Bidirectional Stiffness Research Articles

Analysis of Elastic-Plastic Lateral-Torsional Coupled Earthquake Response of Multilayer Bidirectional Stiffness Eccentric Frame Structure

Analysis of Elastic-Plastic Lateral-Torsional Coupled Earthquake Response of Multilayer Bidirectional Stiffness Eccentric Frame Structure

A bidirectional-controllable magnetorheological elastomer-based quasi-zero-stiffness isolator

To enhance the low-frequency vibration isolation bandwidth of quasi-zero stiffness (QZS) isolators under variable amplitude excitations, this paper proposes an adaptive bidirectional-controllable QZS isolator (Bi-QZS) based on magnetic-controlled smart material named magnetorheological elastomer (MRE) as positive element and tilting spring as negative element. Firstly, the positive element of isolator is composed of laminated MRE and permanent magnet to realize bidirectional stiffness adjustment. Then the magnetic circuit of vibration isolator is designed and the specific parameters are obtained by taking the magnetic field and energy consumption as the optimization objectives. Secondly, a static theoretical model is established to calculate the achievable range of stiffness variation, and match the parameters of the negative element. Static analysis shows that bidirectional stiffness control is beneficial to achieve stiffness matching. Additionally, the adjustment of bidirectional stiffness variation on the dynamic response of the system is deduced by harmonic balance method. Numerical simulation results indicate that adjusting stiffness in reverse can increase the vibration isolation bandwidth when the excitation amplitude increases, and adjusting in forward can reduce the peak value of jump region. Also, increasing the damping ratio under reverse conditions has a certain contribution to reducing the response peak. Finally, static and dynamic tests are carried out, results reveal a bidirectional stiffness adjustment capability, with a 36.4% adjustment in reverse stiffness and a 70% adjustment in forward stiffness. The resonance frequency can be reduced from 14.4 Hz to 5.8 Hz by stiffness bidirectional-controllable.

Mechanistic Analysis and Bio-inspired Applications for a Bidirectional Stiffness of a Water Snail Operculum

Mechanistic Analysis and Bio-inspired Applications for a Bidirectional Stiffness of a Water Snail Operculum

C-Shaped Bidirectional Stiffness Joint Design For Anthropomorphic Hand

In this letter, we propose a C-shaped bidirectional stiffness joint for an anthropomorphic hand. The spring steel piece is used to connect the knuckles with inner concave C-shape as a rotational joint. The finger is bent by the tendon driven with low stiffness and reset by its own elasticity. The reverse bent has high stiffness with the C-shaped structure of the spring steel piece. The model of the designed joint is deduced, and the load-bearing capacity is analyzed. Meanwhile, the finite element simulation of the maximum bending moment of this joint is implemented. Then, an experimental platform was built to test a single finger, and the C-shaped joint was found to be 36 times larger than the maximum bending moment of the rectangular section joint. Finally, a prototype anthropomorphic hand was developed and the effectiveness of the C-shaped joint-based anthropomorphic hand was verified through various gesture, grasping and load bearing experiments.

A Finite Element Investigation on the Design of Mechanically Compatible Functionally Graded Orthopaedic Plate for Diaphyseal Tibia Transverse Fracture

The bidirectional stiffness grading of orthopaedic plate has been investigated for internal fixation of transverse fracture in tibia bone. Highly porous cellular materials made of two types of cubic unit cells were designed. Their effective mechanical properties (elastic moduli and yield strengths) were computationally evaluated using finite element analysis. The Gibson-Ashby model was derived for elastic moduli and yield strengths of the cellular geometries. The modified cellular structure provided the desired minimum stiffness within the selected strut sizes. The developed structures were mapped to seven zones of the orthopaedic plate assigning the bidirectional stiffness grading (longitudinal direction). The effect of functional grading on mechanical stimulation through three stages of healing was studied. The results indicated less stress shielding and improvement in uniformity of distribution of equivalent stress around the newly formed bone. Thus, a functionally designed plate will offer a way to dynamically load the healing tissues by encouraging the patient for a regular walk and exercise. Hence, the generated mechanical signal will significantly help mechanically stimulated bone formation and remodeling in the fractured zone.

Bidirectional deep-subwavelength band gap induced by negative stiffness

Owing to its tremendous potential application in wave manipulation, metamaterials have attracted significant interest since their appearance at the start of this century. The resonant mechanism breaks the dependency of the lattice constant on the operation frequency, successfully achieving wave manipulation in the subwavelength range. However, it fails to simultaneously control two types of wave propagations in the deep-subwavelength range due to the specific configuration of the resonator. In this study, we introduce a novel negative-stiffness mechanism into the resonator to open a bidirectional deep-subwavelength band gap. Both the translational and torsional stiffness of the resonator can be neutralised by the proposed negative-stiffness mechanism. More importantly, adjusting the parameters of the negative-stiffness mechanism provides a convenient way to tune the bidirectional stiffness characteristic of the resonator, which is beneficial for manipulating the elastic wave in a large frequency range. The fundamental principle of opening the bidirectional deep-subwavelength band gap is examined through mechanical analysis, dispersion relation, and wave propagation features. By cascading the presented resonator in a host structure, this study realises the suppression of the propagations of two types of elastic waves within the deep-subwavelength frequency range as well as the filtration of one of these two types of elastic waves in a particular frequency range.

Transformative Electronics: Design Strategy for Transformative Electronic System toward Rapid, Bidirectional Stiffness Tuning using Graphene and Flexible Thermoelectric Device Interfaces (Adv. Mater. 10/2021)

In article number 2007239, Byung Jin Cho, Jae-Woong Jeong, and co-workers present a design strategy for transformative electronics capable of rapid bidirectional stiffness tuning. Transformative electronics are built on a gallium platform interfaced with graphene and a flexible thermoelectric device (f-TED). The graphene works as a catalyst to mitigate the supercooling phenomenon in the liquid-to-solid transition of gallium, and the f-TED offers active temperature control to help accelerate the rigid–soft transformation of the overall system.

Design Strategy for Transformative Electronic System toward Rapid, Bidirectional Stiffness Tuning using Graphene and Flexible Thermoelectric Device Interfaces.

Electronics with tunable shape and stiffness can be applied in broad range of applications because their tunability allows their use in either rigid handheld form or soft wearable form, depending on needs. Previous research has enabled such reconfigurable electronics by integrating a thermally tunable gallium-based platform with flexible/stretchable electronics. However, supercooling phenomenon caused in the freezing process of gallium impedes reliable and rapid bidirectional rigid-soft conversion, limiting the full potential of this type of "transformative" electronics. Here, materials and electronics design strategies are reported to develop a transformative system with a gallium platform capable of fast reversible mechanical switching. In this electronic system, graphene is used as a catalyst to accelerate the heterogeneous nucleation of gallium to mitigate the degree of supercooling. Additionally, a flexible thermoelectric device is integrated as a means to provide active temperature control to further reduce the time for the solid-liquid transition of gallium. Analytical and experimental results establish the fundamentals for the design and optimized operation of transformative electronics for accelerated bidirectional transformation. Proof-of-concept demonstration of a reconfigurable system, which can convert between rigid handheld electronics and a flexible wearable biosensor, demonstrates the potential of this design approach for highly versatile electronics that can support multiple applications.

Bending behaviors of the in-plane bidirectional functionally graded piezoelectric material plates

The transverse bending behaviors of in-plane bidirectional functionally graded piezoelectric material (FGPM) plates are semi-analytically investigated by the scaled boundary finite element method (SBFEM) in association with the precise integration method (PIM). The proposed scheme is able to explore the structural characteristics of FGPM plates with the material coefficients obeying arbitrary form of mathematical functions according to the in-plane coordinates. The present methodology selects only four quantities consisting of three translational displacement components and the electric potential as the fundamental unknowns. Additionally, variations of the four primary variables across the thickness direction are expressed as an analytical exponential matrix. In the developed approach, plates are regarded as a kind of three dimensional structure. But, an arbitrary in-plane surface discretized with two-dimensional spectral elements is set as the research domain. The practice is conducive to cut down the computational effort and increase the calculation efficiency. The SBFEM governing equations are formulated from the three-dimensional basic equations of piezoelectric materials without any assumptions on the plate kinematics and distributions of electromechanical components. By means of the scaled boundary coordinate system and the dual vector methodology, the key partial differential equations of piezoelectric materials are conveniently converted into the easily-solved first order ordinary differential SBFEM governing equation. The stiffness matrix is constructed from the analytical exponential matrix aided by the highly accurate PIM to predict the changing patterns of mechanical and electric quantities. To further improve the precision, the technology of dividing the plate into two parts with equal thickness is exploited. Finally, numerical exercises of square, rectangular and triangular piezoelectric plates are provided to validate the accuracy and fast convergence of the developed technique and reveal the effect of geometrical shapes, gradient functions, types of external loadings and thickness-to-span ratios on the static flexure of FGPM plates owning the in-plane bidirectional stiffness.

Shock Isolation Capability of an Electromagnetic Variable Stiffness Isolator With Bidirectional Stiffness Regulation

This article presents a novel electromagnetic variable stiffness isolator that achieves bidirectional stiffness regulation, which means that the isolator experiences a reduced stiffness when the applied current is positive and an increased stiffness when the opposite current is applied. In addition, the stiffness variations are equal for two currents with the same magnitude but opposite polarities. The proposed isolator can not only ensure the vibration isolation performance in working frequency zone that is relatively far from the natural frequency, but also can realize high-damping-like effect for shock response attenuation, without introducing any additional damping components that may complicate the system. The bidirectional stiffness regulation was realized by combining mechanical springs with hybrid magnets (permanent magnets and coil windings). Variation in the overall stiffness of the proposed isolator occurred when the current was continuously adjusted. A prototype of the isolator was designed, fabricated, and then tested with a round displacement step shock at the base. The theoretical analysis revealed that this device could be utilized as an active vibration isolator through certain control strategies. The experimental results proved the effectiveness of the proposed mechanism in shock isolation and revealed that it outperforms the conventional isolator in suppressing the residual vibration.

Seismic behavior of high-rise modular steel constructions with various module layouts

Owing to their superiority in construction speed and quality, modular steel constructions (MSCs) are extensively used in low-rise buildings in non-seismic regions. Even in areas where the lateral load resistance is not demanding, fully modular steel constructions are not applicable unless additional lateral resistant members are introduced, such as cast-in-situ concrete cores or prefabricated steel frames. The primary focus of this research is to study the seismic behavior of high-rise MSCs with various module layouts, thereby enhancing the flexibility and feasibility of high-rise MSCs in regions of high seismicity. Five three-dimensional (3D) high-rise MSCs with various module layouts, i.e., parallel stacked (Configuration 1), one end staggered (Configuration 2), both ends staggered (Configuration 3), intermediately staggered (Configuration 4), and vertically staggered (Configuration 5), were designed. Seismic analyses were carried out in terms of these five models through response spectrum and elastic-plastic time-history analyses. The natural vibration characteristics of various module layouts show that vibration periods of the first three vibration modes are essentially the same (except Configuration 3), which meets the limit requirement. The first two vibration modes are translational deformation along the X and Z directions, and the third mode is torsional, indicating that MSCs can present excellent integrity with Configurations 1, 2, 4, and 5. Structural deformations show that staggered layouts (Configurations 2–5) can solve the problem of inconsistent bidirectional stiffness in Configuration 1. Through discussing the advantages and disadvantages of different module layouts, this paper provides a preliminary knowledge basis for applications of fully high-rise MSCs in seismic regions.

Computational and ultrafast ultrasound assessment of arterial bi-directional stiffness from spontaneous pulsatile waves

Computational and ultrafast ultrasound assessment of arterial bi-directional stiffness from spontaneous pulsatile waves

Bi-Directional Stiffness for Airfoil Camber Morphing

This paper explores a new design for an airfoil whose chordwise bending stiffness varies with direction of applied load. By designing the region aft of the spar to be very stiff under upward load, uncommanded camber deformation under aerodynamic pressure can be minimized. At the same time, lower stiffness under reversed load reduces actuation requirement to achieve a desired downward camber deformation. Rigid cantilevers extending from the rear of the spar toward the trailing edge, and flush with the lower skin are used to realize this goal. Under upward load the rigid cantilever engages and supplements the chordwise bending stiffness. But under downward load the lower skin breaks contact with the cantilever, and camber deformation can be achieved at low actuation effort. From two-dimensional ABAQUS™ finite element simulations an upward-to-downward stiffness ratio of 13.82 was obtained with a cantilever extending over the entire length of the conformable section, but the maximum downward camber deflection was limited to 10 deg. Reducing the cantilever length reduced the stiffness ratio but allowed higher maximum camber deformations. A three-dimensional prototype was fabricated using “moderate-length” cantilevers and the measured stiffness ratio (under upward-to-downward loading) was determined to be 5.12. The corresponding stiffness ratio from a three-dimensional ABAQUS finite-element simulation was found to be within 6% of experimental results.

Metasilicone

We present a method for designing and fabricating MetaSilicones ---composite silicone rubbers that exhibit desired macroscopic mechanical properties. The underlying principle of our approach is to inject spherical inclusions of a liquid dopant material into a silicone matrix material. By varying the number, size, and locations of these inclusions as well as their material, a broad range of mechanical properties can be achieved. The technical core of our approach is formed by an optimization algorithm that, combining a simulation model based on extended finite elements (XFEM) and sensitivity analysis, computes inclusion distributions that lead to desired stiffness properties on the macroscopic level. We explore the design space of MetaSilicone on an extensive set of simulation experiments involving materials with optimized uni- and bi-directional stiffness, spatially-graded properties, as well as multi-material composites. We present validation through standard measurements on physical prototypes, which we fabricate on a modified filament-based 3D printer, thus combining the advantages of digital fabrication with the mechanical performance of silicone elastomers.

Probabilistic Assessment of Abutment-Embankment Stiffness and Implications in the Predicted Performance of Short Bridges

This article investigates the bi-directional stiffness of abutment-embankment systems in highway overpasses, considering the contribution of the abutment foundation in the force-transfer mechanism and soil material uncertainty. Stiffness is probabilistically assessed through refined, three-dimensional nonlinear static analyses, after validation with large-scale experimental results. The force-displacement relationships as well as the corresponding variance are derived separately for different abutment configurations along the transverse and longitudinal direction. Application of the above expressions for the case of a well-studied highway overpass leads to distinctly different probability of failure at the system level compared to the prediction made based on conventional code-prescribed procedures.

Corrugated Composite Skins

Corrugated structures are flexible in the corrugation direction and stiff in the transverse one. Their bidirectional stiffness properties depend on the special geometries of corrugations. In the paper, a simple analytical model for the initial stiffness of different corrugated composites is developed. The elongation and the effective stiffness in the longitudinal and transverse directions of various corrugated structures (trapezoidal, rectangular, triangular, and quasi-sinusoidal) composites are calculated and compared. Different structural geometries of woven E-glass/epoxy composites are investigated. The validity of the analytical model used is demonstrated by comparing calculation results with experimental data.

Bidirectional Stiffness Material: A Potential Solution for Passive Shape-Morphing Wings

An ornithopter is a flying device created by mimicking the motion of birds or insects. Its wings play significant roles in determining flight performance and stability. For example, butterfly wings are demonstrated to possess significant differences in bending stiffness when considering the bending direction (up or down). Novel concepts are needed to build a passive shape-morphing wing structure that could change shape smoothly during flapping, and thus enable efficient flight. Traditionally, ornithopter wing structures have employed hinges between rigid wing sections or hinges along the leading edge to introduce the desired wing flexibility. Motivated by the scale structure found in butterfly wings, it was hypothesized that a biomimetic scale-type material system would possess the desired bidirectional stiffness response. A material system was manufactured by 3-D printing of polyhedral-shaped particles, assembling such particles in a dense planar array, and joining them with carbon fibers. In particular, the polyhedral shapes considered were tetrahedra, truncated tetrahedra, and Janus-type tetrahedra made of half soft and hard solid. These systems were tested in single-point load bending. For regular tetrahedra, the assemblies possess the same stiffness in both deflection directions ( !! !!#$ = 1 , due to symmetry), while the assemblies of the truncated tetrahedra ( !! !!#$ = 25.2 ) and of the Janus-type tetrahedra ( !! !!#$ = 4.7 ) exhibited significant bending stiffness asymmetries. These results confirm the initial hypothesis that scale-type structures are responsible for the bending stiffness asymmetry in biological wing structures. The results show that the proposed material system can imitate the function of a wing, and that the passive shapemorphing wing constructed using a bidirectional stiffness material presents a potential solution for ornithopters.