discussed and analyzed in the way to highlight the weakness and the potentiality of the two different approaches.