Flexible Beam Research Articles

Comparative Evaluation of Flexural Toughness of Steel Fiber-Reinforced Concrete Beams.

Specifications are available to quantify flexural performance of steel-fiber reinforced concrete beams with several parameters. Each specification provides different results. This study comparatively evaluates existing flexural beam test standards that are used to evaluate the flexural toughness of SFRC beam specimens. Two standards, EN-14651 and ASTM C1609, were followed to test SFRC beams under the three-point bending test (3PBT) and the four-point bending test (4PBT), respectively. Both normal tensile strength steel fiber (1200 MPa) and high tensile strength steel fiber (1500 MPa) in high-strength concrete were considered in this study. The reference parameters recommended in the two standards, which include equivalent flexural strength, residual strength, energy absorption capacity, and flexural toughness, were compared based on the tensile strength (normal or high) of the steel fiber in high-strength concrete. The 3PBT and 4PBT results indicate that both standard test methods yield similar results to quantify the flexural performance of SFRC specimens. However, unintended failure modes were observed for both standard test methods. The adopted correlation model shows that the flexural performance of SFRC is similar for 3PBTs and 4PBTs, but the residual strength obtained from the 3PBTs tends to be greater than that obtained from 4PBTs with an increase in the tensile strength of steel fiber.

Design of a torsional compliant mechanism with given discrete torque-deflection points for nonlinear stiffness elastic actuator

AbstractOwing to inherent flexibility, compliant actuator with physical elastic elements can implement compliant interactions between robot and environment. Nonlinear stiffness elastic actuators (NSEAs) use one motor to adjust position and stiffness, which improve compactness of variable stiffness actuators, and consider high torque/force resolution and high bandwidth. The primary challenge of designing a NSEA is designing a reliable compliant mechanism with a given torque-deflection profile. In this study, a general design method of torsional compliant mechanism through given discrete torque-deflection points was proposed, where a chain algorithm based on 2R pseudo-rigid-body model was used to describe the large deformation in elastic elements. Moreover, the theoretical model of stiffness of a compliant mechanism based on series flexible beams was developed. Based on the proposed model, the dimensional parameters of proposed compliant mechanism were designed satisfying the condition of the given torque-deflection points. Finally, simulation and physical experiment of the designed compliant mechanism through three given torque-deflection points are conducted to show the effectiveness of the proposed method. The designed compliant mechanism was tested and evaluated in the self-developed NSEA.

Effect of low temperature on mode I and mode II interlaminar fracture toughness of CFRP-steel hybrid laminates

Delamination is the dominant failure type in fiber metal laminates (FML), particularly when combining carbon fiber reinforced plastics (CFRP) with steel. Their interface behavior is frequently studied using the double cantilever beam (DCB) and end-notched flexure (ENF) setup for mode I and mode II delamination, respectively. By nature, analysis of hybrid interfaces requires asymmetric laminate layups. Thus, thermal residual stresses (TRS) are acting on the interfaces. A framework for the correction of the apparent fracture toughness from experimental testing and for accurate numerical modeling is provided. The approach is validated using DCB and ENF test results at -55 °C and 23 °C. The results demonstrate the necessity of incorporating TRS in the analysis of asymmetric CFRP-steel FMLs, i.e. including a temperature step and using the true fracture toughness value as simulation input. Otherwise, delamination onset is mispredicted by up to 29 %.

Topologically Optimized Fingerless Versatile Gripper Actuated by a Shape Memory Alloy Coiled Garter Spring

The rapid advancements in 3D printing technologies offer immense design flexibility and the ability to create complex structures with high resolution. Using these cutting‐edge technologies and materials (i.e., a polylactic acid and fused deposition modeling), a novel design principle is introduced for a fingerless gripper, achieved through topological optimization. To realize the grasping capabilities, a coiled garter spring made of shape memory alloy (SMA) is incorporated at the end of the flexure beams. Based on the experiments, it is found that the gripper is very quick to respond, taking only 5 s to heat up and 15 s to cool down. This promising performance is achieved by carefully balancing the net force differential between the restoring force of the flexure beam and the force of the SMA coiled garter spring. In addition to its responsiveness, the gripper demonstrates a high force‐to‐weight ratio of 5.3, allowing it to lift heavy payloads of up to 4.91 N (0.5 kgf) despite its lightweight design (total weight of 94.2 g). Overall, this work showcases the potential of 3D printed fingerless grippers in terms of high holding strength, lightweight, low cost, and simple fabrication.

Effect of Damage Severity and Flexural Steel Ratio on CFRP Repaired RC Beams

The study aims to investigate the effectiveness and failure modes of using CFRP-bonded sheets as a flexural repair system for RC beams, considering the effect of pre-repair damage levels and flexural steel design limits. This study investigated two different flexural design criteria: RC beams reinforced with the minimum flexural steel limit (ρmin) and RC beams reinforced with the maximum flexural steel limit (ρmax). Additionally, three pre-repair damage levels were considered: design limit load, steel yield limit load, and failure limit load. The study results showed that the RC beams’ repair effectiveness depends on the ratio of the flexural steel provided. Specifically, the beams with a minimum steel ratio demonstrated a higher capacity restoration of 49% to 85% (corresponding to the pre-repair damage level, i.e., design load to failure load), while beams with a maximum steel ratio only achieved a capacity restoration of 15.3% to 28.4%. Regarding failure modes, the beams experienced an intermediate-induced crack (IC) debonding due to pre-repair flexural cracks. Despite the debonding of the CFRP sheets, the beams still had the ability to withstand loads close to their unrepaired capacity. This indicates the possibility of re-repairing the beams after the CFRP debonding. Overall, the findings of this study can be used in the industry to repair RC beams and girders that have been damaged due to extreme loading conditions or other reasons. By using CFRP externally bonded sheets, the capacity of the structures can be restored regardless of the pre-repair damage level and the flexural steel design criteria.

Flexible terahertz optics: light beam profile engineering via C-shaped metallic metasurface

The potential of terahertz (THz) imaging implementation in a large variety of applications requires compact, reliable, and relatively low-cost solutions in systems constituents. Here we focus on the development of passive optical elements and demonstrate flexible and reliable THz beam profile engineering for imaging aims via mechanical bending of a stainless steel-based C-shaped metasurface. The designed and laser-ablation technology fabricated metasurface provides compact THz focusing and enables THz light engineering as well as polarization control ability in THz imaging. Focusing, light profile engineering, and polarization control performances of the metasurfaces with different focal distances and C-shape designs are presented. Experimental data are well supported by simulations, using Finite Difference Time Domain (FDTD) method. THz images of different objects at ∼94 GHz using InP Gunn diode, bow-tie sensors, and exclusively metasurfaces-based optics are exposed. Further routes in the development of low-cost multicolor and polarization-sensitive THz imaging are discussed.

Scale-adaptive three-dimensional imaging using Risley-prism-based coherent lidar.

We present a scale-adaptive three-dimensional (3D) imaging architecture for coherent light detection and ranging (lidar) that incorporates Risley-prism-based beam scanning. An inverse design paradigm from beam steering to prism rotation is developed for demand-oriented beam scan pattern generation and prism motion law formulation, which allows the lidar to perform 3D imaging with adaptive scale and configurable resolution. By combining flexible beam manipulation with simultaneous distance and velocity measurement, the proposed architecture can achieve both large-scale scene reconstruction for situational awareness and small-scale object identification against long range. The experiment results demonstrate that our architecture enables the lidar to recover a 3D scene in a ±30° field of view and also focus on distant objects at over 500 m with spatial resolution up to 1.1 cm.

Optical recursional binormal optical visco Landau–Lifshitz electromagnetic optical density

In this manuscript, we study a new version of the optical recursional binormal microbeam model for a flexible binormal microscale beam in terms of a binormal normalized operator. Also, we give new explanations for the optical recursional visco Landau–Lifshitz binormal electromagnetic binormal microscale beam. Finally, we obtain an optical application for the normalized visco Landau–Lifshitz electromagnetic binormal optimistic density with an optical binormal resonator.

Shear capacities of reinforced concrete interior beam-column joints subjected to cyclic loading

The primary focus of this research is the experimental investigation of internal RC beam-column joints with cyclic loads. There were two interior RC beam-column joints test specimens made without shear reinforcement. The longitudinal reinforcement ratio of the beams served as the study’s test variable. The specimen test results were compared to the theoretical capacity given in SNI 2847-2019 after that. The test revealed the following: (a) shear and flexural beam capacities; (b) shear and flexural column capacities; and (c) shear capacities of joints. The results showed that there was a significant impact on the shear capacity of the beam-column joint as a result of the variation in the reinforcement bars of the beam. After the longitudinal reinforcement bars of the beam yielded in both instances, the degradation of the beam-column joint occurred. A sharp decline in the load value that the specimen can support serves as evidence.

Rigid-flexible coupling multi-body dynamics modeling of a semi-submersible floating offshore wind turbine

A 14-degree-of-freedom (14-DOF) flexible multibody dynamics model is developed and verified for a semi-submersible floating offshore wind turbine (FOWT). The model considers the coupled dynamics of the platform, tower, nacelle, blades, and mooring subjected to external wind and wave loads. The platform is simplified as a rigid body connected to the seabed by the mooring system. The tower and blade are modeled as flexible cantilever beams. The energy method is used to derive the governing equations of motion, where the kinetic energy, potential energy, and work done by external wind-wave forces are all deduced in a global coordinate system. The 5-MW baseline semi-submersible FOWT is used to verify the derived model against the results simulated from FAST developed by the US National Renewable Energy Laboratory (NREL) at two scenarios: free decay state and different wind-wave load cases. Results show that the established FOWT model can well reflect the vibration characteristics of FAST model. The application of the model to the control of platform pitch with a tuned mass damper is studied. The simplified model could provide a low-order method for the structural dynamics analysis and advanced vibration control design for the multi-body components of the semi-submersible FOWT in the future.

Performance of Stalite lightweight SCC beam-column joints under reversed cyclic loading

This paper investigates the structural performance of Stalite lightweight self-consolidating concrete (LWSCC) beam-column joints under quasi-static reversed cyclic loading. Six beam-column joints made with different lightweight aggregate types (Stalite lightweight coarse [LC] and fine [LF] aggregates) and designed with/without joint shear reinforcement were cast and tested. The performance of tested specimens was assessed in terms of failure mode, hysteretic response, deformation, strength degradation, ductility, brittleness index, and energy dissipation capacity. The applicability and accuracy of design code provision in predicting the shear and flexural strengths of the tested joints were also investigated. The results indicated that it is possible to design Stalite LWSCC mixtures with a density ranging from 1888–1966 kg/m3, having a sufficient structural performance under cyclic loading. Properly designed LWSCC beam-column joints made with Stalite aggregates slightly reduced the load-carrying capacity by around 8.5% and ductility and dissipated energy by around 11.4% and 15.8%, respectively, compared to the normal-weight SCC (NWSCC) specimen. Despite the brittle nature of Stalite lightweight aggregates, LWSCC joints with sufficient hoops exhibited satisfactory cyclic performance and experienced ductile flexural beam failure. The results also indicated that LWSCC specimens containing Stalite fine aggregates showed better structural performance in terms of load-carrying capacity, strength degradation, ductility, brittleness index, and energy dissipation capacity compared to counterpart specimens made with Stalite coarse aggregates.

Real‐time hybrid simulation for investigating the influence of vertical ground motions on the lateral response of RC piers

AbstractThe vertical component of ground motions can affect the seismic performance of reinforced concrete (RC) piers as significant as its horizontal counterpart. However, real‐time testing for RC piers subjected to both horizontal and vertical ground motions has been scarcely conducted due to the difficulty in multi‐axial control of actuators. In this study, the seismic response of a bridge RC pier was investigated by conducting real‐time hybrid simulation (RTHS), where the RC pier was physically tested in the laboratory and the bridge superstructure was numerically modeled. The test setup that can synchronously apply both horizontal and vertical ground motions was constructed by using three dynamic actuators and a flexible loading beam (FLB). The lateral response of the RC pier was investigated by varying the intensities for vertical ground motions, while the same intensity for horizontal ground motion is used. It was found that the axial force from the dead load of superstructure can significantly affect the initial stiffness, strength, and post‐yield response of the RC pier. For the selected earthquake ground motions, however, the intensity of vertical ground motion did not make a substantial difference in the lateral response, although there was a notable difference in the fracture pattern.

Effective Strengthening of RC Beams Using Bamboo-Fibre-Reinforced Polymer: A Finite-Element Analysis

This paper presents a finite-element model of the structural behaviour of reinforced concrete (RC) beams with and without openings externally strengthened with bamboo-fibre-reinforced composite (BFRC) plates. The simulation was performed using ABAQUS Unified FEA 2021HF8 software. The stress–strain relationship of the RC was modelled using a model code for concrete structures, whereas the concrete-damaged plasticity model was used to simulate concrete damage. The predicted crack pattern of the beams was comparable to that from experimental observations. The ultimate load-bearing capacity of RC beams in flexure was predicted with an error of up to 1.50%, while the ultimate load-bearing capacity of RC beams with openings in shear was predicted with an error ranging from 1.89 to 13.43%. The most successful arrangement for strengthening a beam with openings in the shear zone was to place BFRC plates perpendicular to the crack on both sides of the beam’s surface, which increased the beam’s original load-bearing capacity by 110.06% compared to that of the control beam (CB). The most effective method for strengthening RC beams in flexure is to attach a BFRC plate to the entire bottom soffit of the RC beam. This maximises the ultimate load-bearing capacity at the expense of the beam’s ductility.

Unilateral frictional contact between a rigid wheel traversing on a flexible beam: An analytical investigation

This paper proposes a non-linear dynamic solver to simulate the dynamics of a rigid wheel traversing over a flexible beam involving a unilateral contact at the interface. Euler’s discretization scheme is extended incorporating Linear Complementary approach to perform explicit integration over time domain. The proposed solver is analytically designed to incorporate frictional force acting at the wheel-beam interface along with the possibility of generation of normal gap between the two bodies. Moreover, rotation of the wheel is also appended in the proposed algorithm and change in contact point between the wheel and beam is evaluated at every time step. After validation with existing literature, the solver is applied to study various dynamic responses of wheel and beam. Further, the technique is applied to moving oscillator model traversing over a flexible beam. The effect of initial wheel velocity, coefficient of friction, frequency of the oscillator on overall dynamic response of beam and wheel have been thoroughly investigated. The proposed algorithm delivers an exact solution based on the system’s fundamental mechanics, thus reducing the mesh reliance which amounts to high computational cost in finite element solver. The suggested method provides a broad future potential for solving rigid-flexible contact multibody dynamic problems.

Adaptive neural network independent joint-based control for an ODE-PDE rigid-flexible manipulator with multiple constraints

This paper deals with the adaptive neural network control of a nonlinear rigid-flexible manipulator subject to external disturbances and multiple constraints. The system dynamic is modeled by ordinary and partial differential equation (ODE and PDE) based on Hamilton’s Principle. An adaptive neural network sliding mode control strategy is designed to estimate the unknown disturbances and uncertain parameter. The sliding surface consisting of angular error, angular velocity error, and end-point vibration information is proposed based on the energy analysis of the flexible beam. The tangent barrier Lyapunov function is used to ensure the angle errors and end-point deflection within the restrictions. It is shown that the joint motion and vibration of the flexible beam can be adjusted only with an independent joint control input, and no boundary force input is required for vibration suppression. The stability is obtained by semi-group theory and LaSalle’s Invariance Principle. Simulation results demonstrate the effectiveness of the control strategy.

Machine learning-based model for recognizing the failure modes of FRP-strengthened RC beams in flexure

Plate end (PE) debonding and intermediate crack (IC) debonding are the main failure modes of fiber reinforced polymer (FRP) strengthened reinforced concrete (RC) beams in flexure. Different failure modes exhibit different failure characteristics. Therefore, accurately identifying the failure mode is of great significance in selecting methods to prevent the debonding of the strengthened beams. This study first established a primary indicator system through literature research. Then one hundred and eighty-eight FRP-strengthened RC beams containing PE and IC debonding were collected from the published literature of forty-eight researchers. After that, correlation analysis and grey correlation analysis were used to study the data of two failure modes. Finally, the indicator system for the prediction of failure modes was established. After the indicator system was established, six machine learning algorithms, including K-nearest neighbor algorithm (KNN), decision tree (DT), random forest (RF), back propagation neural network (BPNN), logistic regression (LR), and support vector machine (SVM), were used to build the prediction model of failure modes. The evaluation of the models shows that the coefficient of variation of the accuracy of the decision tree is merely 5.4%, which has the best robustness; the average accuracy of the random forest for the two failure modes reaches 93% and 98%, which has the highest precision.

New optical geometric recursional electromagnetic ferromagnetic microscale

In this paper, we design optical geometric ferromagnetic illustration for recursional optical electromagnetic elastic microscale beams with optical fields. Thus, the modeling of recursional operator for Heisenberg ferromagnetic electromagnetic normalized optical optimistic density is characterized by using recursional operator with optical fields. Also, we collect new optical flexible electroosmotic electromagnetic normalized optimistic density. Finally, optical recursional magnetical flexible elastic microscale beam demonstrated the optical ring resonator.

A mixed-mode fatigue crack growth model for co-consolidated thermoplastic joints

In this work, a mixed-mode fatigue crack growth model for simulating interfacial fracture of co-consolidated thermoplastic joints was developed. The model is based on the cohesive zone modeling approach and was specifically designed to account for any I + II mode-mixity, requiring only pure mode I and II loading data as input. The fatigue crack growth rate is constantly updated using a function of the energy release rates and the computed mode-mixity ratio. A linear mode-mixity law is applied. Both force-controlled and displacement-controlled loads can be modeled in specimens ranging from coupon-scale sizes to larger structural elements. Implementation of the model was done for the low-melt polyaryletherketone (LM-PAEK) material by developing a user-defined subroutine in the LS-Dyna FE software. To feed the model, mode I and mode II fatigue tests were conducted using double-cantilever beam and end-notch flexure specimens, respectively, while to validate the model mixed-mode single lap shear (SLS) tests were conducted. The model reproduces accurately the mode I and II fatigue crack growth while it predicts also accurately the mixed-mode fatigue crack growth of the SLS specimens.

A redundantly actuated 2-DOF 3RRR PKM with flexure joints: less is more

The development of a planar manipulator with flexure joints and redundant actuation has been considered before, showing that the redundancy can be exploited to increase the support stiffness and to reduce static actuator loads. In this previous design the manipulator’s workspace has been defined to encompass all kinematically accessible end effector positions. In the current paper we reconsider the design philosophy. It will be shown that limiting the workspace (“less”) ultimately results in a better performance in a larger area (“more”).The dynamic performance of the manipulator is evaluated with a flexible multibody model. The links can safely be considered as rigid parts, but the model has to account for the nonlinear stiffness behaviour of the flexure joints undergoing relatively large deflections. The nonlinear spatial flexible beam elements implemented in the spacar software result in numerically efficient models that have proven to be well-suited for design optimisation. With such a flexible multibody model, the geometry of the manipulator is optimised to maximise the workspace area while assuring a minimal parasitic natural frequency and limiting the local stresses throughout the full workspace. Furthermore, the simulations show that preloading of the flexure joints results in reduced actuator torques that are needed to counteract the finite joint compliance for stationary positioning anywhere except for the equilibrium position of the end effector.The optimised design has been build and validated experimentally. A control system that handles the actuator redundancy by minimising the 2-norm of the driving torques has been synthesised. It is demonstrated that the setup’s behaviour is similar to the model and that in particular the preloading significantly lowers the required actuator torques.

A Coupled Hydrodynamic–Structural Model for Flexible Interconnected Multiple Floating Bodies

Evaluating the structural safety and seakeeping performance of very large floating structures (VLFS) using the rigid module flexible connector (RMFC) method remains challenging due to the complexity of the coupled hydrodynamic–structural responses in this system. In this study, a coupled hydrodynamic–structural frequency–time domain model is developed based on the RMFC method employing the planar Euler–Bernoulli beam elements to investigate the dynamic responses of multi-module floating systems. To reveal the dynamic characteristics of the systems, the coupled hydrodynamic–structural responses are investigated using a frequency–time-domain numerical model with viscous correction, in which the mass and stiffness attributes of connectors are incorporated into the system. Given the effects of hydrodynamic interaction, consideration is given to the case of three modular boxes connected by flexible beams aligned in series in shallow water to validate the present model. Higher efficiency and accuracy can be found in the system using viscous correction in potential flow theory and introducing state–space model to replace the convolution terms in the Cummins equation for the time domain. Moreover, this model can be extended to a considerable number of floating modules, which provides possibilities to analyze N-module floating systems.