Spring Elements Research Articles

Modified Use of the Component Method to Get More Realistic Force Distribution in Joints of Steel Structures

According to the EN 1993-1-8 Standard, the moment resistance of end-plated connections can be calculated with the use of the component method. In this, a pair-of-force defines the moment resistance. The magnitude and the location of the compression force can be accurately identified. The tension force part is usually the resultant of parallel forces appearing in line with the bolt rows. Following the rules of manual calculation and using a mechanical finite element model, where each component is modelled with spring elements, in some—easily identifiable—cases, leads to different force distribution. The simplifications defined in the Standard provide a longer arm for the same force, and because of this, larger moment resistance at the expense of safety. In this work, an alternative calculation method will be presented that provides the same force values in each bolt row, as the mechanical model of the connection, without constructing the finite element model.

A rate-dependent crack bridging model for dynamic fracture of CNT-reinforced polymers

Carbon nanotubes (CNTs) improve the fracture toughness of polymer-based matrix composites by bridging the crack growth path. This research presents a finite element (FE) rate-dependent crack bridging model of Mode-I dynamic crack growth in CNT-reinforced polymers accounting for rate of loading and rapid crack growth. Two distinct CNT bridging and matrix cracking damage mechanisms are taken into account in the fracture process zone (FPZ) accounting for the dissipation of fracture energy. A viscoelastic-viscoplastic material model is adapted for the matrix phase to capture the strain rate effects. The crack in the matrix phase is modeled using cohesive zone elements characterized by experimental data. A rate-dependent traction-separation law obtained from CNT pull-out simulation at relevant crack opening speeds is used to simulate the CNT bridging in the FPZ. Considering the given traction-separation law as a constitutive equation, the CNTs are replaced with non-linear spring elements to facilitate the FE simulation of crack bridging with numerous CNTs in the FPZ. The proposed rate-dependent FE model for crack bridging enables the study of the effect of key CNT factors such as length, orientation, waviness, volume fraction, and agglomeration on fracture energy dissipation at various crack speeds. The developed model can simultaneously consider the interactive effects of all CNT parameters which is useful for considering all processing-induced uncertainties in analyzing the effects of CNTs on the dynamic fracture toughness of nanocomposites.

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.

Performance Evaluation of Inerter and Negative Stiffness-Based Dampers for Seismic-Induced Vibration Response Control of a Cable-Stayed Bridge: A Comparative Study

The excessive main girder displacement responses of the large-span cable-stayed bridges during seismic events may precipitate collisions between the main girder and the approach bridge. The viscous dampers (VDs) have been extensively employed in the seismic response control of long-span bridges, yet their effectiveness is limited. To augment the seismic-induced vibration control performance of the VD, inerter element, negative stiffness (NS) element, and spring element have been incorporated into the VD to achieve energy dissipation capacity enhancement. The equations of motion for the simplified cable-stayed bridge-damper systems are established under stochastic seismic excitation, and the design parameters of inerter and NS-based damper are optimized by using the genetic algorithm. The seismic control performance of the VD and five types of dampers are systematically compared, demonstrating that these dampers can substantially enhance the main girder displacement mitigation performance in cable-stayed bridges. Owing to the NS characteristics attributes of the inerter element and NS element and the tuning effect of the spring element, the tuned viscous mass damper (TVMD) with NS achieves a 24.56% higher efficiency in control performance compared to the VD.

Utilization of the Resonance Behavior of a Tendon-Driven Continuum Joint for Periodic Natural Motions in Soft Robotics

Continuum joints use structural elastic deformations to enable joint motion, and their intrinsic compliance and inherent mechanical robustness are envisioned for applications in which the robot, the human, and the environment need to be safe during interaction. In particular, the intrinsic compliance makes continuum joints a competitor to soft articulated joints, which require additional integrated spring elements. For soft articulated joints incorporating rigid and soft parts, natural motions have been investigated in robotics research to exploit this energy-efficient motion property for cyclic motions, e.g., locomotion. To the best of the author’s knowledge, there is no robotic system to date that utilizes the natural motion of a continuum joint under periodic excitation. In this paper, the resonant behavior of a tendon-driven continuum joint under periodic excitation of the torsional axis is experimentally investigated in a functional sense. In the experiments, periodic inputs are introduced on the joint side of a tendon driven continuum joint with four tendons. By modulating the pretension of the tendons, both the resonant frequency and the gain can be shifted, from 3 to 4.3 Hz and 2.8 to 1.4, respectively, in the present experimental setup. An application would be the rotation of a humanoid torso, where gait frequencies are synchronized with the resonant frequency of the continuum joint.

Corrosion failure analysis of interfacial bond performance in circular seawater sea-sand concrete encased weathering steel structures

This paper investigated the bond-slip behavior of circular seawater sea-sand concrete encased weathering steel (CSSCEWS) structures after chloride-induced corrosion. Electrochemical corrosion tests and push-out tests were conducted on fifteen designed CSSCEWS specimens. The results revealed that the corrosion ratio and steel section type distinctly influenced the interfacial bond performance. Both the ultimate and residual bond strengths decreased with the increase of the corrosion ratio, and the decline rate slowed down gradually. Compared to the uncorroded specimens, the average damage ratio of the ultimate strength of the specimens with a corrosion ratio of 8% is 25.9%, while the average damage ratio of the residual strength is 49.1%. The bond toughness continuously decreased with prolonged corrosion, while the bond stiffness and energy dissipation index first increased and then decreased. Additionally, formulas for calculating the corroded bond strengths of CSSCEWS specimens were proposed. Considering the strength damage due to corrosion and the stiffness damage due to slip, a three-stage bond-slip constitutive model was proposed. Finally, this model was applied to the nonlinear spring elements in finite element modeling to effectively simulate the interfacial bond behavior during the loading of corroded CSSCEWS specimens.

Numerical Investigation of Fracture Behaviour of Polyurethane Adhesives under the Influence of Moisture.

The mechanical behaviour of polymer adhesives is influenced by the environmental conditions leading to ageing and affecting the integrity of the material. The polymer adhesives have hygroscopic behaviour and tend to absorb moisture from the environment, causing the material to swell without applying external load. The focus of the work is to investigate the viscoelastic material behaviour under ageing conditions. The constitutive equations and the governing equations to numerically investigate the fracture in swollen viscoelastic material are discussed to describe the numerical implementation. Phase-field damage modelling has been used in numerical studies of ductile and brittle materials for a long time. The finite-strain phase-field damage model is used to investigate the fracture behaviour in aged viscoelastic polymer adhesives. The finite-strain viscoelastic model is formulated based on the continuum rheological model by combining spring and Maxwell elements in parallel. Commercially available post-cured crosslinked polyurethane adhesives are used in the current investigation. Post-cured samples of crosslinked polyurethane adhesives are prepared for different humidity conditions under isothermal conditions. These aged samples are used to perform tensile and tear tests and the test data are used to identify the material parameters from the curve fitting process. The experiment and simulation are compared to relate the findings and are the first step forward to improve the method to model crosslinked polymers.

Behavior of steel-plate concrete wall-reinforced concrete slab joint with UHPC-strengthened lap-splice connection

The comprehensive integration of modular technology is the crucial pathway for advancing the upgraded Hua-long Pressurized Reactor (HPR1000). However, previous studies are limited and numerous challenges remain concerning the modular curved steel-plate concrete (SC) wall-reinforced concrete (RC) slab joint. This paper focuses on the behavior and design of the SC wall-RC slab joint through large-scale tests and numerical simulation. Two UHPC-strengthened non-contact lap splice (NS) connections, including versions with normal and headed rebars, were proposed to ensure effective load transfer and modular construction performance. The test results indicated that the four joint specimens subjected to cyclic loading did not experience lap splice failure but instead suffered interface shear failure and shear failure of the RC slab under shear-span ratios of 1.5 and 3.0, respectively. The excellent load transfer performance demonstrated by these two NS connections validates them as effective methods for this joint, with lap lengths of 21d for normal rebar and 13d for headed rebar deemed adequate. Besides, the developed three-dimensional FE model with non-linear spring element accurately simulated the test failure modes and F-Δ curves. The parametric study results recommended that the volumetric steel ratio of tie-bar should not be lower than 1.03 %. The tension of longitudinal rebars for normal and headed rebars can be fully transferred within 80 % of the designed lap length. Furthermore, a complete design method was established based on the load-transfer model, encompassing interfacial shear, lap length calculation and tie-bar configuration, and is applicable to SC-to-RC connections or joints.

Experimental Evaluation of Damping and Stiffness in Optimized Active Sport Utility Vehicle Suspension Systems

On a flat city road, the specificity of the suspension poses a challenge. Sport utility vehicles (SUVs) have less flexibility compared to regular cars, despite providing a firm grip on asphalt and concrete. Constant adjustments to the center of gravity of SUVs are necessary. Surprisingly, they are less reliable and stable in urban settings due to this characteristic. In this study, a mathematical model of the suspension system of SUVs based on the Newtonian approach is introduced and validated with data from experiments carried out by the MTS machine system on the mono-tube (oil/air) mixed damper element. The model accurately predicts the performance of this damper, commonly used in SUVs, across various operating conditions, including different frequencies. A coil spring element, serving as a passive suspension unit with this damper, is also tested experimentally under similar conditions. By integrating passive suspension elements with the active actuator, the proposed modified design reduces the power consumption needed for the actuator to function and ensures a certain level of reliability. The effectiveness and performance of the modified active suspension system in comparison to the traditional passive suspension system are assessed using three different strategies: hybrid PID-LQR, linear quadratic regulator (LQR), and proportional-integral-derivative (PID). The genetic algorithm is utilized to determine the optimal parameter values for each controller by minimizing a cost function, maximizing performance, and minimizing energy consumption. Simulation results demonstrate that the active suspension system controlled by the PID-LQR controller offers significantly improved ride comfort and vehicle stability compared to other systems. This suggests that the performance of the active suspension system is greatly enhanced by the combined application of the hybrid PID-LQR controller compared to other systems.

Factors controlling the water quality of rock glacier springs in European and American mountain ranges

Rock glaciers (RGs) provide significant water resources in mountain areas under climate change. Recent research has highlighted high concentrations of solutes including trace elements in RG-fed waters, with negative implications on water quality. Yet, sparse studies from a few locations hinder conclusions about the main drivers of solute export from RGs. Here, in an unprecedented effort, we collected published and unpublished data on rock glacier hydrochemistry around the globe. We considered 201 RG springs from mountain ranges across Europe, North and South America, using a combination of machine learning, multivariate and univariate analyses, and geochemical modeling. We found that 35 % of springs issuing from intact RGs (containing internal ice) have water quality below drinking water standards, compared to 5 % of springs connected to relict RGs (without internal ice). The interaction of ice and bedrock lithology is responsible for solute concentrations in RG springs. Indeed, we found higher concentrations of sulfate and trace elements in springs sourcing from intact RGs compared to water originating from relict RGs, mostly in specific lithological settings. Enhanced sulfide oxidation in intact RGs is responsible for the elevated trace element concentrations. Challenges for water management may arise in mountain catchments rich in intact RGs, and where the predisposing geology would make these areas geochemical RG hotspots. Our work represents a first comprehensive attempt to identify the main drivers of solute concentrations in RG waters.

A refined track dynamic model considering the bending properties of iron pad: Proposal and validation

Iron pads are crucial components in rail fastening systems, characterized by their load-bearing and force-transmitting capabilities. This study presents and validates a track dynamic model considering the bending properties of iron pad, offering a comprehensive analysis of their dynamic performance under train loads. The primary aim is to employ iron pads as key elements for monitoring and detecting potential defects throughout the track’s service life. Initially, the construction of the track dynamic model is outlined, followed by an in-depth explanation of how the iron pads integrate with the track model. This involves introducing an enhanced Kelvin-Voigt three-element model and elaborating on the parameter selection for the spring element using a nonlinear spring model that accounts for voids and their relevant conditions. Subsequently, a systematic comparative analysis is performed to evaluate the accuracy of simulating iron pads using solid, shell, and beam elements, along with a proposed strain correction method. Finally, the established model and methods are employed to simulate and analyze the dynamic response of iron pads under typical defect conditions. These results indicate that iron pads can effectively reflect the failure conditions of the railway track system, making them ideal sensing elements for the dynamic monitoring of track structures. The enhanced model developed in this study holds significant theoretical and practical value, contributing to the safety monitoring and defect analysis of railway operations.

Coupled vibration of low-medium-speed maglev vehicle-guideway system on isolated bridge with lead rubber bearings

This paper investigates the dynamic response of low-medium-speed (LMS) maglev vehicle moving on the isolated bridge with lead rubber bearings (LRBs). In the vehicle-guideway bridge model, the vehicle is simulated as a 50-degree-of-freedom model consisting of a car-body and ten bogie modules. The guideway bridge with LRB is established by the finite element method, and the guideway is interacted with the vehicle by the actively controlled electromagnetic forces. The LRB is simulated by the nonlinear spring element for reflecting the hysteretic performance, and a fast nonlinear analysis (FNA) method is proposed to achieve the potential nonlinear behavior of LRB under vehicle load. Then, the dynamic response of maglev vehicle running on the isolated bridge with LRB is investigated and compared to that on the non-isolated bridge. The effect of vehicle speed and LRB isolation degree on the coupled system responses is studied. Furthermore, the driving quality of vehicle on LRB bridge is discussed, and the applicability of LRB to maglev line bridge is thoroughly evaluated. The results show that the installation of LRB exhibits relatively insignificant influence on the vertical response of vehicle-guideway system, while could enlarge the lateral response. The lateral response of coupled system is much more vulnerable to the isolation degree, and it is recommended that the isolation degree of LRB should not exceed 2.50 to guarantee the driving comfort and running safety.

Component tests and numerical simulations of 3D steel frame structures for progressive collapse

This paper presents a comprehensive study on three-dimensional steel frame structures subjected to progressive collapse, drawing insights from a full-scale steel frame substructure test. The investigation encompasses connection component tests and numerical simulations, focusing on extended end plate and double-angle cleat connections employed in the substructure test. The mechanical properties of the connection components were tested, forming a basis for defining component properties in subsequent connection models. Finite element (FE) models of the test substructure were developed, utilizing hybrid elements for the steel frame part, which include beam, connector, and spring elements based on the component method. To simulate reinforced concrete slabs, a combination of refined solid elements and simplified shell elements was employed. The former accurately captures detailed failure modes, while the latter efficiently simulates the collapse behavior of large-scale steel frame structures. Validation of the established models against test results encompassed load-displacement responses, internal forces in structural members, and failure modes. The validated FE models were then utilized to analyze and discuss the contributions of various structural components in resisting progressive collapse. Specific focus was placed on the development of load-resisting mechanisms in the floor slab and the influence of beam-column connection types on structural behavior. The paper explores the role of bracing systems in a building in resisting progressive collapse. Additionally, it evaluates the effectiveness of the restraint systems used in the test, shedding light on their ability to accurately reflect real restraint effects from the surrounding structure. The findings presented herein contribute valuable insights to the understanding of progressive collapse behavior in steel frame structures, with implications for robustness design of multi-story steel buildings.

Modified double cantilever beam test method for mode-I energy release rate of elastic adhesive layers

This study proposes a Mode I double cantilever beam (DCB) test method for debonding thick elastic adhesive layers. The approach integrates Bernoulli–Euler beams connected via spring elements akin to Winkler’s foundation. Energy release rate determination considers crack length correlation with elastic deformation in the crack-front region, accounting for both beam rotation and lateral movement. Evaluation of Ti6Al4V samples bonded with FM 309 adhesive revealed higher initial energy release rates with the conventional beam theory and conservative values with the modified beam theory. The proposed method offered improved consistency, and less conservative energy release rate values compared to the modified theory.

Modeling of glubam roof truss, parameter identification and updating based on parallel genetic algorithm

This research introduces an innovative approach to the design and simulation of bio-based laminated structures, specifically focusing on glue-laminated bamboo (glubam) used in roof trusses. Our study fills a critical gap by investigating the mechanical behaviors of bolted connections in bamboo-based structures, which have not been comprehensively studied before. We employ a dual-phase methodology: initially, cyclic tests on bolted steel to glubam joints assess their hysteretic behavior, followed by tests on glubam planar roof trusses to evaluate structural responses under practical conditions. Our novel contribution is the development of a simplified mechanical-based hysteretic model, incorporating connector and spring elements in series or parallel within the ABAQUS software. This model significantly improves on existing models by allowing for initial calibration through a parallel genetic algorithm (PGA), enhancing both accuracy and efficiency. Subsequent incorporation of this model into the simulation of truss joints enabled the creation of an advanced hybrid roof truss model within ABAQUS. The final stage of our research demonstrates the application of a PGA-based model-updating framework, which substantially increases the model’s predictive accuracy. This work not only advances the understanding of structural behavior in bio-based construction materials but also introduces a robust framework for model updating that can be applied to other engineering simulations, contributing to more sustainable and resource-efficient construction practices.

Bonding-slip behaviour of steel-concrete interfaces in CFDST members with PBL ribs

The bonding-slip behaviour of different materials of concrete-filled double skin steel tubular members under different interfacial connection structures, such as ribbed plates and ribbed plates with holes, are studied. The failure mode, the bonding force-slip curve and the strain distribution on the slip surface are obtained. The results show that the hollow ratio is inversely proportional to the bonding strength of the interface. The Perfobond leister (PBL) rib enhances bonding performance through increasing the diameter and holes, the effect of excessive hollow ratio on bonding stress is reduced. Different slip interfaces result in various bonding-slip mechanisms. Based on the typical failure modes and bonding-slip mechanism analysis, the bonding strength formulas and bonding stress-slip constitutive models suitable for CFDST members are proposed. A numerical model using a spring element is established by Abaqus for further mechanism analysis, the loading-slip curve and the stress state of the surface are consistent with measured results.

Experimental Study on the Bonding Performance between Shaped Steel and High-Strength Concrete

The integration of steel fibers into high-strength concrete (HSC) offers a solution to address the brittleness and limited ductility typically associated with conventional HSC structures. To investigate the bonding properties between shaped steel and high-strength concrete with steel fiber (SFRC), thirteen tests of the shaped steel/SFRC specimens are conducted to explore the effects of various factors such as steel fiber volume ratio, concrete strength grade, reinforcement ratio, steel embedment depth, and cover thickness on bond–slip behavior. Three distinct failure modes, such as pushout failure, bond splitting, and yielding failure of steel, are identified during the pushout tests. Three different types of bond strength, such as the initial bond strength, the ultimate bond strength, and the residual bond strength, are observed from the load–slip curves between the shaped steel and concrete. By incorporating nonlinear spring elements, a numerical model for accurately simulating the bond performance between the shaped steel and SFRC specimens is developed. The bond strength between the shaped steel and concrete increase as the concrete strength, cover thickness, steel fiber volume ratio, and stirrup ratio increase, while it decreases as the steel embedment depth increases. A model for the bond strength between shaped steel and SFRC is developed, and it agrees well with the test data.

Highly stabilized fiber Bragg grating accelerometer based on cross-type diaphragm

A fiber Bragg grating (FBG) accelerometer based on cross-type diaphragm was proposed and designed, in which the cross-beam acts as a spring element. To balance the sensitivity and stability, the accelerometer structure was optimized. The experimental results show that the designed device has a resonant frequency of 556 Hz with a considerable wide frequency bandwidth of up to 200 Hz, which is consistent with the simulation. The sensitivity of the device is 12.35 pm/g@100 Hz with a linear correlation coefficient of 0.99936. The proposed FBG accelerometer has simple structure and strong anti-interference capability with a maximal cross-error less than 3.26%, which can be used for mechanical structural health monitoring.

Neural networks-based spring element for second-order analysis of pile-supported structures with nonlinear soil- structure interaction

This paper proposes a novel structural analysis approach, the neural networks-based spring element (NNSE) method, to synergize machine learning (ML) techniques with the line finite element method (LFEM) for the second-order analysis method of pile-supported structures. Traditional LFEM, widely used in upper structure design, showcases limitations in efficiently modeling complex Soil-Structure Interaction (SSI) along piles since it requires dense element mesh for accuracy. Conversely, ML offers a mesh-free alternative for analyzing single piles but struggles in simulating pile-supported structures as the training sample collection for large-scale problems might be unbearable. This paper addresses these challenges by proposing a new analysis framework to utilize the neural network (NN) model, which only describes structural responses of single piles, for the simulation of entire pile-supported structures. In the proposed method, the NN model is not directly used for structural analysis but employed to formulate a new spring element named the NNSE to model single piles in pile-supported structures. This NNSE can be seamlessly implemented within the existing LFEM framework to analyze pile-supported structures, eliminating the dense mesh requirement for single piles and thereby significantly improving the computational efficiency. Extensive examples are provided to verify the effectiveness of the proposed method, indicating its potential in promoting the second-order analysis method to the design of pile-supported structures.

Direct integration of measured viscoelastic relaxation data in time-domain finite element simulations

The current approach to modeling viscoelastic materials in most commercial finite element packages is based on the General Maxwell Model, which views these materials as combinations of spring and dashpot elements. However, the data can be incorporated more directly into a transient finite element study by direct interpolation of the relaxation function. This work explores a linear interpolation scheme to the inclusion of viscoelastic relaxation functions on an example problem. The results show several benefits over the General Maxwell Model for transient studies. Included in the analysis are displacement solutions utilizing both approaches, relaxation function error calculations for both approaches, and parametric runtime studies comparing speed of calculation. The variation in computational flop counts is considered and an argument is made for the preference of the proposed approach.