Hysteretic Model Research Articles

Nonlinear Dynamic Analysis Using the Force Analogy Method and the Ibarra–Medina–Krawinkler Model

ABSTRACTA methodology to integrate the Ibarra–Medina–Krawinkler (IMK) hysteretic model with the force analogy method (FAM) is proposed. FAM is a powerful tool for performing nonlinear structural analysis that reduces analysis time, addressing the main limitation of nonlinear analysis. One area of opportunity for FAM lies in its access to material nonlinearity models, which enable the reproduction of inelastic behavior in structures. The IMK model, utilized in nonlinear analysis for updating the stiffness matrix, incorporates various rules of material nonlinear behavior and considers cyclic deterioration of stiffness and strength. By combining the IMK model with FAM, the capability to model material nonlinear behavior in a computationally efficient manner is enhanced. The proposed methodology is validated through four numerical examples, demonstrating its effectiveness in replicating experimental behaviors and enhancing FAM capabilities in inelastic structural analysis.

Jc(B) transformer rectifier flux pump optimisation via simulation

Abstract Superconducting power supplies commonly known as flux pumps are becoming viable products in various industries. In this work we investigate magnetically switched ( J c ( B ) ) half-wave transformer rectifier flux pumps (TRFPs) via a simulation previously validated against an experimental system. Upgrades to the model are introduced, namely the transition to a fully hysteretic transformer reluctance model and the introduction of a conduction cooling thermal model. The conduction cooling model allows direct comparison between liquid cryogen and conduction cooled systems, highlighting the distinct variations in response. This study focuses on parameter sweeps over some of the most important aspects of a TRFP such as; input power, cooling paths and switch length. The findings from these variable sweeps shed light on how to best design the different aspects of a TRFP for most applications and the conclusions drawn throughout this work can be applied to most TRFP types. Some of the major findings from this work are; i. the need for dedicated cooling busses in TRFP switches, ii. that increased switch lengths increase voltage generation but negatively impact cooling effectiveness iii. that the reduction of the metallic coatings surrounding commercial coated conductors results in larger switch voltages.

Cyclic performance evaluation and hysteretic modelling of a brace-type damper with multi-phase energy dissipation

This paper presents an experimental investigation of a novel brace-type damper for seismic mitigation in steel truss framed structures. The damper exhibits a two-stage energy dissipation behaviour by combining friction damping and yielding of steel struts. The two-stage design allows for adaptability and adjustability to different levels of earthquake events. During low-to-medium intensity seismic events, the friction mechanism is responsible for energy dissipation. While during high-intensity events, the yielding of steel struts is activated to provide additional damping and ensure effective energy dissipation. A test programme comprising five proof-of-concept specimens was conducted to investigate the seismic performance of the damper. The test results demonstrated the anticipated two-stage energy dissipation sequence with exceptional ductility. The sliding surface pairs of stainless steel/mild steel and brass/mild steel performed more stable and predictable friction behaviour compared to surface pairs of mild steel/mild steel. To facilitate practical design of the novel dampers, theoretical hysteretic models were developed to quantify critical mechanical quantities of the damper. The adequacy of the design model was validated by comparing the test responses with the design predictions. The hysteretic model offered a quantitative framework for analysing and predicting the response of brace under cyclic loading.

Improving the roller screen efficiency to classify green iron pellets using DEM simulation, novel roll design and implementing banana configuration

Roller screens play a decisive character in the efficiency of pelletizing circuits and induration furnaces. Unlike vibrating screens, there have been no studies on roller screens to determine their capacity and dimensions. Most studies have utilized the discrete element method (DEM) simulation to assess roller screen performance by employing a spherical shape and the Hertz-Mindlin elastic model. However, this approach is unsuitable due to green pellets’ non-spherical shape and elastic–plastic properties. This study introduces the incorporation of the actual shape of green pellets and a hysteretic spring elastoplastic contact model. In this research work, a novel design of rolls with a grooved surface was recommended for the first time, resulting in a Total Screening Efficiency (TSE) of 96.4% compared to 87.1% for rolls with a smooth surface. Additionally, while exploring the impact of the decks number on the roller screen, a new design, known as the banana roller screen, was introduced. Under similar conditions, the TSE increased by 1.22% compared to the general roller screen type. It was also found that the roller screen’s capacity is directly related to the diameter, speed of rotation, and the number of rolls, while it has a reverse relationship with TSE and deck angle.

An asymmetric pinching damaged hysteresis model for glubam members: Parameter identification and model comparison

The performance of glue laminated bamboo (glubam) members is governed by the nonlinear response at their joints, where high deformation levels and stress concentrations are developed. Numerous phenomenological models are presently employed to describe the hysteresis behavior of these joints, while these models always have an excessive number of parameters, and the physical interpretation of these parameters is often challenging. Moreover, some hysteresis models cannot capture all hysteresis features such as asymmetry, pinching, and damage. Consequently, this paper introduces a novel phenomenological-based hysteretic model named Asymmetric Pinching Damaged (APD) model, and implemented it in Abaqus by combining connector and spring elements in series or parallel. This model encompasses asymmetry, pinching, and strength degradation for bamboo joint components, with parameters that possess clear physical meanings and are readily comprehensible. This study also presented a parameter identification framework coupling the Parallel Genetic Algorithm (PGA) and Bayesian Neural Network (BNN). By merging the FE modeling and optimizing algorithms with the interactive application of ABAQUS and Python software platforms, the integrated identification framework is capable of performing multi-threaded parallel computation of finite element models considering the BNN-based uncertainty quantification, thus greatly improving the efficiency of parameter identification.

Hysteretic Dynamic Modeling and Vibration Characteristics Analysis of Metal-Rubber Isolators

A novel hysteretic constitutive model (HCM) with four parameters was proposed to reproduce the nonlinear elasticity and dry friction characteristics of metal–rubber isolators (MRIs). The HCM accurately characterized the nonlinear hysteretic behavior due to its intrinsic relationship with the geometric properties of the hysteresis loop. A physics-based parameter estimation strategy was developed to provide reasonable initial iteration values. Three MRIs with different design stiffnesses were tested to investigate their hysteretic behavior under various excitation levels. The HCM accurately reproduced the entire experimental hysteresis loops using only a subset of the experimental data. This exhibited higher precision and scalability compared to the classical dynamic model. Friction damping forces were employed to distinguish the stick-slip states of the three MRIs. Additionally, the identified parameters were used to simulate the steady-state vibration response of a complex MRI system. The resulting frequency response functions (FRFs) agreed well with the experimental data. The proposed model can effectively capture the amplitude-dependent effects in MRI systems with various design stiffnesses, enabling more accurate predictions of vibration responses.

Experimental study on seismic performance of glulam structural columns with anchored connections

In current timber structures, the low initial stiffness, and weak bending resistance of the connections result in significant structural deformation and failures. To improve the mechanical capabilities of timber structural joints, a novel timber-component anchorage system with robust bending resistance was introduced. Thirteen scaled-down specimens of glulam columns with anchored connections were meticulously fabricated for testing, scaled at a ratio of 1/2. Cyclic loading tests were conducted, considering three types of the volume compression percentage of confined wood perpendicular to the grain; and five axial-load levels. Subsequently, various seismic performance aspects of glulam columns with anchored connections were examined, including the failure mode, hysteresis behavior, envelope curve, strength degradation, stiffness degradation, energy dissipation capacity, and critical points. During the analysis, the influence of the P–Δ effect on the results was discussed and a damage-based hysteretic model was presented. Finally, a comparison of the mechanical performance for various types of timber structural joints was conducted. The findings revealed that the failure mode of the anchored glulam columns occurred as cracking perpendicular to the grain, and the anchored columns exhibited superior bending resistance and overall seismic performance.

Neural Network Architectures and Magnetic Hysteresis: Overview and Comparisons

The development of innovative materials, based on the modern technologies and processes, is the key factor to improve the energetic sustainability and reduce the environmental impact of electrical equipment. In particular, the modeling of magnetic hysteresis is crucial for the design and construction of electrical and electronic devices. In recent years, additive manufacturing techniques are playing a decisive role in the project and production of magnetic elements and circuits for applications in various engineering fields. To this aim, the use of the deep learning paradigm, integrated with the most common models of the magnetic hysteresis process, has become increasingly present in recent years. The intent of this paper is to provide the features of a wide range of deep learning tools to be applied to magnetic hysteresis context and beyond. The possibilities of building neural networks in hybrid form are innumerable, so it is not plausible to illustrate them in a single paper, but in the present context, several neural networks used in the scientific literature, integrated with various hysteretic mathematical models, including the well-known Preisach model, are compared. It is shown that this hybrid approach not only improves the modeling of hysteresis by significantly reducing computational time and efforts, but also offers new perspectives for the analysis and prediction of the behavior of magnetic materials, with significant implications for the production of advanced devices.

Seismic performance of Li-Tie type brick masonry infilled wooden frames considering joint damage: Degradation mechanism and hysteretic model

This paper investigated the influence of the damage to column-foot (C-F) joints and the gaps of mortise-tenon (M-T) joints on the seismic behavior of Li-Tie style timber frames with masonry-infilled wall. Five full-scale Li-Tie type brick masonry-infilled timber frames, two without the joint damage, two with the damage to C-F, and one with the gaps of M-T joints, were cyclically tested. The failure modes, mechanical and deformation mechanisms were revealed. The second-order effect, strength degradation law, and the changing laws of the equivalent viscous damping coefficient and strain of the specimens were analyzed. The results showed that when the maximum inter-layer drift ratio was less than 2.4 %, the second-order effect of Li-Tie type timber structure with the masonry infill can be ignored. The masonry infilled timber frames considering the joint deterioration suffered a large strength degradation degree, and a more significant loss of the peak load and ductility. The equivalent viscous damping coefficient of the masonry infilled timber frame considering C-F damage increased by up to 24.67 %, while that of the one including the gaps of M-T joint decreased by 6.67 %. The C-F damage led to an increase in the strain at the beam end, the damage to M-T joint resulted in an decrease in the strain at the beam end. However, the damage to C-F and the gaps in M-T joint had little influence on the strain distribution in the C-F area. Based on the hysteretic, stiffness and strength degradation characteristics, and tests results of the specimens, the new tri-linear hysteretic models of Li-Tie type brick masonry infilled wooden frames with and without the joint damage were established and verified. Good agreement between the model predictions and test results was observed.

Research on concrete-filled square CFRP steel tube under compressive-torsional hysteresis loading

Concrete-filled CFRP steel tube structures are presently employed on extensively in various engineering practices. This study examines the mechanical performance of concrete-filled square CFRP steel tubes under compressive-torsional hysteresis loads. Through the analysis of nine specimens, the research focuses on failure modes, torque–angle (T–θ) behavior, triaxial strain, and the synergistic effects of the steel tube and CFRP during cyclic loading. A numerical simulation method is initially introduced based on the test data to predict the actions of concrete-filled CFRP steel tube compressive-torsional specimens under hysteresis loading. This method is subsequently verified by contrasting it with the outcomes from representative experiments. In addition, the stress distribution of each material during the entire loading process of the sample is examined. Finally, using data from experiments and finite elements, combined with the trilinear model, a hysteretic model under compressive-torsional hysteresis stresses has been established for square CFRP steel tube filled with concrete. The calculated outcomes of the developed finite element model closely align with those of the hysteretic model.

Bayesian inference of hysteretic behavior of unfrozen water content and electrical conductivity in saturated frozen rocks

Electrical conductivity is a fundamental geophysical parameter of electrical and electromagnetic techniques. It is widely used to non-intrusively assess and monitor physical and chemical properties in cold regions (i.e., liquid water saturation, ice content, salinity, and temperature). However, the significant hysteretic behavior observed in the temperature-dependent physical properties of frozen porous media (i.e., unfrozen water saturation and electrical conductivity) remains difficult to interpret during freezing and thawing processes. Such hysteretic characteristics are mainly associated with the connectivity and irregularity of the pore network. In this study, a physically-based model is developed to consider micro-scale heterogeneities in finite-size percolation during the freezing and thawing processes using an upscaling procedure. We introduce two simple parameters to describe the constrictivity and irregularity of the pore network: the radial factor and length factor of the pore throats within the capillaries. The proposed model accounts for the hysteretic mechanisms, upscaling single-pore hysteresis at the individual pore scale and pore irregularity hysteresis at the pore network scale. Furthermore, we use a series of experimental datasets to test the proposed hysteretic model. Our findings show an excellent agreement between the predicted values and the experimental dataset, indicating that our new physically-based models can effectively predict and interpret hysteretic behaviors in the temperature-dependent physical parameters of frozen rocks during freezing and thawing processes.

Hybrid-self-centring damper for industrial structure: Development and experimental validation

The seismic resilience of industrial structures has become an increasingly important issue considering the significant role played by industrial structures in social operation and post-earthquake rescue. This study presented a hybrid-self-centring damper (HSCD) incorporating the variable friction device (VFD) and tapered strip device (TSD) for tunable hysteretic behaviour to improve the seismic resilience of industrial structures. The notion of the proposed HSCD was first illustrated, followed by an experimental study on eight test specimens to understand the behaviour of the proposed damper. The test results confirmed that the proposed HSCD exhibited the expected energy dissipation sequence with excellent self-centring ability. The energy dissipation sequence of the proposed HSCD can be achieved by successive inelasticity consisting of the VFD and TSD, and the hysteretic behaviour can be flexibly adjusted by modulating the essential parameters. Detailed finite element models validated by the experimental results were developed to take insights into the behaviour of the proposed damper. To facilitate the design in the seismic application of the proposed HSCD, the hysteretic model and nonlinear-spring-based simplified model verified by test results were developed to quantify the hysteretic behaviour of the proposed damper.

A unified nonlinear dynamic model for bolted flange joint disk-drum structures under different interface states: Theory and experiment

Bolted flange joint disk-drum structures (BFJDDSs) are key components in aero-engines, however, bolt looseness inevitably occurs due to extreme service conditions. This can cause the bolted joint interface to exhibit complex contact behaviors, which significantly complicate the vibration characteristics of BFJDDSs. Existing dynamic models for BFJDDSs have not considered the effect of bolt looseness (slip and separation), so their vibration behaviors are not well understood. In this study, a unified nonlinear dynamic model for BFJDDSs considering different interface states (stick, slip, and separation) is proposed, which is effective under both bolt looseness and non-looseness (stick) conditions. The bi-linear hysteretic model combined with the piecewise linear model is used to simultaneously consider different interface states. The Kirchhoff plate theory, the Sanders’ shell theory, and the Euler-Bernoulli beam theory are used to derive the energy functions of the disk, drum, and flange, respectively. Then, the Lagrange equations are employed to derive the governing equations of BFJDDSs. Modal and nonlinear forced vibration experiments are carried out on a BFJDDS to prove the correctness of the proposed mathematical model. Research results show that the proposed mathematical model is able to achieve good predictions of nonlinear dynamic properties of BFJDDSs under both bolt looseness and non-looseness conditions. This model is also able to well predict the jumping phenomenon observed in the experiment.

Glubam roof truss with riveted glubam connections adopting thin-walled steel tube: Experiment, modeling, and model-updating

Bio-based laminated structures offer a timely solution to meet the pressing demand for resource-efficient and environmentally responsible construction practices in civil engineering. Riveted connections are a kind of commonly used joint and significantly impact the mechanical behaviors of global structure. However, existing studies on the complex behavior of such joints for bamboo-based structures are insufficient. This study investigated the hysteretic behavior of riveted Glued Laminated Bamboo (glubam) connections using thin-walled steel tube and corresponding planar roof truss with thin-walled steel tube connections by experimental and numerical methods. Firstly, cyclic tests were conducted on the riveted glubam connections with thin-walled steel tube to investigate their hysteretic behavior. The test matrix encompasses four distinct connection configurations, carefully selected to assess the connection behavior of glubam. After the investigation of connection behavior, cyclic tests were further conducted on glubam planar roof truss structures to evaluate their global and local hysteretic behavior. Subsequently, the numerical hysteretic models for joints and hybrid roof trusses were developed within the OpenSeesPy framework. To accurately and efficiently calibrate the model parameters, a novel parallel genetic algorithm (PGA) was proposed to carry out an initial calibration on model parameters. Based on PGA, a more comprehensive model updating framework combining the neural network, prior knowledge and PGA was developed to obtain optimal parameters. Finally, the numerical models were successfully validated against the experimental data, demonstrating the effectiveness of the established numerical model and model-updating framework.

Practice-oriented numerical model for seismic response of cold-formed steel-framed mid-rise buildings

Cold-formed steel (CFS) framed buildings are becoming increasingly common, notably in the high seismic regions of the United States (US). However, research to understand the seismic performance of CFS-framed buildings specifically using large-scale (building-level) specimens has begun only recently. Therefore, efforts to validate and improve numerical modeling of whole building systems have been limited due to this lack of experimental data. A recently completed experimental program, conducted at the Large High-Performance Outdoor Shake Table at the University of California, San Diego, involved earthquake testing of a full-scale 6-story CFS-framed building. The test building adopted an assembly of continuous tie-rod and built-up compression stud pack at the ends of individual shear walls to resist seismic overturning moment and uplift forces within the building. The objective of this paper is to present a practice-oriented phenomenological finite element modeling approach intended for design engineers and compare the predictions from this model against the measured seismic response of the 6-story building. The model aims to provide a robust, yet computationally efficient approach, with minimal degrees-of-freedom, while also capturing the salient features of seismic response of mid-rise CFS-framed buildings suitable for nonlinear time history analyses-based design. The building model, developed within the OpenSeesPy finite element platform, includes the shear walls and gravity walls as well as the lateral strength and stiffness contribution from exterior and interior gypsum sheathing. The continuous tie-rod system is also modeled to capture the cumulative floor displacements caused by the axial elongation in the steel rods. The effect of built-up compression stud packs on the lateral behavior of a shear wall was estimated using available experimental data and a detailed numerical model of an isolated shear wall, then subsequently incorporated in the nonlinear hysteretic material model. The numerical model captured the natural frequencies of the translation modes of the building in its undamaged state with <3% error. It also predicted the peak roof drift ratio within an error of 0.03% drift ratio under the design earthquake event. These results provide confidence in the proposed numerical modeling approach as a tool for seismic response prediction of mid-rise CFS-framed buildings with similar structural detailing features.

Spectral incremental dynamic methodology for nonlinear structural systems endowed with fractional derivative elements subjected to fully non-stationary stochastic excitation

A novel spectral incremental dynamic analysis methodology for analysing structural response in nonlinear systems with fractional derivative elements is presented, aligning with modern seismic design codes, like Eurocode 8. Drawing inspiration from the concept of fully non-stationary stochastic processes, the vector of the imposed seismic excitations is characterised by time and frequency evolving power spectra stochastically compatible with elastic response spectra of specified damping ratio and ground acceleration. The proposed method efficiently determines the nonlinear system time-dependent probability density functions for the non-stationary system response amplitude by employing potent nonlinear stochastic dynamics concepts, such as stochastic averaging and statistical linearisation. Unlike traditional incremental dynamic analysis curves found in the literature, the herein proposed method introduces a three-dimensional alternative counterpart, that of stochastic engineering demand parameter surfaces, providing with higher-order statistics of the system response. An additional noteworthy aspect involves the derivation of response evolutionary power spectra as function of spectral acceleration, offering a deeper insight into the underlying system dynamics. Besides its capabilities, the method maintains the coveted element of a particularly low associated computational cost, increasing its attractiveness and practicality among diverse applications of engineering interest. Numerical examples comprising the bilinear hysteretic model endowed with fractional derivative elements subject to an Eurocode 8 elastic design spectrum demonstrate the capabilities and reliability of the proposed methodology. Its accuracy is assessed by juxtaposing the derived results with germane Monte Carlo Simulation data.

Reliability-based ductility reduction factors surfaces using the generalized bojorquez ground motion intensity measure IBg

In this work, reliability-based ductility reduction factors surfaces are obtained through uniform annual failure rate (UAFR) spectra. For this aim, several nonlinear single degree of freedom (SDOF) systems that include various hysteretic behavior models, constant ductility performance and structural reliability levels are subjected to two sets of ground motions recorded on Mexico City. The first set includes 50 ground motion records located on stiff soils, while the second set correspond to 50 soft soil ground motions. In order to compute the UAFR spectra, the ground motion records were scaled at different values of a particular case of the generalized intensity measure IBg named INp for spectral acceleration. The study discusses the influence of different post-yielding stiffness on UAFR spectra obtained for the selected Bojorquez intensity measure, through the bilinear hysteretic model. Additionally, the Takeda model is used to represent structures that exhibit the effect of stiffness degradation. This study is aimed to compute the effect to obtain ductility reduction factors for various uniform annual failure rates, different degrees of post-yielding stiffness, and different ductility capacity for various nonlinear structures. The analyses of the results indicate that strength reduction (through ductility reduction factors) is mainly influenced by parameters such as ductility, failure rate, period of the system and soil conditions. Finally, reliability-based ductility reduction factor surfaces for stiff and soft soil are provided for different UAFR. It is important to say that this is the first time that ductility reduction factors are proposed based on IBg or INp as intensity measure.

Macro-modelling of GFRG infilled RC frames incorporating pivot hysteretic model

GFRG (Glass Fibre Reinforced Gypsum) panels present a viable alternative to conventional masonry infills in masonry infilled RC frames. Based on the experimental study on the lateral load behaviour of GFRG infilled RC frames, it was understood that the GFRG panels enhance the structural performance of the RC framed structure. To delve further into this, numerical modelling of GFRG infilled RC frames with different fillings inside the cavities of the panel was performed using SAP2000. The GFRG panels were modelled using nonlinear layered shell elements, while the interface between the GFRG web and the infill material was represented using multilinear plastic link elements. The monotonic lateral load–deflection behaviour and the in-plane hysteresis response were simulated by performing monotonic and cyclic pushover analyses. The cyclic pushover analysis incorporated pivot hysteretic models for the materials, hinges and links. Validation of the proposed numerical models was carried out by comparing the results with those obtained from the experimental study. Key parameters such as peak load, initial stiffness, stiffness degradation, and energy dissipation were carefully compared to ensure the accuracy and reliability of the proposed model. It was observed that the proposed numerical model was able to capture the monotonic and cyclic load–deflection behaviour and other performance parameters. The numerical model accurately predicted the peak load in the positive direction but overestimated the corresponding value in the negative direction. Moreover, the overestimation observed in the cumulative energy dissipated for all the specimens is relatively minor and does not significantly affect the overall accuracy of the model.

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.

Effect of temperature-dependent and hysteretic sorption in computational mould risk analyses of wood fibreboard sheathing

Wood is known for its complex hygroscopic properties. Previous studies show that both the temperature-dependency and the hysteresis in sorption should be included in the physical models, if the most accurate results are desired from simulations of building assemblies with wood-based materials. Literature is scarce on the topic, where the significance of these aspects on the reliability of mould-risk assessments is inspected. Exterior walls with glass wool insulation and LDF-sheathing were studied by using two different models with previously measured material data. Over 300 hygrothermal simulations were carried out, where mould-indices were computed on the warm side of the sheathing. According to both conventional and more sophisticated model, the studied walls perform well in cold climate if no driving rain leaks in. Temperature-dependent and hysteretic model yields slightly smaller mould-indices in general, but for certain leaky cases the difference is significant, which indicates the importance of sophisticated sorption-properties in modelling.