Stiffness Ratio Research Articles

An elastic-constant stress cohesive zone model for an orthotropic piezoelectric actuator adhesively bonded to a substrate

One of the common failure mechanisms observed in electromechanical systems utilizing actuators, sensors, or flexible electronics is the occurrence of interfacial debonding. In this paper, an elastic-constant stress cohesive zone model is constructed to analyze the interface behavior of piezoelectric actuators used in electromechanical systems when imperfectly bonded to a host medium. The analytical formulation treats the piezoelectric actuator as an orthotropic thin film, employing the membrane assumption. It is assumed that the cohesive zone extends from a point, initially unknown, to the edge of the film. The governing integro-differential equation is solved for various bonding scenarios, including perfect bonding with cohesive zones at the edges, an elastic case with a delaminated zone at the center, and an elastic case with both a delaminated zone at the center and cohesive zones at the edges of the film. Detailed examinations are conducted to explore the effects of stiffness ratio parameters and critical actuating voltage on the stresses within the film and substrate as well as the cohesive zone length. The results indicate that the cohesive zone length covers 45% of the film length when the actuating voltage has a fivefold increase over the critical threshold. For the imperfect bonding, the surface in-plane stress of the substrate exhibits a tensile peak near the boundary of the cohesive zone in addition to compressive singularities at the edges of the film. The shear stress singularity factor has an asymptotic behavior as the actuating voltage goes beyond the critical threshold. The critical actuating voltage reduces by a factor of 5% only if the delamination length does not exceed 70% of the film length.

Shear resistance design of prefabricated corrugated steel plate shear walls with reinforced boundary elements

This paper investigates the buckling behavior and shear-bearing capacity of prefabricated corrugated steel plate shear walls (PCSPSWs) with reinforced vertical boundary elements (VBEs). The PCSPSWs are solely connected to the frame beams, and therefore, they can be positioned flexibly within the frame. However, there is currently no available shear-bearing capacity design method for such PCSPSWs. Firstly, this paper conducts a numerical investigation into the elastic buckling behaviors of PCSPSWs using finite element analysis (FEA). The prediction formulas for elastic buckling loads are fitted considering the influence of VBEs’ stiffness on the corrugated steel plates (CSPs). Then, the elastic-plastic buckling performance of PCSPSWs is analyzed numerically. The stability factor (φ) is proposed to predict the shear-bearing capacity of PCSPSWs by introducing the normalized slenderness ratio (λn). Subsequently, this paper explores the effects of PCSPSWs’ position within the frame and the influence of linear stiffness ratios between the frame beams and columns on the shear-bearing capacity of PCSPSWs through numerical analysis. Finally, the lower stiffness values of VBEs are discussed to provide some guidance for structural designers.

Role of inertial nonlinearity and coupling stiffness on a series of coupled harvesters

This study investigates the effect of coupling configuration on a state-of-the-art harvesting system consisting of a series of spring-coupled piezoelectric nonlinear monostable tip-loaded cantilever-based vibration energy harvesters (VEHs). The investigation finds favorable coupling configurations that exploit complex nonlinear interaction for improving system performance. The system model incorporates the beam's geometric nonlinearities in the governing equation using inertial and stiffness nonlinear terms. The study first analytically investigates the effect of grounding stiffness on a single harvester's performance. Then, it numerically investigates the effect of increasing array size and changing stiffness distribution. The study discovers a novel hardening/softening transition phenomenon at a critical grounding stiffness value induced by the inertial nonlinear effect. This critical event also maximizes peak output power near the largest eigenfrequency at an optimum grounding stiffness value. At larger arrays, the peak power shows a complex bifurcation behavior, hinting at the presence of multiple attractors. The numerical study of different stiffness configurations and linearized eigenanalysis reveals the necessity of a multilevel optimization strategy focused on both the stiffness ratio between the coupling springs' and their overall stiffness level. This study bridges the gap between previous studies on spring-coupled linear and bistable arrays, offering new insights into coupled nonlinear interactions and proposing novel optimization strategies.

Bearing Capacity of Hybrid (Steel and GFRP) Reinforced Columns under Eccentric Loading: Theory and Experiment

In order to reveal the mechanical behavior of short concrete columns reinforced with hybrid steel and glass FRP bars, 10 specimens were designed for eccentric compression tests. The effect of eccentricity and load–displacement/strain of the specimens was studied. Test results indicate that the damage process and failure mode of these hybrid RC columns was similar to those in the conventional steel-reinforced concrete columns. The mode of failure for all specimens is characterized as large eccentricity compression failure, and the ultimate bearing capacity of the columns decreases with the increase in eccentricity. However, the impact of the varying axial stiffness ratio between GFRP and steel bars on the bearing capacity can be considered negligible. In addition, based on theoretical analysis, two boundary states for distinguishing failure mode and the formulae for calculating ultimate bearing capacity in different failure modes of eccentrically loaded hybrid RC columns are proposed. The computed results agree well with test results.

Simplified Approach for Determining Buckling Load in Portal Frames: Elastic Stability Analysis

Abstract The stability of portal frames is a critical aspect of structural engineering, significantly influencing their safety and performance. It refers to their ability to resist buckling or collapse under compressive forces, ensuring structural integrity and safety under various loading conditions. This study aims to provide design charts, created from closed-form solutions, on the probability of forming four different failure modes depending upon stiffness and axial load ratios. These charts provide a simplified and efficient method for quickly and easily assessing the elastic stability of a portal frame without the need for complex analyses or numerical simulations. The results indicate that in most cases, the governing failure mode is the sway-without-shear mode. However, upon further analysis, it is found that when the stiffness ratio (EI2/EI1) exceeds 2 and the force ratio (P2/P1) exceeds 1.33, the observed failure mode typically shifts to the symmetrical failure mode. Moreover, of the concluded results, the study discloses that the stiffer the beam, the higher the critical load ratio, and subsequently, the higher the buckling load. This is due to the fact that the beam behaves more like a rigid element, which prevents joint rotation, as in the fixed-end condition.

Non-Rigid Registration Via Intelligent Adaptive Feedback Control.

Preserving features or local shape characteristics of a mesh using conventional non-rigid registration methods is always difficult, as the preservation and deformation are competing with each other. The challenge is to find a balance between these two terms in the process of the registration, especially in presence of artefacts in the mesh. We present a non-rigid Iterative Closest Points (ICP) algorithm which addresses the challenge as a control problem. An adaptive feedback control scheme with global asymptotic stability is derived to control the stiffness ratio for maximum feature preservation and minimum mesh quality loss during the registration process. A cost function is formulated with the distance term and the stiffness term where the initial stiffness ratio value is defined by an Adaptive Neuro-Fuzzy Inference System (ANFIS)-based predictor regarding the source mesh and the target mesh topology, and the distance between the correspondences. During the registration process, the stiffness ratio of each vertex is continuously adjusted by the intrinsic information, represented by shape descriptors, of the surrounding surface as well as the steps in the registration process. Besides, the estimated process-dependent stiffness ratios are used as dynamic weights for establishing the correspondences in each step of the registration. Experiments on simple geometric shapes as well as 3D scanning datasets indicated that the proposed approach outperforms current methodologies, especially for the regions where features are not eminent and/or there exist interferences between/among features, due to its ability to embed the inherent properties of the surface in the process of the mesh registration.

Influence of fibril aspect ratio, chemical functionality, and volume fraction on the mechanical properties of cellulose nanofibril materials

Nanocellulose has emerged as a widely utilized building block in nanostructured materials due to its availability, sustainability, large surface area, and high stiffness and aspect ratio. The wet or dry elastoplastic properties of these materials are determined by the fibrils' stiffness, chemical properties, hemicellulose content, and the number of fibril contacts. However, the specific contributions and relative importance of each factor remain unclear. Therefore, this work was devoted to systematically comparing the material properties of gels, aerogels, and wet and dry sheets prepared from CNFs with different aspect ratios, chemical functionality, and hemicellulose content. The fibrils were prepared by chemical and mechanical processing of different pulps. By preserving the native structure as much as possible, higher aspect ratio fibrils can be obtained, which allows for the development of more mechanically robust materials. The results demonstrate that higher aspect ratios lead to more interconnected networks at a lower solids concentration, resulting in a more evenly distributed stress and longer-range stress transfer, yielding stiffer and more ductile materials. The most important finding was that the aspect ratio influences the network formation, resulting in different network topologies. The results were also compared to earlier published data and integrated into a theoretical beam-bending model for a complete elastoplastic description of the network properties, including the influence of fibril aspect ratio and chemical functionality. This information improves our understanding and description of nanofibril networks for which general models have been missing. It can be used to optimize nanofibril preparation and, hence, the resulting eco-friendly materials.

Model Test and Numerical Simulation of Two Typical Close-Fitting Pile–Wall Integrated Structures in Deep Excavation

Compared to conventional support methods, the close-fitting pile–wall integration technique features a minimized construction spacing between the retaining pile and the basement retaining wall. This approach leverages the pile stiffness to minimize the wall thickness and enhance underground space utilization. However, it currently lacks significant discussions and measured data about the interaction laws between the pile and the wall. The model test and finite element method (FEM) are employed to study the deformation and internal force interaction laws of two typical close-fitting pile–wall integrated structures, and a comparison with conventional design is conducted. Furthermore, this study separately investigates the impact of sensitivity factors, specifically the pile–wall stiffness ratio and floor plate stiffness, on both structures during the basement construction and serviceability stages. The test results can closely match the numerical simulation. The study results reveal that the wall impacts the bending moment of the pile to some extent. The internal force in the wall is significantly influenced by the lateral deformation of the pile and the floor plate. Compared to conventional designs, this structure significantly reduces the bending moment of the wall, particularly in the composite structure. Additionally, the analysis of sensitivity factors reveals their considerable influence on the pile–wall interaction.

Inelastic Spectra to Predict Constant-Damage Energy Factor of Structures Under Near-Fault Pulse-Type Ground Motions

ABSTRACT A simple relationship is proposed to construct constant-damage energy factor (γ DI) spectra of single-degree-of-freedom (SDOF) oscillators with different levels of damage, expressed by the Park-Ang damage index. γ DI is computed for SDOF oscillators with four hysteretic models when subjected to 80 pulse-like ground motions. The statistical dependence of γ DI on initial period, damage index, postyield stiffness ratio, and ultimate ductility factor is investigated. In comparison with the non-pulse-type ground motions, the near-fault pulse-type ground motions can significantly increase the γ DI of structures, and the magnitude of the increase can reach about 200%. Conservative estimates of mean γ DI of SDOF oscillators are proposed taking into account the combined effect of period, damage level, and ultimate ductility factor.

Regulating chondrocyte senescence through substrate stiffness modulation

AbstractChondrocytes, the resident cells of articular cartilage, play a vital role in tissue maintenance and regeneration. Recent studies have highlighted chondrocyte senescence as a key contributor to cartilage dysfunction. In this study, we investigated the influence of substrate stiffness on chondrocyte senescence using polydimethylsiloxane (PDMS) substrates with varying stiffness ratios (1:5, 1:20, and 1:60). After culturing chondrocytes on these substrates, we found that softer substrates (1:60) significantly reduced chondrocyte senescence, as evidenced by a decrease in senescence‐associated β‐galactosidase (SA‐β‐gal) activity by 33% compared with stiffer substrates (1:5). Furthermore, quantitative real‐time polymerase chain reaction (PCR) analysis revealed that chondrocytes cultured on softer substrates exhibited lower expression levels of senescence‐related genes (e.g., p16INK4a) and matrix‐degrading enzymes (e.g., MMP13). These findings suggest that substrate stiffness plays a critical role in regulating chondrocyte senescence and could potentially inform the design of scaffolds for cartilage tissue engineering.

Seismic vulnerability assessment of RC deck-stiffened arch bridges

Due to the recent damage and collapse of several bridges in Italy, reliable quantification of their vulnerability is paramount for planning various risk mitigation and resilience-enhancing strategies. This paper specifically focuses on the seismic vulnerability and loss assessment of existing reinforced concrete (RC) deck-stiffened arch bridges. The study considers a bridge typology known as the “Maillart–type” arch bridge, a common structural typology in the 1950s and characterised by a particularly stiff deck and a slender vault, i.e., a high deck-to-arch flexural stiffness ratio. Such bridges were typically designed considering only gravity loads and usually without ductile structural detailing and consideration of capacity-design principles. Historical documents and original design blueprints are used to simulate the design of an archetype bridge representative of the Italian “Maillart-type” arch bridge population. Then, nonlinear cloud-based time-history analysis is performed to investigate the seismic response of the considered archetype under varying ground-motion intensities and derive fragility and vulnerability relationships. Specifically, three different models are considered: one that adopts a conservative approach where damage is determined by the shear failure of the shortest pillar, another that provides a more detailed representation of structural damage progression, and a third that assumes retrofitting of the shortest pillar. The vulnerability relationships are combined with site-specific seismic hazard curves for case-study locations to estimate expected annual losses. The results represent a first step in assessing the seismic vulnerability of “Maillart–type” arch bridges to plan seismic risk mitigation interventions for such a bridge typology.

Low-frequency multiple topological interface modes in metamaterial beams with quasi-zero-stiffness resonators

To achieve multiple low-frequency topological interface modes (TIMs) while maintaining lightweight and load-bearing capacities in metamaterial beams, we propose novel topological beams equipped with double quasi-zero-stiffness (QZS) resonators. Following the introduction of the negative stiffness (NS) mechanism, we derived the dispersion relations of the topological beams with double QZS resonators using the transfer matrix method (TMM), and performed comparative and parametric analyses of stiffness ratio on folded Dirac cones (DCs) and locally resonant band gaps (LRBGs). Thanks to the NS mechanism and the double degrees of freedom (DOFs) in the QZS resonators, we can realize double low-frequency DCs (< 500 Hz) in metamaterial beams. It is notable that adjusting the stiffness of oblique springs can tune the resonators’ effective stiffness, implying that we can custom the frequency of DCs and LRBGs by adjusting the QZS resonator. By altering the distance between two QZS resonators, we obtain two topologically distinct unit cells. Transmission simulations confirm the presence of multiple low-frequency TIMs at the interface between these two domains. We also find that the effect of mass and geometric defects at various positions on TIMs is minimal. The proposed metamaterial beams could inspire innovative low-frequency vibration energy harvesters and lightweight topological devices.

Experimental and numerical study on the shear behavior of hybrid BFRP/steel RC beams without shear reinforcement

Hybrid reinforcement of steel and fiber-reinforced polymer (FRP) bars can provide a balanced performance between strength, ductility, and durability for the concrete structures. Thus, this study evaluates the shear performance of hybrid Basalt-FRP/steel-RC beams without shear reinforcement. A total of twelve RC beams were cast and tested under four-point loading to study the influence of reinforcement type, reinforcement ratio of longitudinal bars and axial stiffness between FRP and steel ratio, [Formula: see text] on the shear performance of the concrete beams. The test results were analyzed in terms of crack patterns, load-midspan deflection, load-crack width relationships, and shear strength of the tested beams. In addition, the experimental results were compared with the theoretical results obtained from various design codes and guidelines. Moreover, a finite element (FE) model was created, and the experimental results were used for validation of the FE model. The test results revealed that the beam specimens designed with similar effective reinforcement ratio exhibits comparable shear strength nevertheless the tensile reinforcement used. Experimental test results demonstrated that using hybrid bars increased the shear capacity of the beams by 11% compared to steel bars. Furthermore, the energy absorption of the hybrid-RC beams was enhanced by 16% compared to FRP-RC beams. By elevating the [Formula: see text] ratio from 1.25 to 2.44, both the shear strength and energy absorption improved by approximately 10%. Notably, there was a significant decrease in the deflection and crack width of the hybrid-RC beams in comparison to the FRP-RC beams. The design codes ACI440.11-22 and CSA S806-12 displayed accurate enough estimates of the shear strength, while JSCE-1997 showed a conservative result.

Dynamics of Purcell-type microswimmers with active-elastic joints.

Purcell's planar three-link microswimmer is a classic model of swimming in low-Reynolds-number fluid, inspired by motion of flagellated microorganisms. Many works analyzed this model, assuming that the two joint angles are directly prescribed in phase-shifted periodic inputs. In this work, we study a more realistic scenario by considering an extension of this model which accounts for joints' elasticity and mechanical actuation of periodic torques so that the joint angles are dynamically evolving. Numerical analysis of the swimmer's dynamics reveals multiplicity of periodic solutions, depending on parameters of the inputs-frequency and amplitude of excitation, joints' stiffness ratio, as well as joint's activation. We numerically study swimming direction reversal, as well as bifurcations, stability transitions, and symmetry breaking of the periodic solutions, which represent the effect of buckling instability observed in swimming microorganisms. The results demonstrate that this variant of Purcell's simple model displays rich nonlinear dynamic behavior with actuated-elastic joints. Similar results are also obtained when studying an extended model of a six-link microswimmer.

Application of Perturbation Method to Analytical H2 Optimization for a Damped Structure with Inerter-Based Control

Inherent damping exists in all real engineering systems and it affects the dynamic behavior of the structures in vibration reduction. However, it is generally neglected in existing analytical H2 optimization for inerter-based vibration control. Hence, an analytical H2 optimization of a tuned inerter damper (TID) based on the perturbation method is presented to control the vibration of a damped structure subjected to stochastic acceleration ground excitations. Since relative displacement and velocity are crucial to structural damage and absolute acceleration is related to vibration comfort, three sets of closed-form solutions for the optimal stiffness ratio and damping ratio are derived to suppress the corresponding responses. The expressions of these optimal parameters are functions of the inherent damping and inerter-mass ratio. The accuracy of these analytical solutions is demonstrated by comparison with the results provided by the numerical optimization procedure. The relevant parameters affecting the vibration control performance and the robustness of the TID in a damped structure are analyzed in frequency domain. Finally, time–history response and energy dissipation of TID are also explored by numerical examples under real and artificial seismic waves. The results highlight that more than 10% reduction ratio of the mean square value can be further achieved for a structure with a low inherent damping ratio ([Formula: see text]) if the present multi-order perturbation solutions are used for optimization, instead of the existing method which neglects the inherent damping. This superiority of the present perturbation method will become more prominent with the increase of the inherent damping ratio. Therefore, the present perturbation method has a great significance for designing a TID to achieve the best control performance.

Elastic Foundation Solution for the End Notched Flexure (ENF) Mode II Sandwich Configuration

Abstract This paper presents a closed form solution for the energy release rate of face/core debonds in the Mode II end notched flexure (ENF) sandwich configuration. The finite-length sandwich specimen is considered to have a “debonded” region and a “joined” region. In the later, the interface between the top face and the substrate (core and bottom face) is modeled by an elastic foundation, which is a uniform distribution of shear and normal springs. Based on the Timoshenko beam theory, the solution for a general asymmetric sandwich construction is derived. The energy release rate expression is derived via the J-integral. Another closed form expression for the energy release rate is derived from the energy released by a differential spring as the debond propagates. In this closed form solution there is no fitting and everything, including the foundation constants, are given in closed form. Results are produced for a range of face/core stiffness ratios and debond length/core thickness ratios, and are compared with the corresponding ones from a finite element solution. A very good agreement is observed except for small debond lengths vs specimen thickness.

Seismic Behavior of Steel Reinforced Ultra-High Strength Concrete Composite Frame: Experimental and Numerical Study

The seismic behavior of steel reinforced ultra-high strength concrete (SRUHSC) composite frame was investigated through finite element analysis (FEA) modeling. A FEA model for the seismic analysis of the SRUHSC frame was first established and verified with test results. The numerical model was subsequently used to study the seismic performance of the SRUHSC frame, including the P-Δ skeleton curves, the stiffness degradation, the failure mode, the subsequence mechanisms of plastic hinges and the stress–strain distribution. Finally, a parametric study was carried out to investigate the effect of salient parameters on the behavior of the SRUHSC frame. It was found that with the increment of the concrete strength, yield strength of steel, and linear stiffness ratio of beam to column, the horizontal load-bearing capacity and the elastic stiffness of the structure were improved, but there was no significant effect on the ductility. With the increment of the volume stirrup ratio and structural steel ratio, the horizontal load-bearing capacity and the ductility of the structure were both improved. However, with the increment of the axial-load ratio, there was no obvious change in the elastic stiffness of the structure, but the horizontal load bearing capacity and the ductility of the structure decreased obviously. In addition, the accuracy of a concrete constitutive model in the different degrees of constraint for the SRUHSC frame proposed by the authors was verified with the FEA model.

Curvature programming of freestanding 3D mesostructures and flexible electronics based on bilayer ribbon networks

Three-dimensional (3D) buckling assembly of flexible electronics from strategically designed two-dimensional (2D) precursor structures has enabled important applications in a variety of areas, owing to its versatile applicability to a broad range of length scales and high-performance materials, as well as to a rich diversity of 3D topologies. Rational design methods that allow direct mapping of 3D mesostructures onto unknown 2D precursor structures and loading parameters are foundational to these assembly technologies, but face scientific challenges, such as the high nonlinearity of spatial deformations and tricky bifurcation behaviors. While a few inverse design methods based on the beam theory, topology optimization and machine learning algorithms have been reported, the shape programming of freestanding 3D mesostructures/electronics with highly complex curvature distributions remains elusive. In this work, we propose a curvature programming method based on bilayer ribbon networks, along with a mold-assisted assembly strategy, as a new route to customizable freestanding 3D mesostructures and electronics. Combined mechanics modeling, finite element analyses and experimental measurements allow a clear understanding of nonlinear bending-stretching coupled deformations of bilayer ribbon networks during the 2D-to-3D transformation. A parameter domain with one-to-one mapping of the dimensionless curvature and the bending stiffness ratio is identified, offering a theoretical basis of the curvature programming. By introducing a discretization strategy, a variety of regular (e.g., circles, ellipses, spirals and toroids) and biomimetic 3D curved ribbons and mesosurfaces (e.g., mimicking wavy vines, diatoms and arbitrarily curled leaves) were inversely designed and experimentally realized. A device demonstration capable of strain/temperature sensing and micro-LEDs indication suggests application opportunities in bioelectronics and microelectromechanical systems.

Element-wise parallel deep learning for structural distributed damage diagnosis by leveraging physical properties of long-gauge static strain transmissibility under moving loads

The Transmissibility Function (TF) has gained considerable interest in structural damage detection because of its relatively high sensitivity to damage and robustness to excitation. This study proposed a distributed damage diagnosis method for beam-like structures based on a long-gauge static strain TF defined as the ratio of the Fourier transform of static strain response under moving loads from a target long-gauge sensor to that from the reference sensor. It has been discovered that each long-gauge static strain TF is independent of moving loads, making it an ideal damage indicator. It exhibits direct proportionality to the ratio of bending stiffness between the two measured zones covered by the target and reference long-gauge strain sensors while being unaffected by the stiffness of any other zones not covered by these two sensors. Moreover, the TF at zero frequency was proved to be equivalent to the ratio of static strain time history areas, relying solely on the stiffness of the covered zones. Leveraged by the physical properties of long-gauge static strain TF, an element-wise parallel deep neural network architecture was developed to decompose damage diagnosis into independent sub-tasks on the element level, utilizing a variational autoencoder (VAE) in the Bayesian inference framework for extracting features from the long-gauge strain TF and a regressor for mapping the features to elemental stiffness reduction. The divide-and-conquer strategy and element-wise parallel learning architecture allow for a significant reduction in the number of labeled training samples generated based on the updated numerical baseline model as it only requires simulated scenarios involving a single damage element. The efficiency and robustness of the proposed method were demonstrated through a numerical simply supported beam and a laboratory experiment on a two-span bridge.

A metamaterial with enhanced effective stiffness and negative Poisson's ratio for frictional energy dissipation

Unlike traditional energy dissipation structures that dissipate energy through irreversible plastic deformation or collapse, metamaterials based on friction energy dissipation have attracted attention due to their reusability. This article proposed a novel energy dissipation metamaterial by integrating friction energy dissipation mechanism into negative Poisson's ratio (NPR) structures. The integration of friction energy dissipation mechanism can simultaneously enhance the effective stiffness and NPR effect. The mechanical properties of the proposed structure were investigated using theoretical analysis, experiments, and finite element (FE) simulations. The influence of variables such as internal concave angle, friction coefficient, and number of reinforcing ribs was discussed. The results indicate that both unit cell and honeycomb structure can repeatedly dissipate energy within the elastic range. Compared with the traditional concave hexagonal structure, the effective stiffness and NPR effect were enhanced. This work provides a novel idea for the design of NPR energy dissipation structures.