Elastic Loading Research Articles

Out-of-plane behaviour of imperfect beam-column with sinusoidally corrugated web

This paper presents an analytical formula for the second-order normal stresses in flanges of the imperfect I beam-columns with sinusoidal web corrugation. To deduce the analytical expression, the beam is separated into three parts. The flanges are modelled as thin-walled beam-columns and the corrugated web is modelled as a thin equivalent orthotropic plate with uniform thickness. The indispensable elastic critical loads are derived from the total potential strain energy of the imperfect beam-column using an energy method. To assess the accuracy of the proposed analytical formula, full shell finite element models were created in Abaqus software. The result of the benchmark example showed that the derived expression is accurate and applicable for geometrically nonlinear analysis of beam-columns with sinusoidal web corrugation. Based on the proposed analytical expression, the Ayrton-Perry type solutions for corrugated web columns and beams are also presented in this paper.

Prediction and design of mechanical properties of origami-inspired braces based on machine learning

In order to rapidly and accurately evaluate the mechanical properties of a novel origami-inspired tube structure with multiple parameter inputs, this study developed a method of designing origami-inspired braces based on machine learning models. Four geometric parameters, i.e., cross-sectional side length, plate thickness, crease weakening coefficient, and plane angles, were used to establish a mapping relationship with five mechanical parameters, including elastic stiffness, yield load, yield displacement, ultimate load, and ultimate displacement, all of which were calculated from load-displacement curves. Firstly, forward prediction models were trained and compared for single and multiple mechanical outputs. The parameter ranges were extended and refined to improve the predicted results by introducing the intrinsic mechanical relationships. Secondly, certain reverse prediction models were established to obtain the optimized design parameters. Finally, the design method of this study was verified in finite element methods. The design and analysis framework proposed in this study can be used to promote the application of other novel multi-parameter structures.

Novel hierarchical bioinspired cellular structures with enhanced energy absorption under uniaxial compression

Biological thin-walled cellular structures, such as hierarchical structures of bone, exhibit unique internal structures that offer lightweight characteristics and high energy absorption capabilities. The compact bone shell can protect against local damage during high-impact events, while the porous cancellous bone is essential in absorbing energy. This research proposed five novel bioinspired cellular structures inspired by the well-arranged structure of femur bones. These structures comprise four distinct cell types: hexagonal honeycomb, re-entrant, hybrid, and hierarchical hybrid cells. A comprehensive numerical model, validated with experimental data, was employed to assess the performance of these structures under uniaxial compression. Some key characteristics were revealed, including peak elastic load, plateau load, energy absorption capacity, Poisson's ratio, and the effect of hierarchical cell size. The results demonstrated that the novel bioinspired structures surpassed the energy absorption performance of traditional designs, such as hexagonal design, re-entrant, and trabecular-bone-inspired structures. This enhanced performance was due to the progressive buckling and collapse mechanisms, showing promising implications for future engineering applications, particularly where energy absorption is of paramount importance.

Local Instability and Deformation Control of Steel Roof of Factory Building in a Smart City

Abstract The traditional control methods of instability and deformation of steel structure neglect the analysis of its natural vibration characteristics, which lead to the poor effect of hysteretic vibration of steel structure nodes, and the stability optimization of steel structure is not ideal. Therefore, a new method to control the local instability and deformation of the steel roof is proposed. According to the steel structure composition of the upper door rigid frame and the connection mode of the frame beam and column, the roof steel structure characteristics of the workshop are analyzed. Multi-order natural frequency method is used to obtain the cumulative modal mass contribution rate of steel structure and analyze the natural vibration characteristics of steel structure. Based on the characteristics of natural vibration and element transfer matrix, the local instability control method of roof steel structure is designed. Simulation of strong vibration, using space analysis of tall-building with wall-elements (SATWE) software analysis of strong vibration under elastic load state, to obtain the external deformation of steel structure, under simulation of vibration deformation control model. Taking a chemical plant as an example, a finite element model was established to simulate the vibration wave, and the numerical simulation results of plastic deformation resistance of steel structure were analyzed. The experimental results show that the proposed method can effectively enhance the stability of steel structure and reduce its deformation degree.

Bending and Vibration Behaviour of CLT-Steel Composite Beams

A strengthening of cross-laminated timber (CLT) by a composite effect with steel girders can widen the application of CLT ceilings to spans over 8 m. Most possible shear connectors are not stiff enough to ensure a completely rigid composite. At present, it has not been sufficiently clarified how the elastic bending behaviour is affected by the influences of the flexibility of continuously and discontinuously shear connectors, the number of transverse layers of the CLT and the span width. Thus, 4-point bending tests and vibration tests were performed with different cross-section configurations and two different shear connectors in continuous and discontinuous spacing in spans of 8.10 and 10.80 m. To date, no comparable bending tests have been carried out in these spans, with more than five CLT-layers and discontinuously arranged shear connectors. The composite beams deformed linear-elastically until the yield strength of the steel was reached. The composite effect increased the elastic bending stiffness up to twofold compared to no composite. Increasing the span resulted in a higher bending stiffnesses. The elastic bending stiffness of the composite beams with shear studs was significantly lower than with fully threaded screws. For a worthwhile composite effect, both materials should contribute a balanced share of the stiffness. A larger share of the CLT in the bending stiffness compared to the steel girder created a higher elastic limit load capacity but an equivalent bending stiffness. It is necessary to discuss which cross-sectional configurations are appropriate in terms of load bearing capacity, economic efficiency and sustainability. To assess the practical application potential in spans between 8 and 12 m, the tests were additionally evaluated for the equivalent load level for the serviceability limit state of office or industrial buildings. For spans of 8.10 m, the limits according to EC5 for the initial deflection of L/300 and fundamental frequency of 8 Hz can be met. For spans of 10.80 m, only less strict deflection limits are achieved. However, by increasing the degree of composite through more shear connectors, compliance with the limit values mentioned could already be possible with the cross-sections tested. In case of fire, it may be sufficient to consider only the CLT with the reduced cross-section method (EN 1995-1-2) for load transfer, even for longer fire durations.

Elastic programmable properties and dynamic dissipation of gradient unstable structures

Metamaterials derive promising properties mainly from an internal micromechanical mechanism, rather than their chemical composition. Many interesting mechanical behaviors can be obtained by orderly assembling buckling elements. Elastic programmable properties, corresponding potential energy landscape and dynamic dissipation mechanism of elastic beam structures are studied in detail. To accomplish this work, a combination of theoretical models and extensive numerical calculations are applied to investigate a single element as well as homogeneous and gradient structures. This comprehensive investigation not only provides insights into the complex internal buckling behaviors and mechanisms of a specific unstable structure but also establishes conclusions that are applicable to other unstable structures having similar buckling behaviors. The potential energy of a serial combination of unstable elements is extremely wiggly, enabling multiple equilibrium configurations and resulting in multistable transformations and energy dissipation with elastic deformation and loading timescale independence. To the best of our knowledge, the most of programming properties investigated in this paper, the complex energy landscape, the deformation of internal elements, and programmable dynamic responses of gradient unstable structures have not been reported in previous papers.

A swarm-intelligent based load-shifting strategy for clean and economic microgrid operation

The required load in a typical microgrid structure fluctuates from hour to hour. Based on the peaks and troughs of the load demand curve, the power system utilities preset different price of electricity at various periods of the same day which is referred to as time-of-use (TOU) pricing policy. An optimal economic strategy called demand side management (DSM) reduces load during peak hours by shifting the elastic loads and compensates the shifted load by increasing the demand during valley hours. This recreates the total demand pattern on the demand price elasticity relation. The novel benefaction of this research suggests a DSM approach based on a hybrid intelligence technique to attain a compromised solution between minimum generation costs and pollutants emitted by DERs of an LV grid-connected microgrid system. Several grid involvement strategies, power market pricing types, and demand response mechanisms are examined in five separate instances for the microgrid system. The outcomes achieved in each example show that the recommended DSM technique may be applied and is appropriate in terms of cost reduction. When 30–40% of customers participated in the DSM curriculum, the generation cost was reduced by 10–13%. Environment constrained economic dispatch provided a superior compromise amongst lowest generation cost and emission for different microgrid load models. Statistical analysis and comparison of the results from previously published literatures validates the superiority of the proposed approach incorporated with DSM policy.

A pilot study: effect of somatosensory loss on motor corrections in response to unknown loads in a reaching task by chronic stroke survivors.

Despite recent studies indicating a significant correlation between somatosensory deficits and rehabilitation outcomes, how prevailing somatosensory deficits affect stroke survivors' ability to correct their movements and recover overall remains unclear. To explore how major deficits in somatosensory systems impede stroke survivors' motor correction to various external loads, we conducted a study with 13 chronic stroke survivors who had hemiparesis. An inertial, elastic, or viscous load, which was designed to impose perturbing forces with various force profiles, was introduced unexpectedly during the reaching task using a programmable haptic robot. Participants' proprioception and cutaneous sensation were also assessed using passive movement detection, finger-to-nose, mirror, repositioning, and Weinstein pressure tests. These measures were then analyzed to determine whether the somatosensory measures significantly correlated with the estimated reaching performance parameters, such as initial directional error, positional deviation, velocity deviations, and speed of motor correction were measured.Of 13 participants, 5 had impaired proprioception, as they could not recognize the passive movement of their elbow joint, and they kept showing larger initial directional errors even after the familiarization block. Such continuously found inaccurate initial movement direction might be correlated with the inability to develop the spatial body map especially for calculating the initial joint torques when starting the reaching movement. Regardless of whether proprioception was impaired or not, all participants could show the stabilized, constant reaching movement trajectories. This highlights the role of proprioception especially in the execution of a planned movement at the early stage of reaching movement.

Analysis of Lateral Forces for Assessment of Safety against Derailment of the Specialized Train Composition for the Transportation of Long Rails

This study proposes a theoretical method for evaluating the “safety against derailment” indicator of a specialized train composition for the transportation of very long rails. A composition of nine wagons, suitable for the transportation of rails with a length of 120 m in three layers, is considered. For the remaining recommended rail lengths, the number of wagons is reduced or increased, with the calculation model being modified depending on the required configuration. When the composition is in a curve with the minimum radius (R = 150 m), the rails bend, and some of them come into contact with the vertical stanchions of the wagon and cause additional lateral forces. These forces are then transferred through the wagon body, central pivot, bogie frame, and wheels and act on the wheel–rail contact points. They could potentially lead to derailment of the train composition. The goal of this study is to determine the additional lateral forces that arise because of the bent rails. For the purposes of this study, the finite element method was used. Based on the displacements of the support points of the rails (caused by the geometry of the curve), the bending line of the elastic load is determined and the forces in the supports are calculated. The resulting forces are considered when determining the derailment safety criterion. The analysis of the results shows that the wagon with fixing blocks is the most at risk of derailment. The front and intermediate wagons have criterion values very close to that of the empty wagon. This shows that the emerging horizontal elastic forces do not significantly influence the derailment process. The obtained results show that the transportation of long rails with specialized train composition can be realized on four layers. This will significantly increase the efficiency of delivering new long rails.

Numerical Point Contact Model of Mixed Elastohydrodynamic Lubrication for Transversely Isotropic Coating

Abstract Transverse isotropy, a typical property of coating providing protection or lubrication for transmission parts, is different from isotropy focused in most of previous research, catching increasing attention in recent years. This study aims to make the lubricating contact behavior of transversely isotropic coating under different working conditions better understood, with the assistance of a proposed mixed elastohydrodynamic lubrication (EHL) model for a rigid ball in contact with transversely isotropic coating. Explicit analytical expressions of frequency response functions (FRFs) of the elastic field for transversely isotropic coating were derived, which could be used to work out surface/subsurface displacement and stress if surface pressure is known. The proposed EHL model for transversely isotropic coating was verified by comparing the film thickness and pressure distribution with those from literature by an uncoated model. Furthermore, the effects of coating elastic property, coating thickness, velocity, and load on lubrication performance and mechanical responses are investigated. In addition, the results under different coating parameters are also compared and discussed with those obtained by the Hamrock–Dowson equations to demonstrate the effectiveness of the latter. This investigation may provide a potential application for coating optimal design considering lubrication.

Microstructured silk fiber scaffolds with enhanced stretchability.

Despite extensive research, current methods for creating three-dimensional (3D) silk fibroin (SF) scaffolds lack control over molecular rearrangement, particularly in the formation of β-sheet nanocrystals that severely embrittle SF, as well as hierarchical fiber organization at both micro- and macroscale. Here, we introduce a fabrication process based on electrowriting of aqueous SF solutions followed by post-processing using an aqueous solution of sodium dihydrogen phosphate (NaH2PO4). This approach enables gelation of SF chains via controlled β-sheet formation and partial conservation of compliant random coil structures. Moreover, this process allows for precise architecture control in microfiber scaffolds, enabling the creation of 3D flat and tubular macro-geometries with square-based and crosshatch microarchitectures, featuring inter-fiber distances of 400 μm and ∼97% open porosity. Remarkably, the crosslinked printed structures demonstrated a balanced coexistence of β-sheet and random coil conformations, which is uncommon for organic solvent-based crosslinking methods. This synergy of printing and post-processing yielded stable scaffolds with high compliance (modulus = 0.5-15 MPa) and the ability to support elastic cyclic loading up to 20% deformation. Furthermore, the printed constructs supported in vitro adherence and growth of human renal epithelial and endothelial cells with viability above 95%. These cells formed homogeneous monolayers that aligned with the fiber direction and deposited type-IV collagen as a specific marker of healthy extracellular matrix, indicating that both cell types attach, proliferate, and organize their own microenvironment within the SF scaffolds. These findings represent a significant development in fabricating organized stable SF scaffolds with unique microfiber structures and mechanical and biological properties that make them highly promising for tissue engineering applications.

A mathematica code for evaluating lateral-torsional buckling of tapered cantilevers

Lateral-torsional buckling (LTB) is the primary failure mode where slender cantilevers experience nonuniform twisting and buckling about their weak axes. The studies focused on the elastic LTB load of cantilevers are limited, most of which are numerical since the LTB failure mode of cantilevers is much more complicated than those of simply supported beams. Furthermore, there are only a few studies of the LTB of tapered I-section cantilevers, which are aesthetic and structurally efficient. Structural designers tend to evaluate the LTB of tapered cantilevers using finite element simulations, but it requires specific experience and computational effort. The present study intends to close the gap in the literature related to tapered cantilevers, establish an analytical procedure providing rapid treatment, and develop a code for the solution. The analytical model considers first-order moment gradient through the cantilever, load position along the cross-section, mono-symmetry property of I-section, tapering of web, flange, or simultaneously web and flange to assess LTB of tapered cantilevers. The developed Mathematica code based on the analytical model has been verified with 3D finite element analysis, and it is demonstrated that the proposed code can be safely used to assess the LTB of tapered cantilevers.

Elastic Resistance and Shoulder Movement Patterns: An Analysis of Reaching Tasks Based on Proprioception.

This study departs from the conventional research on horizontal plane reach movements by examining human motor control strategies in vertical plane elastic load reach movements conducted without visual feedback. Here, participants performed shoulder presses with elastic resistances at low, moderate, and high intensities without access to visual information about their hand position, relying exclusively on proprioceptive feedback and synchronizing their movements with a metronome set at a 3 s interval. The results revealed consistent performance symmetry across different intensities in terms of the reach speed (p = 0.254-0.736), return speed (p = 0.205-0.882), and movement distance (p = 0.480-0.919). This discovery underscores the human capacity to uphold bilateral symmetry in movement execution when relying solely on proprioception. Furthermore, this study observed an asymmetric velocity profile where the reach duration remained consistent irrespective of the load (1.15 s), whereas the return duration increased with higher loads (1.39 s-1.45 s). These findings suggest that, in the absence of visual feedback, the asymmetric velocity profile does not result from the execution of the action but rather represents a deliberate deceleration post-reach aimed at achieving the target position as generated by the brain's internal model. These findings hold significant implications for interpreting rehabilitation approaches under settings devoid of visual feedback.

On the evaluation of lateral-torsional buckling of web-tapered cantilevers with doubly symmetric I-section

Recently, structural engineers have tended to design stronger and lighter structures due to economic reasons, technical developments in computer-aided design, and improvements in manufacturing. The demand for designing stronger and lighter structures has led to the compulsory considering structural efficiency and stability loss at the design level. Lateral-torsional buckling (LTB) is a major stability loss for web-tapered cantilevers with doubly symmetric I-section, which are aesthetic and structurally efficient. The elastic LTB loads of these cantilevers should be calculated at the design level since the LTB may happen before bending stress reaches yield. Studies related to the LTB of cantilevers are rare and require numerical solutions since the LTB mode shape of cantilevers is complex compared to simply supported beams. The present study introduces an analytical procedure based on the energy method for calculating elastic LTB of web-tapered cantilevers with doubly-symmetric I-section in two different forms. The analytical model considers different transverse load types, positions of loads, and web tapering degrees. The analytical solutions were validated with one-dimensional finite element analysis using a beam element. Excellent accordance between results was demonstrated. The general LTB behavior of web-tapered cantilevers with doubly symmetric I-section was clarified with detailed comments based on results obtained from the presented analytical model.

Resilience enhancement of distribution networks based on demand response under extreme scenarios

AbstractIn the context of rare but high‐impact extreme scenarios, such as natural disasters, it is crucial to utilize all available resources, including microgrids and distributed power sources, to restore critical loads in the distribution network as much as possible. This paper proposes a two‐stage resilience enhancement strategy for distribution networks considering post‐disaster topology reconstruction and demand response, aiming to facilitate the recovery of critical loads after disasters. In the first stage, a heuristic algorithm is introduced to determine the post‐disaster topology of the distribution network. In the second stage, by employing a step‐wise elastic load curve, user demand response is incorporated to maximize the socio‐economic value of the restoration, and resilience metrics are computed. Finally, the effectiveness of the proposed resilience restoration strategy is validated through simulations on Case33 and Case69 systems.

2d Models of Steel Beams under Patch Loading for Buckling Coefficient Assessment

This paper proposes an equivalent 2d model incorporating translational and rotational springs to simulate constraints in the stability analysis of steel plates under in-plane patch loading. The main objective is to develop an equivalent stability analysis of these plates by accurately calibrating the level of constraint provided by the stiffeners and flanges. The calibration involves determining the spring constants of a 2d equivalent plate model to achieve the same linear elastic critical load and buckled shape as a 3d model. The paper uses the buckling coefficient as the objective function to calibrate the translational and rotational springs. The ultimate goal is to effectively replicate the constraint conditions imposed by the flanges and vertical stiffeners within the structure. The proposed simplified method yields results that closely align with those obtained from the original 3d model, incorporating finite-rigidity restraints.

Lithospheric strength of the Anatolian plateau and implications for strong earthquake activity in Turkey

On February 6, 2023, the doublet earthquake including two main shocks with magnitudes MW7.8 and MW7.5, occurred near the western side of the East Anatolian Fault at the southeast boundary of the Anatolian Plateau in Turkey. Based on the WGM2012 Bouguer gravity anomaly data and the Etopo1 topography data, this study first introduced a joint inversion of admittance and coherence functions and used the Bayesian optimal parameter estimation method to obtain the effective elastic thickness Te and loading ratio F of the lithosphere for various tectonic units in the Anatolian Plateau. Secondly, we discussed the characteristics and influencing factors of the lithospheric mechanical strength and analyzed its relationship with seismic activity. The lithospheric mechanical strength of the Anatolian Plateau showed clear lateral heterogeneity and a "weak-strong-weak" spatial pattern from east to west, reflecting various tectonic processes. At last, the strong seismic activity was found where the lithospheric strength was low in the Anatolian Plate. We also incorporated GPS strain rate and other results to investigate the tectonic background and primary causes of the MW7.8 and MW7.5 doublet earthquakes in Turkey. The results have a good insight into urban safety design in the Turkish region, including post-disaster rehabilitation, earthquake hazard assessment, and loss reduction.

Impacts of artificial dams on terrestrial water storage changes and the Earth's elastic load response during 1950–2016: A case study of medium and large reservoirs in Chinese mainland

The construction of dams for intercepting and storing water has altered surface water distributions, land-sea water exchanges, and the load response of the solid Earth. The lack of accurate estimation of reservoir properties through the land surface and hydrological models can lead to water storage simulation and extraction errors. This impact is particularly evident in many artificial reservoirs in China. The study aims to comprehensively assess the spatiotemporal distribution and trends of water storage in medium and large reservoirs (MLRs) in Chinese mainland during 1950–2016, and to investigate the gravity, displacement, and strain effects induced by the reservoir mass concentration using the load elasticity theory. In addition, the impoundment contributions of MLRs to the relative sea level changes were assessed using a sea-level equation. The results show impoundment increases in the MLRs during 1950–2016, particularly in the Yangtze River (Changjiang) and southern basins, causing significant elastic load effects in the surrounding areas of the reservoirs and increasing the relative sea level in China's offshore. However, long-term groundwater estimation trends are overestimated and underestimated in the Yangtze River and southwestern basins, respectively, due to the neglect of the MLRs impacts or the uncertainty of the hydrological model's output (e.g., soil moisture, etc.). The construction of MLRs may reduce the water mass input from land to the ocean, thus slowing global sea level rise. The results of the impact of human activities on the regional water cycle provide important references and data support for improving the integration of hydrological models, evaluating Earth's viscoelastic responses under long-term reservoir storage, enhancing in-situ and satellite geodetic measurements, and identifying the main factors driving sea level changes.

Asymptotic numerical method for cyclic elasto-plasticity and its application to a steam turbine rotor

Flexible operation of the conventional power plants is necessary for the integration of renewables in the energy mix. Steam turbine rotors are one of the most affected components due to the daily thermal load cycling requirements. In order to accurately study the effect of cycling on fatigue, it is necessary to solve cyclic 3D elasto-plasticity problems for a large number of cycles. The established methods are iterative in nature to arrive at the current yield surface for each elasto-plastic step and are computationally extensive. In this paper, we propose the non-iterative Asymptotic Numerical Method (ANM) based solution technique for 3D cyclic elasto-plasticity problems for the first time by a novel regularized Kuhn-Tucker condition. Regularization techniques used in previous works take care of the partial cycle only, i.e., elastic loading, elastic-plastic transition, elasto-plastic flow and elastic unloading for simple linear work hardening models of plasticity. In the present work, the proposed method extends the applicability of ANM by incorporating elastic-plastic transition and elasto-plasticity in reverse loading, second unloading and repeated loading for any number of cycles so that the computationally efficient fatigue analysis can be carried out. In addition, the extension also includes the application of ANM to non-linear kinematic hardening through the Chaboche plasticity model combined with isotropic hardening. For these advancements, additional regularizations are proposed and implemented in a Finite Element Code. The obtained results are then compared to the solutions obtained from the conventional Newton Raphson (NR) solution technique. The proposed ANM is applied to a steam turbine rotor undergoing a typical thermal load cycling and the cyclic elasto-plastic response is compared with that obtained using the conventional Newton Raphson solution technique.

Analytical model for thermo-mechanical interaction induced residual stress distribution during multi-conditional machining Inconel 718

Residual stress induced by coupling thermo-mechanical fields cannot be completely released and remains inside the workpiece after the cutting process, which has a significant impact on the fatigue resistance, corrosion resistance and deflection of manufacturing parts. This work focused on an analytical model for thermo-mechanical fields induced residual stress distribution during multi-conditional machining superalloy Inconel 718. Based on the relationships of material properties, cutting parameters, and cutting geometric conditions, the proposed analytical model investigated the thermo-mechanical fields based on the semi-infinite space elastic mechanical line load and the uneven film thermal stress distribution under the action of moving heat sources. The development process of residual stress was examined through the changes in the stress release process from loading to unloading based on the in-plane stress assumption solution. The effects of basic cutting variables including cutting speeds, uncut chip thickness and tool wear on the thermo-mechanical fields were discussed. According to the experimental and predicted results, the residual stress distribution characteristics were evaluated including surface residual stress, reverse peak stresses, transition position, and total influence depth, indicating that the proposed analytical model could obtain the residual stress distribution characteristics with the predicted error of approximately 4.3%–11.9%, 3.9%–73.4%, 4%–33.3%, and 3.3%–25.7%, respectively. This work can provide significant theoretical support for the analysis of the residual stress generation to control surface integrity during the cutting process.