Nonlinear Spring Elements Research Articles

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.

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.

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.

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.

Performance comparison of linear and nonlinear compliant liquid dampers-inerter in controlling across-wind response of benchmark tall building

The potential of compliant liquid dampers-inerter (CLDI) for response control of tall buildings, capitalizing on the mass amplification property of the inerter, has been explored. However, the influence of the compliance connection on the damper displacement, energy dissipation, and inerter force is never addressed. The present work introduces a nonlinear compliant liquid damper-inerter (NCLDI), in which the compliance connection is achieved by joining the tank with the building through nonlinear spring and linear dashpot elements. The nonlinear mechanism (restoring force) is generated by connecting two linear springs in series. The effectiveness of NCLDI in reducing the across-wind response of tall buildings is examined and compared with that of a CLDI. For numerical demonstration, the 76-storey benchmark tall building is considered and subjected to across-wind loading. With the building's available mass, damping, and stiffness matrices, the uncontrolled and controlled structural responses are obtained using the Newmark–Beta method in the MATLAB environment. Iterations are executed at each time step to address the nonlinear stiffness term incorporating the Newton-Raphson method. Optimization is performed to estimate the optimum damper parameters utilizing MATLAB's multi-objective genetic algorithm solver, ‘gamultiobj’. The four selected objective functions are the peak and root-mean-square values of the roof displacement and acceleration. The performance of both the dampers is investigated for different inerter topologies with variable inertance ratios. The CLDI is found to be efficient when the inertance ratio and topology are less. However, an enhanced mitigation effect of the NCLDI compared to the CLDI is observed for higher inertance with a large topology. In addition, the stroke length of the damper is reduced significantly in case of NCLDI, which is a notable advantage for any passive damping device.

Computational Modelling of Intra-Module Connections and Their Influence on the Robustness of a Steel Corner-Supported Volumetric Module

This paper investigates the robustness of a single 3D volumetric corner-supported module made of square hollow-section (SHS) columns. Typically, the moment–rotation (M-θ) behaviour of connections within the module (intra-module) is assumed to be fully rigid rather than semi-rigid, resulting in inaccurate assessment (i.e., overestimated vertical stiffness) during extreme loading events, such as progressive collapse. The intra-module connections are not capable of rigidly transferring the moment from the beams to the SHS columns. In this paper, a computationally intensive shell element model (SEM) of the module frame is created. The M-θ relationship of the intra-module connections in the SEM is firstly validated against test results by others and then replicated in a new simplified phenomenological beam element model (BEM), using nonlinear spring elements to capture the M-θ relationship. Comparing the structural behaviour of the SEM and BEM, under notional support removal, shows that the proposed BEM with semi-rigid connections (SR-BEM) agrees well with the validated SEM and requires substantially lower modelling time (98.7% lower) and computational effort (97.4% less RAM). When compared to a BEM with the typically modelled fully rigid intra-module connections (FR-BEM), the vertical displacement in the SR-BEM is at least 16% higher. The results demonstrate the importance of an accurate assessment of framing rotational stiffness and the benefits of a computationally efficient model.

Research on the interfacial bonding performance of novel composite L‐shaped concrete‐filled steel tubes

SummaryThis study aims to investigate the bonding performance of novel composite specially shaped concrete‐filled steel tubes (CFSTs). Seven novel composite L‐shaped CFST specimens were designed utilizing variations in steel tube wall thickness, steel tube length, and concrete strength as the primary parameters. Their failure modes, load–slip relationships, and longitudinal strain distribution patterns were examined through push‐out tests. Additionally, finite element models of the members were established using nonlinear spring elements based on the experimental data and subjected to numerical analysis. The research findings indicate that the ultimate bond strength of the composite L‐shaped CFSTs is positively correlated with steel tube wall thickness, steel tube length, and concrete strength. The strain distributions on the concave and convex faces of the L‐shaped steel tubes are identical. The results obtained from the finite element analysis closely match the experimental findings.

Post-buckling shear capacity of steel plates with opening strengthened by fiber fabric

Shear capacity is one of the most important factors of steel plates and the steel plates with opening is widely adopted in engineering. This study investigates steel plates reinforced with fiber fabric. Opening shapes, positions, panel thicknesses, and material strengths, are considered to assess the effectiveness of fiber fabric in reinforcing steel plates. Two types of fibers, carbon fiber and basalt fiber, are employed. Specimens with various opening positions and shapes are meticulously designed. The study includes an analysis of how effectively fiber fabric improves shear capacity and examines the resulting failure modes. A comparison is made regarding the shear behavior of plates reinforced with different types of fiber fabrics. The study also explores how plate thickness influences the strengthening effect. The results indicate that the presence of fiber fabric does not enhance the shear capacity of steel plates without openings. Carbon fiber demonstrates a greater enhancement in shear capacity compared to basalt fiber. The use of fiber fabric and epoxy resin to reinforce thin steel plates shows limited improvement in shear capacity. A numerical model is proposed to simulate plates reinforced with fiber fabric, incorporating a nonlinear spring element to represent the behavior of epoxy resin.

Validation of a finite-element model of a wind turbine blade bearing

Finite-element analysis is the only means to determine the load situation of slewing bearings with complex interfaces. For reliable results, the finite-element model needs to be validated by comparing the simulation results against measurement results. Most published finite-element bearing models of slewing bearings are not validated at all, and none of the publications investigate the accuracy of the experimental results. For the present work, the authors tested multiple double-row four-point contact ball bearings to compare them with simulation results. As the ball forces cannot be measured directly, strain gauges on the outer bearing ring were used to validate the model. To minimize the computational effort, the ball-raceway contact is modeled with nonlinear spring elements. The experimental results show high deviations for different pitch angles of the bearing at constant load levels. Nevertheless, the mean strain gauge values are reproducible with each tested bearing. That allows a comparison with the simulation and derives a test scenario of at least one bearing with different pitch positions at constant load to validate a bearing simulation. The result of this work is a validated bearing and test rig model.

Experimental and numerical studies on mechanical performance of the grid unit in single-layer reticulated shells with Temcor joints

Temcor joints are widely used in aluminium alloy single-layer latticed shells. However, the research mainly focuses on the connection joints of components, the research on the mechanical performance of the grid unit in single-layer reticulated shells is limit. In this paper, the performances of grid elements in single-layer aluminum alloy latticed shells with Temcor joints are studied through two full-scale tests with different member cross-section size, member length and joint construction. In the conducted tests, the failure mode, the load-displacement curves, and the bending moment-stress curves are recorded and discussed. The results indicate that the capacity and the ductility of aluminum alloy grid cells are affected significantly by the heights of the members. The failure of the grid unit with a height of 550 mm was triggered by the tensile fracture of the bottom flange in the connected members near connection joint. In contrast, the failure of the grid unit with a height of 200 mm was induced by the compression damage of the top flange in the members connected with joint, moreover, in-plane distortion was observed in the member near the gusset region. On this basis, the numerical simulation method using non-linear spring elements is proposed, in which the actual rotational stiffness of joints is considered. The load-displacement curves obtained from the refined finite element analysis model are validated to be in good agreement with the test results.

Model for calculation of thermal stresses in concrete pavement slabs with refined non-linear deformation constraints

Few investigations have considered comprehensive deformation constraints when calculating thermal stress of concrete slab. In this paper, the comprehensive and refined non-linear deformation constraints model of concrete slab is firstly proposed by setting non-linear spring elements at bottom and side of the slab and the capacity of shear load transfer across joints is considered as well. The results show that thermal stresses calculated by refined non-linear deformation constraints model are in good consistent with experimental results. The foundation reaction modulus has little effect on thermal stresses, but has a significant effect on gap between slab and its foundation. The stiffer base results in higher curling stresses at bottom of slab, and the types of base have an important effect on frictional resistance in horizontal direction at bottom of slab. The larger shear stiffness of joints will increase thermal stresses and shear force along joints but decrease deflections of slab.

Stability Analysis of Free-Form Reticulated Shells With Semi-Rigid Joints

Focusing on the free-form reticulated shells with semi-rigid joints, a stability study is conducted in this paper. Firstly, the gradient-based optimization and genetic optimization are conducted respectively, by which the local optimal shell and the global shell are obtained. A parametrical non-linear stability analysis is performed on the local and global optimal reticulated shells using ANSYS. Then, the ultimate bearing capacity and instability modes of both shells are obtained. The semi-rigid joints are modelled by non-linear spring element, named COMBIN39. The effects of bending stiffness, torsional stiffness, initial geometrical imperfection and load cases are investigated.

Structural Design of the Substructure of a 10 MW Floating Offshore Wind Turbine System Using Dominant Load Parameters

Fully coupled integrated load analyses (ILAs) to evaluate not only the load response but also the structural integrity are required to design a floating offshore wind turbine, since there has been no firmly established approach for obtaining the structural responses of a FOWT substructure in the time domain. This study aimed to explore if a direct strength analysis (DSA) technique that has been widely used for ships and offshore structures can adequately evaluate the FOWT substructure. In this study, acceleration and nacelle thrust were used for the dominant load parameters for DSA. The turbine thrust corresponding to the 50-year return period was taken from the literature. The acceleration response amplitude operator (RAO) was obtained through frequency response hydrodynamic analysis. The short-term sea states defined by the wave scatter diagram (WSD) of the expected installation area was represented by the JONSWAP wave spectrum. To account for the multi-directionality of the short-crested waves, the 0th order moments of the wave spectrum were corrected. The probabilities of each short-term sea state and each wave incidence angle were applied to derive the long-term acceleration for each return period. DSA cases were generated by combining the long-term acceleration and nacelle thrust to maximize the forces in the surge, sway, and heave directions. Linear spring elements were placed under the three outer columns of the substructure to provide soft constraints for hive, roll, and pitch motions. Nonlinear spring elements with initial tension were placed on the three fairlead chain stoppers (FCSs) to simulate the station-keeping ability of the mooring lines; they provided initial tension in the slacked position and an increased tension in the taut position. The structural strength evaluation of the coarse mesh finite element model with an element size same as the stiffener spacing showed that high stresses exceeding the permissible stresses occurred in the unstable members of the substructure. The high stress areas were re-evaluated using a fine mesh finite element model with an element size of 50 mm × 50 mm. The scope of structural reinforcement was identified from the fine mesh analyses. It was found that the DSA can be properly utilized for the substructure strength assessment of a FOWT.

Experimental study and numerical simulation on the bonding properties of rubber concrete and deformed steel bar

In this study, the pull-out test was carried out by placing strain gauge in the groove of steel bar. The effects of rubber volume incorporation rate (0%, 10%, 20%, and 30%), steel bar diameter (14 mm,16 mm,18 mm, and 20 mm) and anchorage length (4d, 5d, and 6d) on the bonding performance of deformed steel bar and rubber concrete were studied. The failure modes of the specimens are observed and the ultimate bond stress and slip of the specimens are calculated. On this basis, the distribution laws of relative bond stress under different influencing factors and the bond stress-slip curves at different anchoring positions are obtained. In addition, the bond stress-slip constitutive model of deformed steel bar and rubber concrete considering rubber incorporation rate is established. Through non-dimensional treatment of the bond stress at different positions x (distance from the free end) under the same slip value, the bond position functions of deformed steel bar and concrete with different rubber incorporation rates are obtained. Finally, the nonlinear spring element Spring2 is used to simulate and analyze the bonding property and slip. The experimental results are in good agreement with the simulation results.

CALIBRATION OF HOLZAPFEL-GASSER-OGDEN COLLATERAL LIGAMENT PROPERTIES IN A HYBRID POST-ARTHROPLASTY KNEE JOINT MODEL FOR LAXITY TESTING

This study aims to create a novel computational workflow for frontal plane laxity evaluation which combines a rigid body knee joint model with a non-linear implicit finite-element model wherein collateral ligaments are anisotropically modelled using subject-specific, experimentally calibrated Holzpfel-Gasser-Ogden (HGO) models.The framework was developed based on CT and MRI data of three cadaveric post-TKA knees. Bones were segmented from CT-scans and modelled as rigid bodies in a multibody dynamics simulation software (MSC Adams/view, MSC Software, USA). Medial collateral and lateral collateral ligaments were segmented based on MRI-scans and are modelled as finite elements using the HGO model in Abaqus (Simulia, USA). All specimens were submitted varus/valgus loading (0-10Nm) while being rigidly fixed on a testing bench to prevent knee flexion. In subsequent computer simulations of the experimental testing, rigid bodies kinematics and the associated soft-tissue force response were computed at each time step. Ligament properties were optimised using a gradient descent approach by minimising the error between the experimental and simulation-based kinematic response to the applied varus/valgus loads. For comparison, a second model was defined wherein collateral ligaments were modelled as nonlinear no-compression spring elements using the Blankevoort formulation.Models with subject-specific, experimentally calibrated HGO representations of the collateral ligaments demonstrated smaller root mean square errors in terms of kinematics (0.7900° +/− 0.4081°) than models integrating a Blankevoort representation (1.4704° +/− 0.8007°).A novel computational workflow integrating subject-specific, experimentally calibrated HGO predicted post-TKA frontal-plane knee joint laxity with clinically applicable accuracy. Generally, errors in terms of tibial rotation were higher and might be further reduced by increasing the interaction nodes between the rigid body model and the finite element software. Future work should investigate the accuracy of resulting models for simulating unseen activities of daily living.

Research on Tunnel-Boring Machine Main Bearing Fatigue Damage and Vibration Response

Based on the damage evolution equation of bearing steel, a user subroutine was developed to simulate the fatigue damage behavior of the TBM main bearing under the condition of low speed and heavy load. In addition, the damage evolution law of the main bearing in the time domain and the space domain was studied. Then, a nonlinear spring element was introduced to simulate the interaction between the roller raceway, and the vibration response of the TBM after the main bearing damage was studied using the transient dynamic method. The research shows that the damage risk of the raceway is greater than that of the roller, and the damage risk of the main pushing raceway is greater than that of the other two raceways. The damage of the main bearing will not only lead to the increase in the peak vibration response of the TBM but also cause more frequency components of the response. By monitoring the time domain index of vibration signal, the damage degree to the main bearing can be mastered in real time, providing a reference for the maintenance of the main bearing.

Experimental Characterization, Modeling, and Numerical Evaluation of a Novel Friction Damper for the Seismic Upgrade of Existing Buildings

The paper presents the experimental characterization, the formulation of a numerical model, and the evaluation, by means of non-linear analyses, of a new friction damper conceived for the seismic upgrade of existing building frames. The damper dissipates seismic energy through the friction force triggered between a steel shaft and a lead core prestressed within a rigid steel chamber. The friction force is adjusted by controlling the prestress of the core, allowing the achievement of high forces with small dimensions, and reducing the architectural invasiveness of the device. The damper has no mechanical parts subjected to cyclic strain above their yield limit, thereby avoiding any risk of low-cycle fatigue. The constitutive behavior of the damper was assessed experimentally, demonstrating a rectangular hysteresis loop with an equivalent damping ratio of more than 55%, a stable behavior over repeated cycles, and a low dependency of the axial force on the rate of displacement. A numerical model of the damper was formulated in the OpenSees software by means of a rheological model comprising an in-parallel system of a non-linear spring element and a Maxwell element, and the model was calibrated on the experimental data. To assess the viability of the damper for the seismic rehabilitation of buildings, a numerical investigation was conducted by performing non-linear dynamic analyses on two case-study structures. The results highlight the benefits of the PS-LED in dissipating the largest part of seismic energy, limiting the lateral deformation of the frames, and controlling the increase in structural accelerations and internal forces at the same time.

Numerical analysis of traditional Chinese timber structure: Simplified finite element model and composite elements of joints

Mortise-tenon (M-T) joint, column foot joint, and Dou-Gong joint play a key role in the seismic behavior and energy dissipation of traditional timber structures. To simplify the modeling process and predict accurately the hysteretic behaviors of traditional timber joints as well as the global seismic responses of traditional timber structures, three types of composite elements, which were composed of varying non-linear one-dimensional spring elements available in the ANSYS finite element (FE) software, were proposed to characterize the hysteretic performance of the M-T joint, the column foot joint, and the Dou-Gong joint, respectively. The beam element was used for simulating the timber components with large size and not easily damaged. The parameters of the composite elements were identified from the simplified hysteretic model or test hysteretic curve of each type of joint. The simplified FE models of the M-T joint, M-T jointed timber frame, column foot joint, and Dou-Gong joint were developed, and verified using the cyclic loading tests of joints, respectively. Based on the validated composite elements and simplified FE models of varying joints, the three-dimensional simplified bar system FE model of a 1/3.52-scaled palace-style ancient timber structures was established using the ANSYS, and also validated using the shaking table tests, in terms of its dynamic characteristics and responses. Good agreements between the model predictions and test results were observed. Additionally, parametric analyses were performed, while revealing and quantifying the effects of performance degradation for the M-T joint, column foot joint, and Dou-Gong joint on the dynamic responses to the structure. It is found that the damage to the Dou-Gong joint had little effect on the maximum story drift of column frame layer, however, the damage to the M-T joint and column foot joint would significantly increase the maximum story drift of column frame layer. When the damage degree of the M-T joint, Dou-Gong joint, and column foot joint in the structure was up to 60%, the maximum story drift ratios of column frame layer were close to 1/48, 1/50, and 1/39, respectively, the maximum story drift ratios of Dou-Gong layer were approximately 1/164, 1/98, and 1/125, respectively.

Numerical Modelling of the Constitutive Behaviour of FRCM Composites through the Use of Truss Elements.

The modeling of the mechanical behavior of Fabric Reinforced Cementitious Matrix (FRCM) composites is a difficult task due to the complex mechanisms established at the fibre-matrix and composite-support interface level. Recently, several modeling approaches have been proposed to simulate the mechanical response of FRCM strengthening systems, however a simple and reliable procedure is still missing. In this paper, two simplified numerical models are proposed to simulate the tensile and shear bond behavior of FRCM composites. Both models take advantage of truss and non-linear spring elements to simulate the material components and the interface. The proposed approach enables us to deduce the global mechanical response in terms of stress-strain or stress-slip relations. The accuracy of the proposed models is validated against the experimental benchmarks available in the literature.

Crowning Method on Bearing Supporting Large Wind Turbine Spindle Considering the Flexibility of Structure of Shaft System

To meet the precision design of bearings on large wind turbine spindles, a crowning method of bearing on wind turbine spindles considering the flexibility of the support structure is proposed. Firstly, a finite element (FE) model of the shaft system with a flexible structure is constructed by connecting the shaft and bearing through constraint equations (CE) and multi-point constraint (MPC) algorithms and replacing the bearing rollers with nonlinear spring elements and dampers. Then, the Newmark integration algorithm is used to solve the model and analyze the effect of the structure’s rigidity on the load distribution of bearings. Then, perform convergence analysis of the sequences of the spring load distribution using a high-pass filter based on fast Fourier transform (FFT) and root mean square error (RMSE) to obtain a suitable number of replacement springs. Finally, a sub-model of the upwind bearing is constructed with structured mesh. With the maximum Von Mises stress of the roller profile as the design target, the optimal logarithmic crowning of the roller and its tolerance zone under the given working conditions are obtained. The results show that the FE model of the shaft system proposed has good convergence. The FE model of the shaft system considering the flexibility of the support structure can obtain more accurate load distributions of bearings and can make the accurate crowning design of the bearing rollers based on the actual working conditions. This provides support for the precision design of bearings in large shaft systems.