Force-displacement Relationship Research Articles

Seismic performance of squat UHPC shear walls subjected to high-compression shear combined cyclic load

Cyclic tests of five UHPC squat shear walls and one high-strength concrete counterpart were carried out in this study to investigate the seismic performance of UHPC shear walls with high design axial load ratio ranging from 0.5 to 0.6, and web distributed reinforcement ratio varying from 0.19% to 0.56%. The failure mode, crack pattern, force–displacement relationship, deformation mechanism, energy dissipation, the strength and stiffness degradation are comprehensively investigated. In addition, the stress development and shear contribution of horizontal rebar in the web is calculated and analyzed. Finally, design suggestions for UHPC squat shear walls are proposed in terms of minimum horizontal reinforcement ratio and axial load ratio. It is demonstrated by the test results that UHPC specimens showed an excellent crack control ability with narrow shear-related cracks distributed in a dense array. The shear capacity and ultimate deformation of UHPC specimen were significantly improved by almost 85% and 95% in comparison with high-strength concrete specimen. Noticeably, the UHPC specimen with the minimum amount of transverse rebars reached the highest ultimate drift ratio of 1.75%. The stress level of horizontal rebars in UHPC specimens can be reduced by at least 72%. The test results show the potential to reduce the horizontal reinforcement ratio to 0.19% for the UHPC squat shear walls under the high design axial load ratio of 0.5. A modified strut-and-tie model for predicting the shear strength of UHPC shear walls is proposed with an error of no more than 4%.

A theoretical justification of the slip index concept in fretting analysis

Fretting in the partial-slip and gross-slip regimes under a constant normal load is considered. The tangential force—displacement relations for the forward and backward motions are described based the generalized Cattaneo—Mindlin theory of tangential contact and Masing’s hypothesis on modelling the force—displacement hysteretic loop. Besides the critical force and displacement parameters (characterizing the triggering of sliding), the model includes one dimensionless fitting parameter that tunes the tangential contact stiffness of the friction—contact interface. Explicit expressions are derived for the main tribological parameters of the fretting loop, including the slip index and the signal index. The presented phenomenological modelling approach has been applied to the analysis of two sets of experimental data taken from the literature. It has been shown that the experimentally observed simple relation of a rational type between the slip index and the slip ratio corresponds to the gross-slip asymptotics of the corresponding model-based predicted relation. The known quantitative criteria for the transition from the partial slip regime to the gross slip regime are expressed in terms of the stiffness parameter, and a novel geometric transition criterion is formulated.

Constant ductility inelastic displacement ratio spectra of shape memory alloy-friction self-centering structures based on a hybrid model

Previous researches on the constant ductility inelastic displacement ratio spectra (\({C}_{\upmu }\)) of self-centering structures have been conducted based on the typical flag-shaped self-centering (FS) model. However, the arising shape-memory-alloy-friction self-centering structures (SMAFSs) own their specialized force–displacement relationship different from the typical FS model. In this research, a hybrid force–displacement model composed of the typical FS model and Coulomb friction model is employed and an efficient calculating procedure is proposed to statistically investigate the \({C}_{\upmu }\) of SMAFSs. Comparison with the \({C}_{\upmu }\) of the typical FS system with similar self-centering capacity shows that the \({C}_{\upmu }\) of the SMAFS is significantly different from that of the typical FS system, which explains the necessity of employing the hybrid model for SMAFSs and the effects of the friction. The effects of seismic parameters and structural parameters on the \({C}_{\upmu }\) of SMAFSs are investigated. Furthermore, the formula for estimating the \({C}_{\upmu }\) of SMAFSs is proposed through statistical regression. This proposed formula could estimate the \({C}_{\upmu }\) of SMAFSs and describe the effects of structural parameters more accurately. The research could provide a basis of estimating the \({C}_{\upmu }\) of SMAFSs to obtain reliable seismic design results of the structures.

Theoretical and experimental investigation on disc spring isolation system with loading rings

A novel disc spring isolation system (DSIS) design for buildings is proposed to isolate vibrations in the vertical direction. The system with nonlinear stiffness consists of disc springs and loading rings that reduce the influence of Coulomb friction between multiple disc springs. Theoretical analysis was first applied to establish a four-curve (FC) model to describe the force-displacement relation of DSIS by considering the influence of slip behavior and Coulomb friction between the loading rings and disc springs. Then, a series of vertical cyclic loading tests were carried out to study the different mechanical properties of DSIS with or without loading rings, and the effectiveness of the loading rings was verified. By comparing with the test results, the accuracy of the proposed FC model was verified. Then, the numerical solution method using the proposed FC model to solve the dynamic response of the single degree of freedom (SDOF) system was investigated. The nonlinear transfer function curves of DSIS with loading rings were compared with those of DSIS without loading rings by numerical analysis. Finally, the comparison study of SDOF for DSIS under the specific harmonic and train-induced vibration was carried out as a case study. The comparison shows that DSIS with loading rings more effectively reduces the start frequency of the isolated system, revealing the significant advantages of adopting DSIS with loading rings in vertical isolation.

Development of a negative stiffness friction damping device with an amplification mechanism

This paper proposes an innovative negative stiffness friction damping device (NSFDD), which is characterized with a combination of negative stiffness and friction damping force. The large force capacity of the NSFDD is realized by the amplification mechanism of a two-consecutive lever and using the pre-compressed gas springs. A mechanical model is developed to represent the force–displacement relationship of the proposed NSFDD. The influence of key parameters on the NSFDD performance is analyzed using this mechanical model and demonstrates the advantage of using pre-compressed gas springs. A NSFDD specimen was manufactured and examined by experimental tests. The NSFDD specimen exhibits an obvious negative stiffness and stable energy dissipation, demonstrating the feasibility and effectiveness of the NSFDD. Finally, a refined finite element (FE) model is developed to represent the NSFDD. Both the experimental tests and FE simulation validate the accuracy of the mechanical model of the NSFDD.

Nonlinear indentation of second-order hyperelastic materials

The classical problem of indentation on an elastic substrate has found new applications in the field of the Atomic Force Microscopy. However, linearly elastic indentation models are not sufficiently accurate to predict the force–displacement relationship at large indentation depths. For hyperelastic materials, such as soft polymers and biomaterials, a nonlinear indentation model is needed. In this paper, we use second-order elasticity theory to capture larger amplitude deformations and material nonlinearity. We provide a general solution for the contact problem for deformations that are second-order in indentation amplitude with arbitrary indenter profiles. Moreover, we derive analytical solutions by using either parabolic or quartic surfaces to mimic a spherical indenter. The analytical prediction for a quartic surface agrees well with finite element simulations using a spherical indenter for indentation depths on the order of the indenter radius. In particular, the relative error between the two approaches is less than 1% for an indentation depth equal to the indenter radius, an order of magnitude less than that observed with models which are either first-order in indentation amplitude or those which are second-order in indentation amplitude but with a parabolic indenter profile.

The compliant version of the 3-RRR spherical parallel mechanism known as “Agile-Eye”: Kinetostatic analysis and parasitic displacement evaluation

The compliant version of the 3-RRR (R - revolute joint) spherical parallel mechanism known as “Agile-Eye” is presented. The kinetostatic analysis of this Compliant Spherical Parallel Mechanism (CSPM) is conducted using the Compliance Matrix Method (CMM) evaluating two different types of Rotational Compliant Joints (RCJs) and with three inputs. These independent inputs could be forces or displacements. Expressions that relate the input forces/displacements with the displacement of the moving platform are obtained from the kinetostatic analysis. These expressions are used to obtain the required inputs to perform a rotational trajectory of the moving platform; parasitic displacements are computed during this process. Analytical results are validated through Finite Element Analysis (FEA). Additionally, the CSPM geometric parameters-parasitic displacements relation is characterized. Those parameters resulting with lower parasitic displacements are determined. Finally, expressions from the kinetostatic analysis are corroborated experimentally using input displacements in a manufactured prototype with parameters selected to have reduced parasitic displacements. Results from the FEA-simulations and experimental tests demonstrated that the expressions obtained from the kinetostatic analysis can accurately describe the force–displacement relations of the proposed CSPM.

Anti-blast analysis and design of a sacrificial cladding with graded foam-filled tubes

Foam-filled tubes are excellent energy absorption structures for impact resistance, and graded foam may have superiority for the design of anti-blast sacrificial cladding. The anti-blast response of density-graded foam-filled tubes as a core layer is investigated numerically and theoretically. Mesoscopic finite element models for graded foam-filled tubes are constructed, and their constant-velocity compression and anti-blast performance are simulated. One-dimensional analytical shock models based on an empirical force–displacement relationship are developed to analyze the axial collapse wave propagation in graded foam-filled circular tubes. Single-/double-wave deformation patterns are observed for graded foam-filled tubes under blast loading, especially the negatively graded foam-filled tubes with gradient parameters close to zero may also show a single-wave deformation pattern. The results demonstrate that the negatively graded foam-filled tube with a small density gradient is a good choice to design anti-blast sacrificial cladding with a small critical length and a low transmitted force. A contour map of the critical length required to absorb the impulse of blast loading for different gradient parameters and diameter-thickness ratios of the outer tube is established. This study proposes a new design guideline for superior blast resistance structures in engineering applications.

Development of a High-Sensitivity Proximal Force/Torque Sensor Based on Optical Sensing for Intravascular Robots

This work proposes a proximal force/torque sensor with high sensitivity, adjustable measurement range, and decoupled force and torque detection for intravascular robots. The proposed sensor design primary consists of a force/torque-sensitive flexure that comprises a series of ortho-planar springs and an annulus cross-beam structure, an optical sensing unit with wireless communication. The ortho-planar component demonstrates equivalent functions as a parallel mechanism and achieves an outstanding linear force-displacement relationship along its axial direction. The rotational cross-beam structure has been parallelly arranged to form the torque-sensing component and enhanced sensing range. The utilized optical sensing unit can precisely detect the linear and angular displacement from the sensitive flexure based on a series of coherent CMOS images and support simultaneous detection and decoupling of force and torque. The FEM simulation has been performed for structure design and performance investigation. The prototyped sensor achieved a high force resolution of 8.7 mN within [−2.5, 2.5 N] and 0.13 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{N}\cdot $ </tex-math></inline-formula> mm within [−60, 60 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{N}\cdot $ </tex-math></inline-formula> mm] for torque, with the corresponding linearity error values of 1.43% and 1.95%. The average crosstalk error values are 0.32% for force detection and 2.8% for torque measurement, indicating excellent anti-interference performance. To investigate the practicability of the proposed sensor, the phantom experiment has been conducted to evaluate its effectiveness for intravascular catheterization.

Force-displacement relationships for NiTi alloy helical springs by using ANSYS: Superelasticity and shape memory effect

Abstract Shape memory alloys are smart materials which have remarkable properties that promoted their use in a large variety of innovative applications. In this work, the shape memory effect and superelastic behavior of nickel-titanium helical spring was studied based on the finite element method. The three-dimensional constitutive model proposed by Auricchio has been used through the built-in library of ANSYS® Workbench 2020 R2 to simulate the superelastic effect and one-way shape memory effect which are exhibited by nickel-titanium alloy. Considering the first effect, the associated force-displacement curves were calculated as function of displacement amplitude. The influence of changing isothermal body temperature on the loading-unloading hysteretic response was studied. Convergence of the numerical model was assessed by comparison with experimental data taken from the literature. For the second effect, force-displacement curves that are associated to a complete one-way thermomechanical cycle were evaluated for different configurations of helical springs. Explicit correlations that can be applied for the purpose of helical spring's design were derived.

Hybrid Experimental-Numerical Investigation on Plastic Deformation and Ductile Failure of Anisotropic Sheet Metals

The plastic deformation and ductile failure behaviors of anisotropic AISI 1018 low carbon steel and C260 Cu-Zn brass under uniaxial tensile loading were investigated. The full-filed surface deformation of U-notched sheet metal was measured by digital image correlation technique. Three-dimensional finite element modeling using the Hill model and calibrated post-necking strain hardening curve was performed to obtain the force and strain history till the crack initiation. The crack propagation was numerically simulated employing a strain-to-failure model. The results from computations as global force-displacement relation, local strain distribution, and failure process are found in good agreement with experimental observations.

Nonlinear Reduced Order Modeling of Structures Near Buckling and Application to an Energy Harvester

Abstract The focus of this investigation is first on assessing the validity to structures under in-plane forces, in particular near buckling, of the reduced order modeling approach for nonlinear geometric response that has been extensively developed in the last two decades. This focus is motivated by a class of piezoelectric energy harvesters that rely on strongly nonlinear behavior, such as large amplitude responses, to achieve broadband energy harvesting. A simple, two-rigid bars linkage that approximates a buckling beam is first considered to discover the features of the nonlinear force–displacement relationship induced by an in-plane loading. It is observed that the corresponding form of this relationship is not consistent with the one derived from a reduced order model (ROM) but can be closely approximated by it over a large displacement range. This analysis emphasizes in particular the role of a group of ROM coefficients that are usually considered unimportant. A similar study is performed next for the buckled harvester modeled within nastran and it is again found that a close match of the force–displacement relationship can be achieved. Based on that positive outlook, a six basis functions ROM of this beam harvester that includes piezoelectric effects is built and identified. It is found to provide a close match of nastran nonlinear predictions over a broad range of transverse and in-plane loadings in static and dynamic conditions. The ROM usefulness in predicting the open-circuit voltage is demonstrated.

Study on New Anti-drop-beam Device of High-speed Railway Bridge in High Intensity Seismic Region

Falling beam is one of the most common seismic damages for high-speed railway bridges, and it influences the running safety of trains. To prevent falling beam and then ensure the running safety of trains, a new anti-drop-beam device is developed for high-speed railway bridge in high intensity seismic regions in this paper. Firstly, the formulas are derived through the theoretical analysis to calculate mechanical parameters and force-displacement constitutive relation of device. Secondly, two groups of experiments are carried out to study mechanical performance of device and validated derived formulas. Finally, the finite element model of a high-speed railway continuous bridge is established to study seismic performance of device. The results show that the derived formulas can accurately calculate mechanical parameters and force-displacement constitutive relation of device. The energy dissipation capacity and low-cycle fatigue performance of device are good. The device can effectively limit the beam end displacement and well dissipate seismic energy under earthquakes, and it can be applied in engineering practice.

A simplified analytical model of equipment-pipe-shell structure

In addition to being directly connected to the base, the mechanical equipment in the ship is often connected to the shell through attachment elements such as pipelines. There are multiple vibration transmission paths in the system, and there is still a lack of in-depth theoretical research on this type of system. To study the vibration transmission characteristics of the system, a simplified analytical model of equipment-pipe-shell structure is proposed. The equipment and shell are approximated by rigid bodies, and the pipe is represented by an elastic cylindrical shell. In addition to the pipe, the equipment is also connected to the shell through several vibration isolators. Travelling wave solution is used to express pipe response, and the forces on the equipment and the shell can be obtained through the continuity condition at both ends of the pipe and the internal forcedisplacement relationship. By solving the system dynamic equation, the response of any point in the system can be obtained. The comparison of the analytical model calculation results and finite element simulation results verifies the accuracy of this analytical model.

A Substructure Condensed Approach for Kinetostatic Modeling of Compliant Mechanisms with Complex Topology.

Compliant mechanisms with complex topology have previously been employed in various precision devices due to the superiorities of high precision and compact size. In this paper, a substructure condensed approach for kinetostatic analysis of complex compliant mechanisms is proposed to provide concise solutions. In detail, the explicit relationships between the theoretical stiffness matrix, element stiffness matrix, and element transfer matrix for the common flexible beam element are first derived based on the energy conservation law. The transfer matrices for three types of serial–parallel substructures are then developed by combining the equilibrium equations of nodal forces with the transfer matrix approach, so that each branch chain can be condensed into an equivalent beam element. Based on the derived three types of transfer matrices, a kinetostatic model describing only the force-displacement relationship of the input/output nodes is established. Finally, two typical precision positioning platforms with complex topology are employed to demonstrate the conciseness and efficiency of this modeling approach. The superiority of this modeling approach is that the input/output stiffness, coupling stiffness, and input/output displacement relations of compliant mechanisms with multiple actuation forces and complex substructures can be simultaneously obtained in concise and explicit matrix forms, which is distinct from the traditional compliance matrix approach.

A brief review of variable stiffness and damping magnetorheological fluid dampers

With the development of magnetorheological fluid (MRF) technology, variable stiffness and damping MRF dampers as semi-active controllers gradually show their unique advantages in the vibration control field. This paper reviews recent journal articles on the principles, characteristics, structure design, modelling and applications of variable stiffness and damping MRF dampers. The principle includes the force behaviour of the MRF fluid and the mechanism of the variable stiffness and damping MRF damper. Characteristics introduce the damper’s force-displacement relationships, which have frequency dependence and amplitude dependence. Following this, typical dampers structures are discussed, including electromagnetic design and coil configuration. After that, some common models and parameter optimization methods are presented. Furthermore, taking vehicle suspension as an example, the applications of variable stiffness and damping MRF dampers in some fields are proposed in this paper.

A mixed XFEM and CZM approach for predicting progressive failure in advanced SiC/SiC CMC component

This research work focused on simulating different fracture modes in the high-stress concentrated region of an advanced SiC/SiC CMC component at the macroscopic scale in consideration of increasing cost and time during experimental tests of CMCs. A hybrid of extended-finite-element-method (XFEM) and cohesive-zone-modeling (CZM) was utilized to predict mode-I and mode-II fracture behavior, respectively. The cohesive element (CE) layers were used as fiber-tow interfaces in the stress-concentrated region where mode-II failure was supposed to occur. The 1st crack initiation and its further propagation were found to be dependent on XFEM damage criteria, whereas delamination was observed at the damage-front CE layers. The simulated force-displacement relationships were compared with the experimental ones, where stiffness and serrations in the force-displacement curve corresponding to the delamination matched quite well. With concern to predicting the fracture behavior in a complex-shape component of SiC/SiC CMCs, XFEM with CZM methodology can be a reliable method in the near future.

Sustainability Study of Concrete Blocks with Wood Chips Used in Structural Walls in Seismic Areas.

The concept of sustainability has become a priority in the construction field, in a context where there is an increasing discussion about reducing carbon dioxide emissions, as the construction industry is one of the most polluting industries with a focus on the production of building materials. At present, the classic solution used for structural masonry walls worldwide is the ceramic block. Given that the production of ceramic blocks represents an environmentally polluting process, the alternative solution of using concrete blocks with wood chips is proposed. The proposed solution is more environmentally friendly, both in terms of production technology and materials used, as it is made of wood chips, wood being a sustainable material. These types of blocks are currently used in non-seismic areas due to their poor structural performance. This paper deals with a study on the use of recyclable materials, such as wood chips, from waste materials and aims to propose viable solutions for the use of this type of blocks for structural walls in seismic areas. Two solutions, including concrete blocks with wood chips, have been proposed and numerical analyses have been carried out. Numerical analyses were also carried out for the classical solutions, so that, finally, a comparison could be made between them from a structural point of view. Following the numerical analysis of four types of walls, the two proposed solutions of concrete blocks with wood chips had the best results in terms of force–displacement relationship. Moreover, the quantitative results are presented in a force–displacement graph for the four wall types. This stage represents the first phase of the research, while phase II will continue with experimental tests of the proposed solutions.

Initial Postcontact Behavior of an Axially Compressed Fiber Constrained Inside a Rigid Cylinder: Experimental, Analytical, and Numerical Investigation

Abstract The postbuckling behavior of a clamped-clamped elastic fiber constrained inside a rigid cylinder is analyzed theoretically, numerically, and experimentally. We concentrate on characterizing the contact configuration between the fiber and the cylinder wall during initial postcontact stages of the fiber deformation, in which only a small segment of the fiber length maintains contact with the cylinder wall. This is apparently the first study of that phenomenon presenting an in-depth investigation of the fiber deformation and contact stages in experiments, along with a detailed examination of the effect of fiber geometrical imperfection. The main experimental challenge was to identify regions of contact between the fiber and the cylinder wall and to distinguish them from segments of the fiber that are very close to the cylinder wall but make no contact with it. To this end, we employed a novel experimental setup consisting of a transparent rigid cylinder filled with an opaque milky fluid, combined with image processing, and synchronized force measurements. The results of the experiments are supported by finite-element analysis and are also compared to available theoretical predictions based on the elastica model of an initially perfectly straight fiber. A small strain analytical solution reveals the role of minor initial geometrical imperfections in deriving the force–displacement relation during fiber bending. This study provides new understanding of the influence of key parameters on the behavior of such systems and may have practical implications in the fields of stent procedures, medical endoscopy, deep drilling, and more.

Mechanical properties and damage constitutive of recycled aggregate concrete with polyvinyl alcohol fiber under compression and shear

This paper researched the mechanical properties and damage constitutive of polyvinyl alcohol (PVA) fiber recycled aggregate concrete (RAC) under compression and shear. A total of 102 cube specimens were performed considering the effects of PVA fiber volume content, replacement ratios of recycled coarse aggregate, and normal stress. The shear strength, peak shear displacement and shear force-displacement relation of RAC were analyzed. The test results show that the shear strength increases with increasing normal stress and decreases with increasing replacement ratios of recycled coarse aggregate. The maximal shear strength generally appears at a PVA fiber content between 0.05 % and 0.1 % when identical to the normal stress and replacement ratios of recycled coarse aggregate. The peak shear displacement increases with increasing normal stress and PVA fiber volume content. The optimal PVA fiber content was 0.1 % considering the shear strength and shear displacement. It is suggested that a damage constitutive model be used to explain the shear force-displacement relationship of PVA fiber RAC in a compression-shear composite stress condition. The test findings and calculation results showed good consistency, proving that the damage constitutive model suggested in this research is applicable to PVA fiber RAC.