Rigid Block Research Articles

Preparation and characterization of low CTE thermoplastic copolyimide resins based on the structural design of block sequence

In order to solve the challenge of balancing the thermoplastic processing properties and thermal dimensional stability of polyimide (PI) resin, in this research, 3,3′,4,4′-biphenyl tetracarboxylic diandhydride (BPDA) and 2,2′-bis(trifluoromethyl)benzidine (TFMB) were used as rigid components, 4,4′-oxydiphthalic anhydride (ODPA) and 4,4′-diaminodiphenyl sulfone (DDS) as flexible components. A series of random copolyimide resins was prepared by adjusting the molar ratio of rigid and flexible monomers. Determining the molar ratio which could balance the thermoplastic processing properties and thermal dimensional stability, block copolyimide resins with different rigid and flexible block lengths were then prepared in this ratio. The research showed that the molar ratio of monomers and the sequence structure of molecular chains had a strong influence on the performance of PI resins. When the content or block length of rigid component increased, the coefficient of thermal expansion (CTE) decreased but the glass transition temperatures (Tg) and melt viscosity increased. The PI-B343 resin had a CTE value of 40.63 ppm/K and the lowest melt viscosity reached 675 Pa·s, achieved the simultaneous regulation of the thermoplastic processing properties and thermal dimensional stability for PI resin.

Study on the Compressive Properties of an Elastomeric Porous Cylinder Using 360° Three-Dimensional Digital Image Correlation System.

To study the compressive properties of an elastomeric porous cylinder, a 360° 3D digital image correlation (DIC) system is proposed. This compact vibration isolation table system captures different segments of the object from four different angles and fields of view, enabling a comprehensive measurement of the full surface of the object. To increase the stitching quality, a coarse-fine coordinate matching method is presented. First, a three-dimensional rigid body calibration auxiliary block is employed to track motion trajectory, which enables preliminary matching of four 3D DIC sub-systems. Subsequently, scattered speckle information characteristics guide fine matching. The accuracy of the 360° 3D DIC system is verified through a three-dimensional shape measurement conducted on a cylindrical shell, and the maximum relative error of the shell's diameter is 0.52%. A thorough investigation of the 3D compressive displacements and strains exerted on the full surface of an elastomeric porous cylinder are investigated. The results demonstrate the robustness of the proposed 360° measuring system on calculating images with voids and indicate a negative Poisson's ratio of periodically cylindrical porous structures.

Pore partition in two-dimensional covalent organic frameworks

Covalent organic frameworks (COFs) have emerged as a kind of crystalline polymeric materials with high compositional and geometric tunability. Most COFs are currently designed and synthesized as mesoporous (2–50 nm) and microporous (1–2 nm) materials, while the development of ultramicroporous (<1 nm) COFs remains a daunting challenge. Here, we develop a pore partition strategy into COF chemistry, which allows for the segmentation of a mesopore into multiple uniform ultramicroporous domains. The pore partition is implemented by inserting an additional rigid building block with suitable symmetries and dimensions into a prebuilt parent framework, leading to the partitioning of one mesopore into six ultramicropores. The resulting framework features a wedge-shaped pore with a diameter down to 6.5 Å, which constitutes the smallest pore among COFs. The wedgy and ultramicroporous one-dimensional channels enable the COF to be highly efficient for the separation of five hexane isomers based on the sieving effect. The obtained average research octane number (RON) values of those isomer blends reach up to 99, which is among the highest records for zeolites and other porous materials. Therefore, this strategy constitutes an important step in the pore functional exploitation of COFs to implement pre-designed compositions, components, and functions.

Seismic displacement prediction methods, procedure, comparison and application

The methodology in the seismic design of slopes has evolved with technological advancement and the development of geotechnical engineering. Since methods with great limitations such as pseudo-static analysis to rigorous methods that require a lot of information for a better understanding of the behavior of the soil such as the dynamic analysis.&#x0D; This article develops the procedure, comparison, and application of methods for estimating seismic displacements, which are the Newmark (1965), Sarma (1975), Makdisi &amp; Seed (1978) and Bray, Macedo &amp; Travasarou (2018). Each of these methods considering the criteria of each one to obtain permanent displacements, such as yield acceleration, degraded period, spectral acceleration, magnitude, etc.&#x0D; As an applicative case, a rockfill dam and core central 50 m high placed in sandstone strata and moraine deposits interspersed with shale intrusions is shown, as seismic scenarios the Lima 1974 earthquake, the Attic 2001 earthquake and the earthquake were used. of Pisco 2007, considering both NS and EW directions. Likewise, the response spectrum on the base of the failure surface, resulting from a nonlinear seismic response analysis from 3 columns in the dam, is considered as information. The methods of Newmark (1965), Sarma (1975), Makdisi &amp; Seed (1978), and Bray, Macedo &amp; Travasarou (2018) were applied, obtaining deformation results between 1 to 30 cm that according to their order of magnitude represent a stable condition for the dam.

Discrete element modelling of the effect of aspect ratio on compaction and shear behaviour of aggregates

Coarse aggregates are essential for constructing railways and highways, as they affect structural performance through their compacted state and shear strength. Particle geometry influences these properties, but little research has quantitatively investigated how shape indexes impact mechanical indicators. This study addresses this gap by exploring the effect of particle aspect ratio on coarse aggregate compaction and shear behavior using the discrete element method (DEM). The study's key contribution is the development of novel equations that describe the correlation between packing porosity, inter-particle contact state, and aspect ratio control thresholds in a practical format. To do so, first, a point cloud database is compiled from laser scans of 700 natural aggregate particles. Each particle is classified using three aspect-ratio parameters: elongation, flatness, and flatness-elongation index (FEI). They are then digitized as rigid block particle models and compared against actual point clouds. Next, nine aggregates of representative shapes are assessed for their macro and mesoscopic mechanical responses using DEM-based vibro-compaction and direct shear tests. The compaction simulations indicate an exponential relationship between porosity and inter-particle coefficient of friction and show that aggregates with FEI ≈ 0.5 are a good choice. The direct shear simulations consider the same initial porosity, and show that the relationship between peak shear strength and vertical stress follows a power function. Finally, the analysis of contact forces and fabric tensors implies that FEI ≈ 0.5 may also facilitate particle fragmentation control.

Practical finite element modelling of segmented vaulted structures with assessment of imperfect dry-joints

The response of vaulted structures with dry-joints such as arches and shells can be predicted using graphical methods, limit state analysis, and rigid block analysis. However, these approaches assume material deformations are negligible. While acceptable for conventional masonry structures, there is a growing body of work investigating segmented vaulted structures where the segments comprise a large portion of the overall span. In such cases, material deformations and non-linearities can play a significant role. Typical analysis tools available are usually difficult to use and are not widely used by industry practitioners. In this paper, a modelling approach using a widely used finite element analysis package (LS-DYNA) is presented, using an ‘out-of-the-box’ approach for parameter tuning and modelling. This was then benchmarked against five experimental tests of dry-joint arches undergoing support displacements and a segmented concrete shell with large segments tested under a central point load. Crucially, the segmented shell exhibited imperfect dry-joints, with gaps occurring throughout various locations. A method of modelling and assessing such imperfections in a simple and practical manner is investigated through the use of a positive penetration allowance in the contact surfaces. The results show that the modelling approach is able to predict the collapse mechanism and failure support displacement for arches well, with further experimental tests required for 3D systems. It is envisioned that this work will add to the number of tools designers will have for analysing segmented vaulted structures with dry-joints.

Influence of bio-based 2,5-furandicarboxylic acid on the properties of water-borne polyurethane dispersions

Two sets of polyesters derived from 1,6-hexanediol, succinic acid, and varying amounts of a second aromatic dicarboxylic acid have been prepared. In the first set, isophthalic acid has been used as an established rigid building block for these types of materials. In the second set, isophthalic acid was replaced by the bio-based aromatic diacid 2,5-furandicarboxylic acid. The structure and properties of the polyesters have been characterized. All polyesters prepared were subsequently used as polyols for the synthesis of water-borne polyurethane dispersions. Films were prepared from the aqueous dispersions to characterize the performance of the materials. It was observed that the bio-based 2,5-furandicarboxylic acid not only has similar beneficial effects on the thermal and mechanical properties of the polyurethane coatings, but in some cases, like pendulum hardness, tensile strength and glass transition temperature, it was even able to surpasses the properties of its fossil-based counterpart.

Pullout Strength of Pedicle Screws Inserted Using Three Different Techniques: A Biomechanical Study on Polyurethane Foam Block

Pullout strength is an important indicator of the performance and longevity of pedicle screws and can be heavily influenced by the screw design, the insertion technique and the quality of surrounding bone. The purpose of this study was to investigate the pullout strength of three different pedicle screws inserted using three different strategies and with two different loading conditions. Three pedicle screws with different thread designs (single-lead-thread (SLT) screw, dual-lead-thread (DLT) screw and mixed-single-lead-thread (MSLT) screw) were inserted into a pre-drilled rigid polyurethane foam block using three strategies: (A) screw inserted to a depth of 33.5 mm; (B) screw inserted to a depth of 33.5 mm and then reversed by 3.5 mm to simulate an adjustment of the tulip height of the pedicle screw and (C) screw inserted to a depth of 30 mm. After insertion, each screw type was set up with and without a cyclic load being applied to the screw head prior to the pullout test. To ensure that the normality assumption is met, we applied the Shapiro–Wilk test to all datasets before conducting the non-parametric statistical test (Kruskal–Wallis test combined with pairwise Mann–Whitney-U tests). All screw types inserted using strategy A had a significantly greater pullout strength than those inserted using strategies B and C, regardless of if the screw was pre-loaded with a cyclic load prior to testing. Without the use of the cyclic pre-load, the MSLT screw had a greater pullout strength than the SLT and DLT screws for all three insertion strategies. However, the fixation strength of all screws was reduced when pre-loaded before testing, with the MSLT screw inserted using strategy B producing a significantly lower pullout strength than all other groups (p &lt; 0.05). In contrast, the MSLT screw using insertion strategies A and C had a greater pullout strength than the SLT and DLT screws both with and without pre-loading. In conclusion, the MSLT pedicle screw exhibited the greatest pullout strength of the screws tested under all insertion strategies and loading conditions, except for insertion strategy B with a cyclic pre-load. While all screw types showed a reduced pullout strength when using insertion strategy B (screw-out depth adjustment), the MSLT screw had the largest reduction in pullout strength when using a pre-load before testing. Based on these findings, during the initial screw insertion, it is recommended to not fully insert the screw thread into the bone and to leave a retention length for depth adjustment to avoid the need for screw-out adjustment, as with insertion strategy B.

Composite material identification as micropolar continua via an optimization approach

A strategy based on material homogenization and heuristic optimization for the structural identification of composite materials is proposed. The objective is the identification of the constitutive properties of a micropolar continuum model employed to describe the mechanical behaviour of a composite material made of rigid blocks and thin elastic interfaces. The micropolar theory (Cosserat) has been proved to be capable of properly accounting for the particles arrangements as well as their size and orientation. The constitutive parameters of the composite materials, characterized by different textures and dimensions of the rigid blocks, are identified through a homogenization procedure. Thus, the identification is repeated exploiting the static or modal response of the composite materials and using the Differential Evolution algorithm. The benchmark structures assumed as target are represented by discrete models implemented in ABAQUS where the blocks and the elastic interfaces are modelled by rigid bodies and elastic interfaces, respectively. The obtained results show that proposed strategies provide accurate results paving the way to the experimental validation and in field applications.

Fast optimisation of the formability of dry fabric preforms: A Bayesian approach

A new framework for optimising the process of forming dry textile materials using finite element (FE) analysis and Gaussian Process (GP) regression is explored in this work. FE models were generated to simulate the double diaphragm forming process of non-crimp fabric over a hemisphere tool. A GP emulator was developed to regress the dataset generated by FE model, then used to optimise the forming process. Importantly the FE simulations can capture the formation of wrinkles during the process under different forming configurations and boundary conditions. Rigid blocks (risers) were introduced to the forming process to affect the defects generation by controlling the block positions. Several indices abstracted from FE output files were used to assess the wrinkle level of the forming simulations and compared, as the model output. A small dataset was generated by Latin hypercubic sampling (LHS) to train an initial GP surrogate model. Then, the prediction error of the model was reduced to an acceptable level (<10 %) through a Bayesian active learning method. The trained surrogate model was then used to optimise a forming process using only tens of simulations, rather than hundreds or even thousands, as required by traditional optimisation methods.

Upper bound solution of passive instability on the face of longitudinal inclined shallow buried shield tunnel based on rotation–translation mechanism

To better evaluate the passive failure mode of shallow shield tunnel faces in sandy soil strata, tunnel faces passive failure mode was investigated considering the longitudinal inclination in this study. A three-dimensional rotation–translation mechanism that simultaneously considers the longitudinal inclination of the tunnel and partial failure of the tunnel face based on the upper bound limit analysis method was presented. The mechanism comprised two rigid translation blocks and one rigid rotation block. Subsequently, the reliability of the proposed mechanism was verified using the horizontal rigid translation mechanism and numerical simulation considering the longitudinal inclination. Finally, the effects of tunnel longitudinal inclination (δ), cover depth ratio (C/D), soil internal friction angle (ϕ), and the possible presence of uniform surface surcharge (σS) on the limit support pressure of the tunnel face and the partial failure range was assessed. The results indicated that the partial failure range of the tunnel face gradually increased with δ When C/D<1. Conversely, global failure of the tunnel face occurred at different longitudinal inclinations when C/D≥1. The rotation angle (θ) of the rotational failure zone was sensitive to the longitudinal inclination (δ) and decreased with δ at the same coverage depth ratio.

Analysis of seismically‐isolated two‐block systems using a multi–rocking‐body dynamic model

AbstractA novel multibody rocking model is developed to investigate the dynamic response of two stacked rigid blocks placed on a linear base isolation device. The model is used to investigate the dynamic response of a realistic statue‐pedestal system subject to pulse‐like ground motions. The analysis shows that, in general, base isolation increases the safety level of the rocking system. However, for large period pulses or small size blocks, the isolator can amplify the ground motion, resulting in a lower minimum overturning acceleration than for the nonisolated system. Further, the amplification or shock spectrum of a linear mass‐dashpot‐spring oscillator, was found to be the reciprocal of the minimum nondimensional overturning acceleration of the investigated rocking system. Novel rocking spectra are obtained by normalizing the frequency of the pulse by the frequency of the isolator. The analysis also demonstrates how the dynamic response of the two stacked blocks is equivalent to that of a single‐block configuration coincident with the whole system assumed monolithic or the upper block alone, whichever is more slender.

Measurements of Rayleigh wave ellipticity anisotropy and implications for distinct crustal deformation styles across the SE Tibet margin

Plateau growth of southeastern Tibet is often understood by applying the end-member conceptual models, such as ductile material flow in the deep crust, and lateral extrusion of coherently deforming or rigid blocks. Though recent studies suggest the local crustal flow and movements of rigid blocks may be compatible in a way, ambiguities still persist in the formation of the gently sloping margin of southeastern Tibet and interactions between the plateau and the outer forelands. Here we present a 3D crustal deformation model in southeastern Tibet and adjacent regions, by summarizing different types of seismic anisotropy measurements including a newly obtained continuous map of uppermost crustal anisotropy, which are derived from observations of the directionally dependent teleseismic Rayleigh wave ellipticity. Layered deformation is observed within the crust beneath the southeastern Tibet Plateau, while the outer foreland shows an overall coherently deforming mode. The conspicuous change of the crustal deformation styles across the southeastern Tibet margin is against the idea that the low topographic gradients of the plateau margin were produced by leakage of ductile deep crust beneath the plateau. We argue that both the crustal flow beneath the plateau interior and lateral extrusion of the outer foreland accommodate the intracontinental convergence at southeastern Tibet.

A GPU based Hybrid Material point and Discrete element method (MPDEM) algorithm and validation

The interaction between granular material and rigid bodies or complex boundaries are common in geotechnical engineering and industry. A hybrid MPDEM algorithm is proposed to simulate these kinds of problems. It is combined with the ability for solving granular material in MPM and the advantages of contact detection in DEM, which can be applied to solve sliding and impacting behavior of rigid blocks. Furthermore, the coupling algorithm based on GPU can be adopted for large-scale simulation to improve the calculation efficiency which has powerful advantages in geologic hazards simulation with high efficiency. To validate the algorithm, the sliding friction and impact effects are conducted to check the contact detection and force calculation for interaction between granular and block or boundary. Besides, the simulation results of granular impacting on the blocks are in good agreement with the experiment, which represents the feasibility and ability of algorithm to solve the interaction with granular materials and rigid-blocks or boundary systems. Through efficiency analysis, it is concluded that the computational performance is higher with the increase in particle number, compared with the pure MPM contact method. Additionally, the Tesla V100 card is a better choice for large-scale (particle number more than 1 million) simulations.

Rocking of rigid blocks standing on a horizontally-moving compliant base

In this paper the dynamic response of rectangular rigid blocks standing on a horizontally-moving compliant base that is not rigidly connected to its excitation source is investigated for the first time through a combination of analytical, numerical and experimental studies. A novel model combining the well-established studies of a rigid block supported by horizontally-moving rigid base and recent advances on the dynamics of a block rocking on compliant surfaces is derived. Specifically, the impact between the block and the moving base is modelled through a series of springs in parallel with dampers, leading to the generally known Winkler and Hunt–Crossley models. Model parameters are calibrated through forced harmonic rocking tests and then validated through extensive experimental tests with both free and forced rocking. Comparisons of numerically determined trajectories versus those experimentally determined highlight the accuracy of the compliant base model. The main advantage of the compliant base model over the traditionally adopted rigid base model is that it can better predict when rocking will be initiated. This feature is further highlighted from overturning charts numerically evaluated and experimentally verified.

A Late Palaeozoic disconformity in the Moqinwula area: Insights into the tectonic evolution and basement nature of the Junggar Block, NW China

The recognition of unconformities is important for stratigraphic subdivision and correlation and for determining the timing of tectonic activity and the ocean‐continent transition process. Here, we have identified a Late Palaeozoic disconformity in the Moqinwula area of the northern Junggar Block, NW China. Integrated field relationship observations and sedimentological, biostratigraphical, geochemical and detrital zircon geochronological data, suggest that the underlying Hongliugou Formation is of Devonian age and was deposited in a passive continental margin setting. The overlying Tamugang Formation formed in the Early Carboniferous and was deposited in a foreland basin setting. Integrating the published data and our new work, we suggest a new tectonic evolution model related to the Karamaili ocean‐continent transition process. During the Early Devonian, northward subduction of the Karamaili Ocean plate beneath the East Junggar Belt formed the Yemaquan arc. At this time, a passive margin sequence was deposited on the northern Junggar Block. During the Early Carboniferous, the closure of the Karamaili Ocean resulted from the collision between the Junggar Block and the East Junggar Belt. Foreland basins subsequently developed, forming an extensive unconformity in the accretionary wedge to the north and a disconformity in the relatively rigid and stable Junggar Block to the south. This significant difference in stratigraphic contact relationships confirms that regional convergence‐induced shortening deformation had no significant influence on the northern margin of the Junggar Block, suggesting the existence of a relatively rigid basement, probably an oceanic plateau, under the cover sediments of the Junggar Block.

Seismic analysis of failure mechanisms in adjacent interacting stone masonry buildings via rigid block modeling

Groups of contiguous unreinforced stone masonry buildings are a common type of housing seen in old European downtowns. However, assessing their response to earthquakes poses several challenges to the analysts, especially when the housing units are laid out in compact configurations. In fact, in those circumstances a modeling technique that allows for the dynamic interaction of the units is required. The numerical study carried out in this paper makes use of a rigid block modeling approach implemented into in-house software tools to simulate the static behavior and dynamic response of an aggregate stone masonry building. Said approach is used to reproduce the results of bi-axial shake-table tests that were performed on a building prototype as part of the activities organized within the Adjacent Interacting Masonry Structures project, sponsored by the Seismology and Earthquake Engineering Research Infrastructure Alliance for Europe. The experimental mock-up consisted of two adjacent interacting units with matching layout but different height. Two rigid block models are used to investigate the seismic response of the mock-up: a 3D model allowing for the limit analysis of the building on one hand, and a 2D model allowing for the non-linear static pushover and time-history analysis on the other. The 3D model was built for the blind prediction of the test results, as part of a competition organized to test different modeling approaches that are nowadays available to the analysts. The 2D model was implemented once the experimental data were made available, to deepen the investigation by non-linear static pushover and time-history analysis. In both models, the stonework is idealized into an assemblage of rigid blocks interacting via no-tension frictional interfaces, and mathematical programming is utilized to solve the optimization problems associated to the different types of analysis. Differences between numerical and experimental failure mechanisms, base shears, peak ground accelerations, and displacement histories are discussed. Potentialities and limitations of the adopted rigid block models for limit, pushover and time-history analyses are pointed out on the basis of their comparisons with the experimental results.

Shake-table testing of a stone masonry building aggregate: overview of blind prediction study

City centres of Europe are often composed of unreinforced masonry structural aggregates, whose seismic response is challenging to predict. To advance the state of the art on the seismic response of these aggregates, the Adjacent Interacting Masonry Structures (AIMS) subproject from Horizon 2020 project Seismology and Earthquake Engineering Research Infrastructure Alliance for Europe (SERA) provides shake-table test data of a two-unit, double-leaf stone masonry aggregate subjected to two horizontal components of dynamic excitation. A blind prediction was organized with participants from academia and industry to test modelling approaches and assumptions and to learn about the extent of uncertainty in modelling for such masonry aggregates. The participants were provided with the full set of material and geometrical data, construction details and original seismic input and asked to predict prior to the test the expected seismic response in terms of damage mechanisms, base-shear forces, and roof displacements. The modelling approaches used differ significantly in the level of detail and the modelling assumptions. This paper provides an overview of the adopted modelling approaches and their subsequent predictions. It further discusses the range of assumptions made when modelling masonry walls, floors and connections, and aims at discovering how the common solutions regarding modelling masonry in general, and masonry aggregates in particular, affect the results. The results are evaluated both in terms of damage mechanisms, base shear forces, displacements and interface openings in both directions, and then compared with the experimental results. The modelling approaches featuring Discrete Element Method (DEM) led to the best predictions in terms of displacements, while a submission using rigid block limit analysis led to the best prediction in terms of damage mechanisms. Large coefficients of variation of predicted displacements and general underestimation of displacements in comparison with experimental results, except for DEM models, highlight the need for further consensus building on suitable modelling assumptions for such masonry aggregates.

Rocking Analysis of Towers Subjected to Horizontal Forces

In seismic-prone areas, ecclesiastical masonry complexes have shown very high vulnerability, as detected after the last Italian earthquakes, such as those that occurred in L’Aquila (2009), Emilia-Romagna (2012), Central Italy (2016), and Ischia (2017). Partial collapses often affect these types of aggregate buildings due to the presence of highly vulnerable elements, such as bell towers. Preliminary analyses, including straightforward and quick methods, are necessary to assess their vulnerability. This paper proposes a simplified method to analyse bell tower dynamic behaviour and the results obtained are compared with several different approaches. The first is based on the dynamics of two rigid blocks (bell tower and lower building), and the second concerns a single block (bell tower only). The proposed method can be considered as a quick procedure involving few parameters to provide a preliminary analysis before use of more complex models such as finite element models. It aims to provide a valuable tool for the initial evaluation of the stability and risk index of the structure. The double-block model considers the associations between the rocking of the bell tower and the sliding motion of the underlying building. A parametric evaluation for different friction coefficients is proposed. The results are represented as rotation time histories and compared with analysis of the single vulnerable element, i.e., the bell tower subjected to the floor spectrum. The results show that high excitation frequency and friction coefficient values make the bell tower stable, and that the simplified model provides a clear safety advantage.

Analysis of a Simplified Model of a Rigid Rocking Block on Winkler Foundation

It has been observed from previous large earthquakes that weakening the structural foundation can reduce the damage of the structure itself by allowing a rocking motion to release the seismic energy, and this seismic design philosophy is gradually applied to new constructions. In this paper, a simplified model of the motion process of a rigid rocking block is proposed, the rocking motion equation of rigid rocking block is derived, and the parameter analysis is carried out. It was found that the height–width ratio and damping have a great impact on the rocking response of the structure. On this basis, combined with the Winkler foundation model, the equation of motion of the rigid rocking block considering the flexibility of the foundation is established. Through the analysis of an example, it is found that damping plays an important role in the overturning resistance of high-rise buildings and the soil elastic coefficient has a greater impact on the higher structure.