Relative Stiffness Research Articles

An equivalent beam approach for assessing tunnelling-induced distortions of frames with infills

This paper presents an approach to evaluate the response of low- and medium-rise frames with continuous foundations, either with or without infills, to tunnelling employing an equivalent beam with a behaviour dominated by shear deformations. Simplified soil-structure interaction models, consisting of a beam resting on an elastic continuum half-space, are compared against advanced three-dimensional analyses in which the tunnel, the soil, and the building are explicitly modelled. In the simplified approach, the frame is schematised as a Timoshenko beam and reliable procedures to estimate both bending and shear stiffness are discussed. In the refined modelling strategy, an advanced elastoplastic constitute law is employed, capable of reproducing fairly well the soil response to the excavation for increasing values of volume loss, while the full geometry of the structure is considered. First, the results of the proposed numerical approaches are compared in terms of tunnelling-induced foundation displacements, bay deformations and maximum tensile strains in the infills. Then, for the infill panels, the reliability of estimating the maximum tensile strain from the angular distortion of the frame bays is assessed. Finally, a meta-model is proposed to predict the maximum angular distortion based on greenfield settlements, eccentricity, and relative soil-structure stiffness.

Influences of Wall Configurations on Earthquake Behavior of Cantilever Retaining Walls Considering Soil-Structure Interaction Effects

Cantilever walls are frequently and necessarily built not only in earthquake prone regions but also on different foundation subsoils with various physical and mechanical characteristics. The response of these structures is a complicated soil-structure interaction (SSI) problem, in which the relative stiffness between the soil and structure is of critical importance. In addition to different soil conditions and earthquake motions, the wall configurations have an important role in the cantilever retaining wall design. Thus, the major objective of this work is to investigate the effects of various configurations on seismic response of the cantilever retaining walls considering SSI. Accordingly, the seismic response of the interaction systems is revealed using the 3D finite element models (FEM) in time domain, assuming linearly elastic behavior for the wall, and elastoplastic behavior for backfill and foundation soil. Viscous absorbent boundaries are employed to both simulate radiation scenario and avoid undesirable wave reflections generated by soil lateral boundaries. Backfill-wall interfaces are modeled using the unidirectional interface elements with nonlinear force-deflection abilities. The interaction systems are analyzed considering three different cantilever wall configurations (inverted T-type, L-type, and the wall with a base key), four different ground motion records, and four different subsoil systems. Nonlinear seismic analyses are carried out to visit how considering the variation of these parameters influences the wall behavior. The results from parametric studies show that the wall configuration, SSI effects and ground motions are remarkably influential on seismic responses of the cantilever walls such as the stresses and horizontal displacements.

Classification of inter-modular connections for stiffness and strength in sway corner-supported steel modular frames

Corner-supported modular steel buildings, made of volumetric bespoke prefabricated units, are one of the most efficient construction systems for the next generation of prefabricated prefinished building construction. In these systems, the influence of connections between the units, so-called inter-connections, on the distribution of forces, moments, stability, and deformations of the frame is the key to the overall structural performance that differentiates the design of these systems from that of their conventional counterparts. In the design of modular buildings, the structural properties of inter-connections, such as stiffness, strength, and rotation capacity, are elements directly impacting their performance. This paper proposes a classification system for rotational stiffness and strength properties of inter-connections in sway corner-supported modular frames. The stiffness' boundary values corresponding to the rigid/semi-rigid and semi-rigid/nominally-pinned zones are represented by parametric charts based on the variation of relative bending stiffness ratios of elements such as beams, columns, and joints. To develop the classification system corresponding to stiffness properties of inter-connections, three performance criteria are assumed as (i) buckling criterion, which represents the classification based on the ultimate limit state; (ii) displacement/drift criterion, which considers the behaviour of the structure in the serviceability limit state; and (iii) combined buckling and displacement/drift criterion at the ultimate limit state. Furthermore, inter-connections are classified into three categories of fully-strength, partial-strength, and nominally-pinned in terms of their strength properties based on the ultimate moment capacity of inter-connections. The proposed classification system can be employed in the initial phase of a modular structure design to classify joints, and select a proper design method and process according to their category. Numerical examples are included to verify the validity of the proposed classification system. Finally, design recommendations are suggested for the accurate design of inter-connections in sway corner-supported modular frames without the need for complicated nonlinear analyses.

Seismic analysis of underground structures: Influence of the soil type, the relative stiffness and seismic intensity

Las estructuras subterráneas se desempeñan como medios para llevar a cabo actividades esenciales en una sociedad moderna. Por lo tanto, su apropiado desempeño sísmico es importante para la reducción del riesgo de desastres. El presente trabajo trata sobre los efectos sísmicos sobre las estructuras subterráneas ubicadas en zonas altamente sísmicas, como la costa del Perú. Se empleó el programa de cómputo FLAC para realizar varios análisis dinámicos de estructuras subterráneas de sección rectangular, considerando condiciones de borde de tipo campo libre y el comportamiento no lineal e inelástico del suelo ante siete sismos ajustados a un mismo espectro objetivo. Dichos análisis se llevaron a cabo variando factores como el tipo de suelo (homogéneo o estratificado), la geometría y espesores de la estructura y el periodo de retorno del sismo. Se ha encontrado que cuando la estructura está implantada en suelo homogéneo las fuerzas y desplazamientos presentas poca variación. Sin embargo, cuando la estructura está en suelo heterogéneo los resultados muestran variaciones importantes. De manera que el ajuste a un mismo espectro elástico no implica uniformizar la demanda sísmica. La geometría de la estructura y el espesor de los muros tienen considerable influencia. En suelos heterogéneos las estructuras muy flexibles pueden tener grandes deformaciones que implicarían niveles de daño importante.

Modelling and analysing failure modes of buried pipelines perpendicularly crossing landslide boundaries

The pipeline response to shallow translational landslides is investigated using semianalytical and numerical methods. The orthogonality of a pipeline and the landslide boundary is considered in this study. In the finite element (FE) analyses, ground movements are simplified as spatially distributed horizontal transverse deformation. The pipe-soil interaction is modelled accounting for large ground deformation, inelastic material behavior, and special contact conditions at the soil–pipe interface. Pipeline failure patterns are summarized based on a series of FE models with varying diameter thickness ratios of the pipe and soil conditions. According to the FE analysis results and the published literature, the existing failure criteria are evaluated and extended to cover new failure modes. The dynamic evolution in the predominant failure modes due to the pipe elongation effects is investigated. A semianalytical solution for the sliding distance to the onset of pipe wall wrinkling is given. In addition, a pipeline failure criterion is proposed based on the relative stiffness. This dimensionless parameter is correlated with failure features, including failure modes, sliding distances to failure initiation, and failure positions. The reliability of the proposed FE model and failure prediction methodology is validated using published results from centrifuge tests and FE analyses. Simple charts for failure prediction in terms of relative stiffness parameters are provided. The proposed approach allows efficient and reliable safety evaluation on X65 steel pipelines subjected to horizontal transverse ground deformation without conducting numerical modelling.

Design and characterization of novel bi-directional auxetic cubic and cylindrical metamaterials

Traditional auxetic structures only exhibit lateral contraction when axially compressed. In this paper, a strategy of bi-directional auxetic metamaterials with tunable effective Poisson's ratio is proposed. The bi-directional auxetic metamaterials based on two-dimensional double arrow structures are designed and then fabricated through additive manufacturing. The deformation mechanisms of the proposed structures are investigated through numerical simulations combined with experiments in the present study. The results show that the relative specific stiffness and the effective Poisson’s ratios of the proposed structures depend on geometrical parameters and geometrical configuration. The relative specific stiffness of the three-dimensional cubic structure (TCU) is between the internal and external stiffness of the structure, as is the case of the effective Poisson’s ratio. The axisymmetric deformation mechanism of the three-dimensional cylindrical structure (TCY) generates transversely isotropic Poisson’s ratio and enhances stiffness compared to the TCU with the same geometric parameters. This work systematically characterizes the deformation mechanism of innovatively designed structures and widens the potential applications of metamaterials in the fields of machinery, encompassing biomedicine, and electronic devices.

An analytical model for 2D seismic tunnel-aboveground structure interaction with considering the influence of tunnel longitudinal shear deformation

The influence of tunnel longitudinal shear deformation on the response of its adjacent ground building is investigated based on a 2D analytical model considering a flexible circular tunnel and a shear wall standing on a semi-circular rigid foundation under SH-waves excitation. Soil-tunnel relative stiffness is introduced, and a closed-form analytical solution is presented for the system response. Tunnel stiffness significantly affects the foundation impedance function of the building. Rayleigh scattering frequency can accurately predict the position of the fluctuation peaks of the foundation impedance function. At locations where the tunnel–building interaction is strong, the tunnel cannot be considered as rigid even if the tunnel relative stiffness to the soil reaches 100. At locations where constructive and destructive wave interference occurs, the building relative response increases or decreases accordingly. Considering the influence of tunnel relative stiffness, the amplitude of the building relative response can be amplified by 27.0% or reduced by approximately 28.0%, respectively. This analytical model is also used to qualitatively predict the amplitude of the relative response transfer function of the Hollywood Storage Building under the influence of the tunnel longitudinal shear deformation, and its accuracy is verified.

Study on the impact of temperature, salts, sugars and pH on dilute solution properties of Lepidium perfoliatum seed gum.

The functional properties of food gums are remarkably affected by the quality of solvent/cosolutes and temperature in a food system. In this work, for the first time, the chemical characterizations and dilute solution properties of Lepidium perfoliatum seed gum (LPSG), as an emerging carbohydrate polymer, were investigated. It was found that xylose (14.27%), galacturonic acid (10.70%), arabinose (9.07%) and galactose (8.80%) were the main monosaccharaide components in the LPSG samples. The uronic acid content of LPSG samples was obtained to be 14.83%. The average molecular weight and polydispersity index of LPSG were to be 2.34 × 105 g/mol and 3.3, respectively. As the temperature was increased and the pH was decreased and the concentration of cosolutes (Na+, Ca2+, sucrose and lactose) presented in the LPSG solutions was enhanced, the intrinsic viscosity [η] and coil dimension (R coil , V coil , υ s ) of LPSG molecular chains decreased. Activation energy and chain flexibility of LPSG were estimated to be 0.46 × 107 J/kg.mol and 553.08 K, respectively. The relative stiffness parameter (B) of LPSG in the presence of Ca2+ (0.079) was more than that of Na+ (0.032). Incorporation of LPSG into deionized water (0.2%, w/v) diminished the surface activity from 76.75 mN/m to 75.70 mN/m. Zeta potential (ζ) values (-46.85 mV--19.63 mV) demonstrated that dilute solutions of LPSG had strong anionic nature in the pH range of 3-11. The molecular conformation of LPSG was random coil in all the selected solution conditions. It can be concluded that temperature and presence of cosolutes can significantly influence on the LPSG properties in the dilute systems.

On the role of elasticity in focal adhesion stability within the passive regime

Within a purely mechanical setting, we investigate the behavior, up to full decohesion, of a system modeling the interactions exchanged between focal adhesions and extra-cellular matrix in the passive regime. In our work, decohesion is described as a homogenized effect of low scales events leading to the rupture of the molecular bonds between integrin receptors and the extra-cellular matrix ligands. We propose a simple three-layers scheme of this mechanical system and, based on a Griffith-like approach, we analytically describe the transition from an elastic regime to the nucleation of a decohesion front, up to full decohesion. We focus our attention on the important role played by elasticity and deduce how the relative stiffness of the layers modulates the decohesion behavior, with the system undergoing a ductile–fragile detachment transition. The comparison with known experimental results on focal adhesions and DNA shear denaturation supports the effectiveness of the proposed model in predicting the mechanical behavior of decohesion phenomena in biological systems. Interestingly, we show the possibility of predicting focal adhesion lengths distribution based on the obtained force saturation as the focal adhesion dimension is increased theoretically deduced.

Effects of Relative Positions of Defect to Inclusion on Nanocomposite Strength.

It is generally accepted that material inhomogeneity causes stress concentrations at the interface and thus reduces the overall strength of a composite. To overcome this reduction in strength, some groups experimented on coating the nanoinclusions with a layer of rubbery material, aiming for higher energy absorption. However, representative volume element (RVE) nanocomposite models, established with randomly distributed core–shell nanoparticles and single nanoparticle cells, show that the enhancement in strength observed in some experiments remains elusive computationally. By including a pre-existing crack in the matrix of the RVE, the stress concentration at the crack tip is reduced for cases where the nanoparticle and precrack are aligned away from the loading direction. This suggests that stress concentrations around inherent defects in materials can sometimes be reduced by adding nanoparticles to improve material strength. The effect is reversed if the crack and nanoparticle are aligned towards the loading direction. Parametric studies were also carried out in terms of the relative stiffness of the nanoparticle to the matrix and crack length. Validation tests were performed on 3D RVEs with an elliptical crack as the initial defect, and the results match with the 2D findings.

The behavior of piled rafts in soft clay: Numerical investigation

Abstract This research aims to investigate the applicability and performance of piled rafts in soft clay. This aim has been achieved by studying how the pile length, pile number, raft-soil relative stiffness, and presence of a sand cushion beneath the raft would affect piled raft settlement, differential settlement, and load sharing. Piled rafts have been numerically simulated using PLAXIS 3D software. Experimental testing results were used to verify the numerical simulation. The portion of the load carried by the piles to the total applied load was represented by the load sharing ratio (GPR). The results indicated that with increasing pile length and number, settlement and differential settlement decreased. It was also noticed that with increasing raft-soil relative stiffness, the differential settlement decreased. The GPR decreased with increasing thickness and relative density of the sand cushion, whereas it increased with increasing pile length and number. This increase in GPR was 13.7, 36, and 58% with an increase in pile length to diameter ratio from 10 to 30 for the number of piles 4, 9, and 16, respectively. Additionally, the raft-soil relative stiffness was observed to have a marginal effect on the GPR.

Non-symmetric stiffness of origami-graphene metamaterial plates

Mechanical metamaterials exhibit exceptional mechanical properties that originate from their topological design. In the current study, we designed a novel metamaterial which incorporates origami-graphene with single crystal copper matrix. Unlike classical auxetic materials which have void phase, the proposed origami-graphene based metamaterials appear to be solid in the microscopic scale, and the origami-graphene metamaterial plates may have relative stronger stiffnesses. Based on the molecular dynamics (MD) simulations, we confirmed that the elastic properties of origami-graphene/Cu metamaterials are anisotropic, size-dependent, and temperature-dependent, and the in-plane Poisson’s ratios are negative. More important, we discovered that the stiffness of the origami-graphene/Cu metamaterial plates is non-symmetry in the phase of linear elasticity.

Broadband mechanical metamaterial absorber enabled by fused filament fabrication 3D printing

Rationally designed porous structures are promising as broadband electromagnetic (EM) wave absorbers for counteracting military radar signal or reducing EM interference between electronic components. However, their poor mechanical properties associated with low density limit the scalability. Here, we report a three-dimensional printed, broadband mechanical metamaterial absorber (BMMA) that implements a dual-function of EM wave absorption and reinforced relative stiffness. Based on tuning the lattice unit-cells and comprising materials, the proposed BMMAs feature a multilayered design comprising geometrically optimized octet-truss structures composed of carbon black-based backbone composites. Three-dimensionally printed BMMAs achieve > 90% absorbance (~98.66% on average) for frequencies spanning 5.8–18 GHz, while maintaining nearly constant stiffness per unit mass density of 1.37 at a low density (~200 kg/m3). This design strategy will inspire versatile metamaterials that offer multi-functions enabled by adjusting unit-cell parameters via a single structure.

Damage mechanism of U-shaped ribs stiffened steel flat plates subjected to close-in explosion

The U-shaped ribs stiffened plates are widely used in civil and marine engineering structures for their high bending resistance performance. Moreover, these structures may be exposed to blast scenario especially terrorist and accidental explosions. Based on this background, this investigation carried out a study on the damage modes and the damage mechanisms of the U-shaped ribs stiffened plates subjected to close-in blast loads. The work used both field experimental and numerical methodologies. In this investigation, field blast tests were conducted on two flat plates and a stiffened plate. Furthermore, a fine numerical model was developed on the LS-DYNA platform and validated by the experimental results. Numerical analysis was conducted follow the validated model, and three typical damage modes (five detailed damage modes) of the single U-shaped stiffener stiffened plates subjected to blast loads were revealed through the numerical calculation of 40 specimens. Furthermore, a new damage number (Φ) was proposed for the classification of the damage modes. Meanwhile, maximum incident angle (α) and relative stiffness (κ) were put forward for further identification of the damage modes. It is proven that the damage modes of the single U-shaped stiffener can be well identified by the combination of damage number, maximum incident angle, and relative stiffness. Damage mode I occurred when Φ is less than Φ1 (0.042). And while the Φ is more than Φ2 (0.071), the stiffened plates exhibited mode IIIb damage. For Φ is between Φ1 and Φ2, the damage modes can be classified as mode IIa (κ < 0.0032) and IIb (κ≥ 0.0032) when α is less than 45°. While α is greater than 45°, the damage modes can be classified as mode IIa (κ < 0.001), IIIa (0.001 ≤κ < 0.0032) and IIIb (κ≥ 0.0032).

Influence of the Shod Condition on Running Power Output: An Analysis in Recreationally Active Endurance Runners.

Several studies have already analysed power output in running or the relation between VO2max and power production as factors related to running economy; however, there are no studies assessing the difference in power output between shod and barefoot running. This study aims to identify the effect of footwear on the power output endurance runner. Forty-one endurance runners (16 female) were evaluated at shod and barefoot running over a one-session running protocol at their preferred comfortable velocity (11.71 ± 1.07 km·h−1). The mean power output (MPO) and normalized MPO (MPOnorm), form power, vertical oscillation, leg stiffness, running effectiveness and spatiotemporal parameters were obtained using the Stryd™ foot pod system. Additionally, footstrike patterns were measured using high-speed video at 240 Hz. No differences were noted in MPO (p = 0.582) and MPOnorm (p = 0.568), whereas significant differences were found in form power, in both absolute (p = 0.001) and relative values (p < 0.001), running effectiveness (p = 0.006), stiffness (p = 0.002) and vertical oscillation (p < 0.001). By running barefoot, lower values for contact time (p < 0.001) and step length (p = 0.003) were obtained with greater step frequency (p < 0.001), compared to shod running. The prevalence of footstrike pattern significantly differs between conditions, with 19.5% of runners showing a rearfoot strike, whereas no runners showed a rearfoot strike during barefoot running. Running barefoot showed greater running effectiveness in comparison with shod running, and was consistent with lower values in form power and lower vertical oscillation. From a practical perspective, the long-term effect of barefoot running drills might lead to increased running efficiency and leg stiffness in endurance runners, affecting running economy.

Mechanical Characterization of Compliant Cellular Robots. Part I: Passive Stiffness

Abstract Modular active cell robots (MACROs) are a design paradigm for modular robotic hardware that uses only two components, namely actuators and passive compliant joints. Under the MACRO approach, a large number of actuators and joints are connected to create mesh-like cellular robotic structures that can be actuated to achieve large deformation and shape change. In this two-part paper, we study the importance of different possible mesh topologies within the MACRO framework. Regular and semi-regular tilings of the plane are used as the candidate mesh topologies and simulated using finite element analysis (FEA). In Part 1, we use FEA to evaluate their passive stiffness characteristics. Using a strain-energy method, the homogenized material properties (Young's modulus, shear modulus, and Poisson's ratio) of the different mesh topologies are computed and compared. The results show that the stiffnesses increase with increasing nodal connectivity and that stretching-dominated topologies have higher stiffness compared to bending-dominated ones. We also investigate the role of relative actuator-node stiffness on the overall mesh characteristics. This analysis shows that the stiffness of stretching-dominated topologies scales directly with their cross-section area whereas bending-dominated ones do not have such a direct relationship.

Experimental investigation on pipe-soil interaction due to ground subsidence via high-resolution fiber optic sensing

Understanding the pipe-soil interaction is critical for the design and safety assessment of buried pipelines subjected to large differential ground motion. Laboratory model tests were conducted to study the mechanical response of polyvinyl chloride pipes to ground subsidence. The optical frequency domain reflectometry technique was employed to perform distributed strain sensing of the pipe-soil system. An analytical method was proposed to estimate greenfield settlements in terms of fiber optic strain measurements. The pipe-soil interaction mechanism due to ground subsidence was investigated concerning four aspects, i.e., displacement profile of the pipe-soil system, pipe bending, soil arching, and interfacial shearing. Accounting for three-dimensional soil arching effects, a limit equilibrium solution for the earth pressure imposed on the pipe crown was given. This solution was developed from the two-dimensional Terzaghi soil arching theory and was validated based on the measured earth pressures. The feasibility of distributed fiber optic strain sensing technique in monitoring pipe-soil deformation was discussed through the comparison with the data of displacement transducers. In addition, the change in relative pipe-soil stiffness with increasing ground movements was studied based on the bending behavior of the pipe. A simplified method was given for quantifying the axial pipe-soil interaction based on longitudinal strains. This paper presents new inspiration on the intricacies of pipe-soil interaction using high-resolution distributed fiber optic sensing, which can be applied to structural health monitoring and optimum design of buried pipelines.

A single collision between three objects cannot be described using only two conservation equations

A collision of one object with two or more objects is relatively complicated in general, but a simple example is provided by Newton’s cradle since all the objects are identical and in line. In the present paper, an experiment is described where a heavy mallet collides head-on with two billiard balls. The two conservation equations indicate that many different outcomes are possible. The experimental results are surprising but can be explained in terms of the relative mass and stiffness of the mallet and the balls.

Structural design of responsive under-deck cable-stayed footbridges

The use of prestressing through external tendons has been extensively adopted in bridges to optimize the internal stress distribution. The contribution in withstanding permanent and live loads depends on the initial stressing and the relative stiffness between the deck and the tendons. However, these configurations only allow an optimal structural behaviour for a specific load distribution. This paper proposes to extend this ideal behaviour for any loading condition, using a responsive system which gradually modifies the tension in the cables as the live load increases. The responsive system is applied to a footbridge, where the adaptive behavior is materialized through a linear actuator located between the deck and the under-deck cable-stayed system.This study presents analytical and numerical analyses to shed light on the structural design of these systems. Considering a variable degree of responsiveness, it is possible to quantify the benefits of the responsive system. Furthermore, several parametric analyses are carried out to identify the optimal solution in terms of material savings. In addition, it is verified that fatigue in cables, vibrations and the eventual shutdown of the actuator do not compromise the structural performance of the system.Results show that a relevant material reduction can be achieved using partially responsive systems. Specifically, the slenderness of the structure can almost be doubled if compared to the same system without any responsive behaviour.

The effects of geometry on stiffness measurements in high-field magnetic resonance elastography: A study on rodent cardiac phantoms

PurposeCardiac magnetic resonance elastography (MRE) can be used to assess myocardial stiffness in vivo. Rodents play an important role in modern cardiovascular research, and small animal cardiac MRE may reveal important aspects of myocardial stiffness. The aim of this study was to explore the feasibility of small animal cardiac MRE through investigation of stiffness measurements of small cardiac phantoms that have known underlying stiffness. MethodsAgarose gel phantoms of three different geometrical designs were used: homogeneous gels, solid hearts, and biventricular phantoms. The size of the heart phantoms was comparable with that of an end-diastolic rat heart. All phantoms were made with different underlying stiffnesses agarose concentration, (7.5, 10.0,15.0)g/l, and MRE acquisition was performed with three different frequencies (360, 380, 400)Hz. Two different post-processing methods were applied to the MRE wave images: local frequency estimate (LFE) and direct inversion (DI). ResultsThe stiffness associated with the different agarose concentrations (7.5, 10.0, 15.0)g/l in the homogenous gels at 400 Hz were (1.80 ± 0.18, 3.13 ± 0.20, 4.13 ± 0.37)kPa for LFE and (2.25 ± 0.24, 4.35 ± 0.45, 6.54 ± 0.44)kPa for DI, respectively. Significant differences in MRE-derived stiffness were observed among phantoms with different agarose concentrations for all geometries. However, biases in the stiffness measurements among the different geometries were observed and could not be explained by the measurement variability. The relative stiffness uncertainty was smallest for the LFE inversion algorithm. ConclusionsThe stiffness measurements validate the use of the MRE technique to differentiate between various underlying stiffnesses in small cardiac phantoms. The stiffness measurements seemed to be dominated by geometrical effects when the cardiac MRE wavelength was longer than half the size of the heart. LFE was the inversion algorithm that was most sensitive to the changes in underlying stiffness.