Theoretical Stiffness Research Articles

Target‐drift seismic‐force‐based design of one‐story reinforced concrete precast buildings considering the requirements of the second generation of the Eurocode 8 standard

AbstractResults are presented concerning the force‐based design of a wide range of reinforced concrete, single‐story precast buildings, considering the requirements of the new Eurocode 8 standard. The relevant criterion defining the cross‐sectional dimensions of the columns was the 2% drift limitation. Buildings were designed considering a behavior factor of 3 and a 50% reduction in stiffness corresponding to the gross cross‐section. The design evaluation, using a nonlinear pushover analysis, revealed that all the buildings could expect approximately twice the drift considered in the design with significant second‐order effects, particularly in very tall columns. The main reasons for large discrepancies between the elastic and nonlinear analyses were the arbitrarily selected behavior factor and the arbitrarily selected reduction in stiffness corresponding to the gross cross‐section (the stiffness considered in the design was approximately double what the nonlinear analysis revealed). The analysis revealed that these two quantities are closely correlated. Once the dimensions of the columns had been selected, the force and initial stiffness reduction could not be chosen arbitrarily. Correlations were determined between the column dimensions, theoretical stiffness reduction, seismic force reduction (behavior factor) and second‐order effects. From these correlations, a new target‐drift force‐based design methodology was proposed. All considered buildings were redesigned using the proposed method. The results of the new design and the nonlinear‐pushover‐based analysis correlated well.

Failure mode maps for glass fibre-reinforced polymer/polyvinyl chloride foam-cored sandwich structures

Purpose This study aims to understand how the facesheet size, orientation and core size influence the analytical failure mechanism mode of glass fibre reinforced polymer (GFRP)/polyvinyl chloride (PVC) sandwich structures subjected to three-point bending. The purpose of this study was to develop failure-mode map of GFRP/PVC sandwich structures. Sandwich structures with different facesheet and core thicknesses were used to develop the failure map. Design/methodology/approach The sandwich structure and facesheet were fabricated using a vacuum-assisted resin infusion method with core sizes of 10, 15 and 20 mm and facesheet thicknesses of 1.5 and 3 mm and were arranged in three different orientations: angle-ply, cross-ply and quasi-isotropic. The key failure modes that occur in sandwich structures were used to predict possible failures in the developed material. Analytical equations were used in MATLAB for each observed failure mode. The probable failure modes, namely, face yielding, core shear and indentation equations, were used to construct the failure maps and were compared with the experimental data. Findings The boundary of the two failure modes shifts with changes in the facesheet and core thicknesses. The theoretical stiffness of sandwich panels was higher than the experimental stiffness. Based on strength-to-weight ratio, specimens E10-4, A15-8 and E20-8 exhibited the best optimum values owing to their shorter distance to the boundary lines. Originality/value In this study, a failure map was used to predict the possible failure modes for different GFRP facesheet orientations and thicknesses and PVC core thickness sandwich structures. Little is known about the prediction of the failure modes of unidirectional GFRP arranged in different orientations and thicknesses and PVC core thicknesses for sandwich structures. Few studies have used failure mode maps with unidirectional GFRP oriented in angle-ply, cross-ply and quasi-isotropic directions as a facesheet for sandwich structures compared to bidirectional mats. This study can serve as a guide for the correct selection of materials during the design process of sandwich structures.

Static and dynamic load test on concrete hollow-core slab bridge

In this paper, dynamic and static load test were carried out on a multi-span reinforced concrete simply supported hollow core slab bridge in Shenyang, Liaoning Province. Through the static load test, the quality and reliability of the project are evaluated, and the results show that under the action of 0.88 times of highway-classⅠload, the deflection and strain check coefficients of the control section of the tested condition are less than 1, which meets the specification requirements, and the measured relative residual deformation and relative residual strain are less than 20%, and the bridge structure is basically in the elastic working state. And combined with the finite element analysis model, the comparison between measured data and calculated data is carried out. Through the dynamic load test, the self-oscillation frequency and damping ratio of the superstructure were tested, and the results showed that the measured damping ratio was 0.690%, the first-order measured vibration pattern conformed to the variation rule of the vibration pattern of the simply supported girder bridge, and the measured self-oscillation frequency was 13.594 Hz, and the measured self-oscillation frequency (fundamental frequency) was greater than the calculated frequency, and the structural actual stiffness was greater than the theoretical stiffness, and the working condition was good. This study is of great significance for the assessment of bearing capacity and quality control of concrete hollow core slab bridge, and provides a useful reference for bridge design and operation.

Study on the Vibration Characteristics of the Helical Gear-Rotor-Bearing Coupling System of a Wind Turbine with Composite Faults

As the core component of the wind turbine generation gearbox, the gear-rotor-bearing transmission system typically operates in harsh environments, inevitably leading to the occurrence of composite faults in the system, which exacerbates system vibration. Therefore, it is necessary to study the vibration characteristics of wind turbine helical gear-rotor-bearing transmission systems with composite faults. This paper uses an improved energy method to calculate the theoretical time-varying mesh stiffness of a helical gear with a root crack failure. On the premise of considering the time-varying meshing stiffness of the faulty helical gear, the gear eccentric fault, and the nonlinear support force of the faulty bearing, a multi-degree-of-freedom helical gear-rotor-bearing transmission system with compound faults was established by using the lumped parameter method. The dynamic model of the system was solved based on the Runge–Kutta method, and the vibration response of the system under healthy conditions, single faults with gear eccentricity, single faults with tooth root cracks, and coupled bearing composite faults were simulated and analyzed. The results show that the simulation results based on KISSsoft software 2018 version verify the effectiveness of the improved energy method; the existence of single faults and composite faults will cause the fault characteristics in the time domain and frequency domain responses. In this paper, the influence of a single fault and a complex fault on the time domain and frequency domain of the system is mainly discovered through the fault study of the helical rotor-bearing system, and the influence of the fault degree on the vibration of the gear motion system is discussed. The greater the degree of the fault, the more vibration of the system occurs; accordingly, when the system is under the coupling of tooth root crack and bearing fault, there is a significant difference compared with the healthy system and the single fault system. The system vibration has obvious time domain and frequency domain signal characteristics, including periodic pulse impacts caused by gear faults and time domain impact caused by bearing. The fault characteristic frequencies can also be found in the frequency domain. In this paper, the fault study of a helical gear of wind turbine generation provides a reference for the theoretical analysis of the vibration characteristics of the helical gear-rotor-bearing system under various fault conditions, lays a solid foundation for the simulation and subsequent diagnosis of the composite fault signal of the system, and provides help for the fault diagnosis of wind turbine gearboxes in the future.

Seismic performance verification and theoretical stiffness calculation for a novel assembled concrete dry-connected beam-column node

This paper proposes a novel assembled concrete dry-connected beam-column node, which consists of a precast concrete beam with steel haunch plates at the end and a precast concrete column connected by ordinary strength long bolts. The quasi-static test study and finite element numerical simulation of the node are used to analyze the hysteresis curve, skeleton curve, and other performance indexes and investigate mechanical properties under low-cycle reciprocating load. The results demonstrate that the overall stress performance of the column specimen is outstanding; the specimen node possesses large deformation and good ductility, presenting semi-rigid characteristics; the damage of the specimen mainly includes the bending deformation of the connecting bolts. By analyzing the damage and force mechanisms of the node, an "equivalence method" for the initial rotational stiffness calculation of the beam-column combination node is established. Moreover, the formula for calculating the stiffness of this semi-rigid node is deduced.

The contribution of lower-limb joint quasi-stiffness to theoretical leg stiffness during level, uphill and downhill running at different speeds.

Humans change joint quasi-stiffness (k joint) and leg stiffness (kleg) when running at different speeds on level ground and during uphill and downhill running. These mechanical properties can inform device designs for running such as footwear, exoskeletons and prostheses. We measured kinetics and kinematics from 17 runners (10 M; 7 F) at three speeds on 0°, ±2°, ±4° and ±6° slopes. We calculated ankle and knee k joint, the quotient of change in joint moment and angular displacement, and theoretical leg stiffness (klegT) based on the joint external moment arms and k joint. Runners increased k ankle at faster speeds (p < 0.01). Runners increased and decreased the ankle and knee contributions to klegT, respectively, by 2.89% per 1° steeper uphill slope (p < 0.01) during the first half of stance. Runners decreased and increased ankle and knee joint contributions to klegT, respectively, by 3.68% during the first half and 0.86% during the second half of stance per 1° steeper downhill slope (p < 0.01). Thus, biomimetic devices require stiffer k ankle for faster speeds, and greater ankle contributions and greater knee contributions to klegT during the first half of stance for steeper uphill and downhill slopes, respectively.

Design and analysis of parallel six-dimensional force sensor based on near-singular characteristics

The high sensitivity six-dimensional force sensor is the core component of intelligent robot force feedback perception, which is related to the structure of the sensor. This paper proposes a new modeling method to chain the near singular eight-branch Stewart mechanism, which indicates the relationship between structural parameters and sensitivity. The new method gains 16 new configurations by innovating the traditional Stewart institution. A configuration with high sensitivity in Fz, Mx and My directions is selected for further study. The theoretical stiffness model and force mapping model show that the sensitivity of the new structure can be amplified by 4 times in specific degrees of freedom. The results show that the nonlinear error and coupling error are 2.77% and 2.26%, respectively. The proposed method can be widely applied in the field of parallel six-dimensional force sensors.

Development and Investigation of the Hysteretic Behavior of an X-Shaped Metal Damper with an Oblique Angle

To investigate the hysteretic behavior of an X-shaped metal damper (XMD) with an oblique angle, cyclic loading tests were carried out on nine specimens, including two XMDs without buckling-restrained devices, four XMDs with stiffening ribs, and three XMDs with cover plates as references. The test results showed that the oblique angle could effectively increase the stiffness, strength, and energy dissipation of the XMD. When the oblique angle of an XMD with stiffening ribs increased from 0° to 30° at the applied displacement of 8.4 mm, the mean strengths and cumulative energy dissipation of specimens increased by about 80.77% and 80.57%, respectively. Although asymmetric hysteretic loops were also observed in specimens with an oblique angle and buckling-restrained devices, stable hysteretic curves were obtained. This indicated that the stiffening ribs and cover plates can effectively constrain the buckling behavior of XMDs. Additionally, the mean strengths of specimens with stiffening ribs were a little higher than those of specimens with cover plates. Subsequently, the finite element analysis models of the XMDs were proposed, in which the metal plasticity model considering isotropic and kinematical hardening was used to model the material properties of steel, and the simulation results matched well with the test results. Finally, the theoretical calculation method was proposed to predict the elastic stiffness of specimens, and the theoretical elastic stiffness matched well with the test results.

Optimal Design of Nonlinear Negative-Stiffness Damper with Flexible Support for Mitigating Cable Vibration

Negative-stiffness damper is a promising device to mitigate cable vibrations effectively. In contrast to traditional rigid supports, recent study has found that flexible supports are actually beneficial for enhancing the performance of negative-stiffness dampers. This study extends the understanding of the impact of support flexibility under nonlinear condition, followed by an optimization process to obtain required negative-stiffness dampers and corresponding supports. First, taking damping nonlinearity into account, a unified model is established for the negative-stiffness damper with flexible support. Theoretical equivalent negative stiffness and damping are obtained for a linear case, followed by numerical verification. Thereafter, equivalent parameters under a friction case are presented. Experiments are conducted to validate the analytical derivation. Then, problem formulation is developed for the controlled cable. Optimization process is proposed to determine the required negative-stiffness damper and support for multimodal cable vibration. A series of numerical simulations are performed to demonstrate the design process. Moreover, nonlinear examples are presented to show the potential for improving control performance. As indicated by the research results, a flexible support is capable of amplifying the equivalent negative stiffness and damping under linear and nonlinear conditions. For multimodal cable vibration, it is sufficient to determine the optimized negative stiffness and support by only considering the highest mode. Nonlinear negative-stiffness dampers exhibit superior performance due to the leakage of vibration energy toward high-order modes.

ANALYSIS OF FINGER-JOINTS IN GLASS FIBER-REINFORCED POLYMER (GFRP) COMPOSITE GLUED LAMINATED TIMBER BEAMS

The objective of this paper was to evaluate the effect of finger-joint reinforcement on thebending strength and stiffness of glulam beams made from high-density Eucalyptus spp. glued with resorcinol-formaldehyde adhesive.Six glulam beams were tested: three reinforced with glass fiber-reinforced polymer(GFRP) and three unreinforced for comparison. The GFRP was placed between the last two laminatesand at the bottom edge of theglulam only in the finger-joint position. The stiffness and strength of glulam beams were evaluated using static bending tests, which showed that the use of GFRP reinforcement resulted in a gain of more than 100% in average ultimate bending moment and about 10% in average bending stiffness. Tocalculate the theoretical bending stiffness and normal stresses, a theoretical analysis of beam bending was performed using the transformed section method, which showed agreement with the experimental results.

Modeling Contact Stiffness of Soft Fingertips for Grasping Applications.

Soft fingertips have distinct intrinsic features that allow robotic hands to offer adjustable and manageable stiffness for grasping. The stability of the grasp is determined by the contact stiffness between the soft fingertip and the object. Within this work, we proposed a line vector representation method based on the Winkler Model and investigated the contact stiffness between soft fingertips and objects to achieve control over the gripping force and fingertip displacement of the gripper without the need for sensors integrated in the fingertip. First, we derived the stiffness matrix of the soft fingertip, analyzed the contact stiffness, and constructed the global stiffness matrix; then, we established the grasp stiffness matrix based on the contact stiffness model, allowing for the analysis and evaluation of the soft fingertip's manipulating process. Finally, our experiment demonstrated that the variation in object orientation caused by external forces can indicate the contact force status between the fingertip and the object. This contact force status is determined by the contact stiffness. The position error between the theoretical work and tested data was less than 9%, and the angle error was less than 5.58%. The comparison between the theoretical contact stiffness and the experimental results at the interface indicate that the present model for the contact stiffness is appropriate and the theoretical contact stiffness is consistent with the experiment data.

Novel metamaterial structures with negative thermal expansion and tunable mechanical properties

The thermal expansion and stiffness characteristics are significant in determining the responses of lightweight mechanical metamaterials in a thermal environment. This paper proposed a novel trapezoid unit with negative thermal expansion (NTE) by three conventional materials with positive thermal expansion, and constructed a series of lightweight metamaterials by sharing edges and sharing vertexes. The effective linear coefficients of thermal expansion (CTE) of these metamaterial structures are theoretically explored by considering axial and bending deformations. Based on Euler beam theory, the effective linear elastic stiffnesses of these metamaterials are given accurately by the stiffness matrix method. The accuracy of the theoretical effective CTE and stiffness is well verified by numerical modeling. The effective linear CTE, elastic stiffness, and Poisson's ratio of these metamaterials can be programmable by controlling geometrical parameters and material properties. The NTE effect can be achieved in ET, EQ, EH, and VT metamaterials due to the presence of re-entrant structures, in which the ET metamaterial can fulfill the maximum magnitude NTE. The NTE and negative Poisson's ratio can simultaneously be realized in EQ metamaterial. Significantly, a broader range of CTE from negative to positive values can be fulfilled in these metamaterials compared with the conventional triangle unit. Furthermore, the high specific stiffness with extremely low thermal stress can be obtained in EQ, VT, and VH metamaterials, which benefits the stability controlling and enhancing natural frequencies of structures in a thermal environment.

A Large Force Haptic Interface with Modular Linear Actuators

This paper presents a haptic interface with modular linear actuators that addresses the limitations of conventional devices based on rotary joints. The proposed haptic interface is composed of parallel linear actuators that provide high backdrivability and small inertia. The performance of the haptic interface is compared to those of conventional mechanisms in terms of force capability, reflected inertia, and structural stiffness. High stiffness, large range of motion, and high force capability, which are in trade-off relationships in traditional haptic interfaces, are achieved. The device can apply up to 83 N continuously, i.e., three-fold more than most haptic devices. The theoretical minimum haptic force density and stiffness of the proposed mechanism are 1.3 to 1.9 and 37 times those of the conventional mechanisms under similar conditions, respectively. The system is scalable because the structural stiffness depends on only the timing belt stiffness, whereas that of conventional haptic interfaces is inversely proportional to the cube of the structural length. The modular actuator enables changes in the degrees of freedom (DOFs) for different applications. The proposed haptic interface was tested through an interaction experiment in a virtual environment with virtual walls.

Theoretical Stiffness Modeling and Application Research of a Novel Stacked Flexure Hinge

This study investigates and designs a novel stacked hinge with low stiffness, large rotation angle, high strength, and length-adaptive functionality. Firstly, based on the large deformation theory of cantilever beams and relevant theories of leaf springs, a stiffness theoretical model for stacked flexure hinges is established. Subsequently, the stiffness theoretical model is further modified by considering the frictional force, aiming to reduce errors. Secondly, a stiffness-testing experimental platform for this flexure hinge is designed to verify the correctness of the theoretical model. Finally, the stacked flexure hinge is applied to the trailing-edge mechanism of a variable camber wing, achieving a deformation target of 15° downward bending of the wing and demonstrating good shape retention, thereby proving the feasibility of the application.

Short Jute Fiber Preform Reinforced Polypropylene Thermoplastic Composite: Experimental Investigation and Its Theoretical Stiffness Prediction.

Natural-based lignocellulose fibrous materials can be used as a sustainable alternative to conventional fossil-based fibers such as glass fibers, in lightweight fiber-reinforced thermoplastic composites for marine, automotive, aerospace, or other advanced applications. However, one of the main challenges in using natural fiber-based thermoplastic composites is the low mechanical performance of composite structures. This can be improved significantly through the development of an optimized novel fiber architecture with enhanced fiber packing properties, following a low-cost production process. In this context, this study demonstrates a less energy-consuming and cheaper manufacturing process, for developing highly individualized short jute fiber-based dry fiber preform architecture, with an improved fiber packing property. Short jute fibers were chemically treated with alkali and PVA sizing treatments in the processing of new fiber preform architectures, and they were used in manufacturing of ultimate short jute fiber/polypropylene (PP) thermoplastic composites. The newly developed short fiber thermoplastic composites showed a significant improvement in mechanical properties (tensile, flexural, and impact) compared to any other natural fiber architecture-based (woven, knitted, nonwoven, unidirectional, etc.) composites found in the literature. Due to the use of new fiber architecture, the developed composites' fiber content was observed to increase. In addition, the compatibility of jute fibers with the polypropylene matrix was strengthened with the application of chemical treatments on highly individualized jute fibers. These reasons were responsible for the enhancement of mechanical properties of developed composites. Micromechanics of the fibers in composites were evaluated using the modified rule of the mixture and Halpin-Tsai equations for stiffness prediction of the composites in order to develop a theoretical understanding of newly developed composites' mechanics. It is thought that the improved mechanical performance of short jute fiber/PP thermoplastic composites can extend the use of these composites in many load-demanding applications, wherein normally synthetic fiber composites are used.

Elastic stiffness and bearing mechanism of eccentrically braced steel frames

Eccentrically braced steel frames have great ductility and energy dissipation, but their elastic stiffness is influenced by the length of the braces. The stiffness of these frames is important for computing story drifts and link rotations, which have prescribed limits. The yield and ultimate bearing capacity of eccentrically braced steel frames can be predicted by analyzing their individual components. This paper proposes a method to calculate the elastic stiffness and bearing capacity of K-type, D-type, and V-type eccentrically braced steel frames. To calculate the elastic stiffness of these frames, the displacement of a story can be obtained by summing the deformations of the individual components. The link shear and brace axial force of a story are also considered using structural mechanics. This allows for estimating the elastic stiffness of eccentrically braced steel frames in the early design phase. Based on the virtual work principle and the ideal failure mode of these frames, the yield and ultimate bearing capacity of eccentrically braced steel frames are proposed using frame drift angle and verified by experimental results. The theoretical stiffness of these frames is compared with finite element models. The finite element analysis and experimental results show that the elastic stiffness, yield bearing, and ultimate bearing are very close with only about 10% error, verifying the high accuracy of the formula suggested in this paper.

Study on the Performance of laser-assisted fast tool servo machining device for glass-ceramic

As an optical hard brittle material, glass-ceramic is widely used in radome, astronomical telescopes, and laser industries. However, an efficient method for machining optical free-form surface of glass-ceramic still needs to be studied by academia and industry. In this study, a laser-assisted fast tool servo machining device for glass-ceramic is developed. The theoretical stiffness of semicircular flexure hinge in the device is calculated by flexibility matrix method. The displacement output characteristics of the device are verified by simulation and displacement measurement experiment. Static and dynamic temperature measurement experiments of glass-ceramic are carried out respectively. The free-form surface morphology of glass-ceramic is obtained through machining experiment. Laser-assisted fast tool servo machining can reduce surface roughness by 24.4% and tool wear by 35.7% compared to conventional machining, which fully proves that the laser-assisted fast tool servo machining device can obtain higher machining quality of optical free-form surface.

Parametric plate lattices: Modeling and optimization of plate lattices with superior mechanical properties

Recent advancements in additive manufacturing have made it possible to fabricate complex structures at the microscale, leading to increased interest in lattice structures for achieving high-performance materials. Among lattice structures, plate lattices have shown superior mechanical properties. However, conventional plate lattices are typically designed based on cubic crystals and their mixing structures, which limits the range of available morphologies and properties. In this study, we propose a parametric plate lattice (PPL), which is a unified parametric model integrated with shape optimization to generate plate lattices with desired mechanical properties. The parametric model allows for the generation of plate lattices with controlled topology continuity and quadrilateral mesh directly. When combined with a level-set optimization method, the parametric model thoroughly explores the property space of plate lattices and can achieve the target mechanical properties. We validate the performance of PPL through a comprehensive evaluation using both simulations and physical experiments. The results demonstrate that PPL can generate a large set of novel plate lattices with mechanical performance surpassing that of traditional lattices, both in isotropic and orthotropic conditions. These novel PPLs exhibit a larger property space and higher stiffness, which may approach or even exceed the theoretical stiffness upper bound.

Uncertainty in identifying contact stiffness in a dovetail attachment for turbine blades

Designing bladed disks in turbo engines requires accurate dynamic models to correctly estimate resonance frequencies and related stresses. The contact parameters – stiffness and damping in the blade attachments – are currently among the most significant uncertainties of such models. Dry friction and alternating relative motions between the contact interfaces determine the transition between stick and slip that causes the nonlinear behavior of attachments. Commercial and in-house finite element software make use of specific contact elements to simulate dry friction and the resulting nonlinear behavior. These elements require the friction coefficient as input while the normal and tangential contact stiffness can be directly evaluated by the software or set up by the user. The main objective of the present research is to discuss the uncertainty associated with identifying with experimental data the normal and tangential stiffness in a dovetail coupling. In addition, the reliability of available theoretical contact models will be addressed. The response of the blade/attachment system was measured as a function of the axial load (simulating the centrifugal force) and of the blade vibration amplitude. An identification procedure using a finite element model was set up to identify the normal and tangential contact stiffness of the attachment. These stiffnesses were compared with the values predicted by a theoretical model. The comparison highlights a significant difference between measured and predicted stiffness. The final discussion focuses on the significance of theoretical contact stiffness and its use in finite element models.

Seismic performance of stone supported traditional timber frames with or without cap beams

Traditional timber frames in East Asia rest on stone bases, and are uncapped or capped with flat timber beams on their top. This study quantified the influence of the cap beam on the seismic performance of stone supported traditional timber frames. Four column foot and head joints were half-scale fabricated and reversed cyclically tested. Typical damage modes of the joints were identified. Methods were proposed to characterize the joints' rotational behavior. Finite element models of stone supported traditional timber frames with or without cap beams were developed. Lateral performance analysis was conducted on typical full-scale frames based on the developed models; fragility analysis was further performed to evaluate the full-scale frames' seismic performance. The tests indicated that the column foot joints were self-centering and had minor residual parallel to grain deformation. However, the column head joints were found with the embedment deformation at the cap beams, resulting to the pinching of their moment-rotation hysteretic curves. By use of existing hysteretic models in OpenSess whose parameters expressed by the theoretical maximum moment and elastic rotational stiffness, the joints’ rotational behavior was well captured. The numerical study indicated that the cap beam significantly increased the lateral performance and deformability of a frame. The elastic stiffness, lateral load-resisting capacity and cumulative energy dissipation of the frame increased by 77%, 81% and 42%, respectively. Fragility analysis indicated that the cap beam increased more than 33% and 23% of the PGAs corresponding to 50% probability exceedance under life safety drift limit and collapse prevention drift limit, respectively.