Optimal Stiffness Research Articles

Test-retest reproducibility of human brain multi-slice 1 H FID-MRSI data at 9.4T after optimization of lipid regularization, macromolecular model, and spline baseline stiffness.

This study analyzes the effects of retrospective lipid suppression, a simulated macromolecular prior knowledge and different spline baseline stiffness values on 9.4T multi-slice proton FID-MRSI data spanning the whole cerebrum of human brain and the reproducibility of respective metabolite ratio to total creatine (/tCr) maps for 10 brain metabolites. Measurements were performed twice on 5 volunteers using a short TR and TE FID MRSI 2D sequence at 9.4T. The effects of retrospective lipid L2-regularization, macromolecular spectrum and different LCModel baseline flexibilities on SNR, FWHM, fitting residual, Cramér-Rao lower bound, and metabolite ratio maps were investigated. Intra-subject, inter-session coefficient of variation and the test-retest reproducibility of the mean metabolite ratios (/tCr) of each slice was calculated. Transversal, sagittal, and coronal slices of many metabolite ratio maps correspond to the anatomically expected concentration relations in gray and white matter for the majority of the cerebrum when using a flexible baseline in LCModel fit. Results from the second measurements of the same subjects show that slice positioning and data quality correlate significantly to the first measurement. L2-regularization provided effective suppression of lipid-artifacts, but should be avoided if no artifacts are detected. Reproducible concentration ratio maps (/tCr) for 4 metabolites (total choline, N-acetylaspartate, glutamate, and myoinositol) spanning the majority of the cerebrum and 6 metabolites (N-acetylaspartylglutamate, γ-aminobutyric acid, glutathione, taurine, glutamine, and aspartate) covering 32 mm in the upper part of the brain were acquired at 9.4T using multi-slice FID MRSI with retrospective lipid suppression, a macromolecular spectrum and a flexible LCModel baseline.

Stiffness performance analysis of a 3-PRPS kinematically redundant parallel mechanism

The stiffness performance of a spatial kinematically redundant parallel mechanism (KRPM) with three relative degree-of-freedom (RDOF) is analyzed. Firstly, the composition principle of the KRPM is introduced, the RDOF is analyzed, the kinematics model is established, and the overall Jacobian matrix is established based on the screw theory. Secondly, the workspace of the KRPM is drawn, and the theoretical stiffness model is established considering the internal restraint force and the external load. The stiffness variation in the workspace is drawn, and the effectiveness of the theoretical stiffness model is verified through finite element analysis. Finally, according to the theoretical stiffness model, four task-based stiffness performance evaluation indexes are obtained, and they are optimized based on the NSGA-II multi-objective genetic algorithm. The results show that adding and adjusting redundant actuators in a parallel mechanism can effectively improve the stiffness performance of the mechanism. In the meantime, different stiffness optimization schemes can be proposed for different task paths based on the NSGA-II genetic algorithm.

Optimal design of functionally graded lattice structures using Hencky bar-grid model and topology optimization

Presented herein is a novel design framework for obtaining the optimal design of functionally graded lattice (FGL) structures that involve using a physical discrete structural model called the Hencky bar-grid model (HBM) and topology optimization (TO). The continuous FGL structure is discretized by HBM comprising rigid bars, frictionless hinges, frictionless pulleys, elastic primary and secondary axial springs, and torsional springs. A penalty function is introduced to each of the HBM spring’s stiffnesses to model non-uniform material properties. The gradient-based TO method is applied to find the stiffest structure via minimizing the compliance or elastic strain energy by adjusting the HBM spring stiffnesses subjected to prescribed design constraints. The optimal design of FGL structures is constructed based on the optimal spring stiffnesses of the HBM. The proposed design framework is simple to implement and for obtaining optimal FGL structures as it involves a relatively small number of design variables such as the spring stiffnesses of each grid cell. As illustration of the HBM-TO method, some optimization problems of FGL structures are considered and their optimal solutions obtained. The solutions are shown to converge after a small number of iterations. A Python code is given in the Appendix for interested readers who wish to reproduce the results.

Distribution law of strain energy density for stiffness design of GFRP, UT/GFRP, and VRB/GFRP hybrid hat‐shaped beams

AbstractThe structural optimization for stiffness performances with hundreds or thousands of design parameters is a complex and time‐consuming process. This is because, on the one hand, the direct relationship between the stiffness and the many design parameters is unknown, and on the other hand, the sensitivity of a single design parameter to the global stiffness is hardly obtained. Therefore, transforming the global stiffness performance to the strain energy density (SED) distribution over the whole structure can significantly simplify the optimization problem. In this work, the relationships among the design parameters, SED distribution and stiffnesses of glass fiber reinforced plastic (GFRP), uniform thickness metal (UT)/GFRP, and variable‐thickness rolled blanks (VRB)/GFRP hat‐shaped beams are investigated through numerical simulations. It is found that the higher SED of the all hat‐shaped beam structure indicates a worse stiffness performance under both bending and torsional conditions. When the SED of the GFRP hat‐shaped beam increases 6.65%, its bending stiffness decreases 10.8%. It is also found that the smaller SED distribution variance of the all hat‐shaped beam structures indicates a better stiffness performance. When the SED distribution variances of the VRB and GFRP in the VRB/GFRP hybrid beam are, respectively, reduced by 70.78% and 85.56%, the bending stiffness of the hybrid beam is increased by 50.83%. The above relations and conclusions indicate that the structural stiffness optimization problem with many design parameters can be replaced with the structural SED distribution variance minimization problem, which would not need the unavailable sensitivities of the design parameters to the global stiffness. Besides, compared to the GFRP hat‐shaped beam, with the same mass, volume or cost, the bending stiffnesses of the VRB/GFRP hat‐shaped beam, respectively, increases by 196.1%, 476.5%, and 676.4%, and its torsional stiffnesses, respectively, increases by 70.9%, 233.0%, and 348.4%. This means the combination of VRB and GFRP in the beam structure can reach a better stiffness performance and a higher lightweight level.

Tail-stiffness optimization for a flexible robotic fish

Undulation regulation in a robotic fish propelled by a passive flexible tail is more similar to that of a natural fish than with a rigid tail, owing to the smooth curvature of the flexible tail. Moreover, it has been observed that fish change the stiffness of their bodies to adapt to various swimming states. Inspired by this, a stiffness optimization scheme is explored for a novel elastic tail, which can improve the performance of the robotic fish. Spring steels are used as passive flexible joints of the fishtail; these can be easily expanded into multi-joint structures and the joint stiffness can be altered by changing the joint size. In this study, the Lagrangian dynamic method is employed to establish a dynamic model of the robotic fish in which passive flexible joints are simplified by a pseudo-rigid-body model. In addition, the hydrodynamics of the head and tail are analyzed using the simplified Morison equation and quasi-steady wing theory, respectively. Furthermore, to determine unknown hydrodynamic parameters in the dynamic model, a parameter identification method is applied. The results show that the identified simulation speeds fit the experimental speeds well within a wide range of stiffness values. Finally, to improve performance, the influence of joint stiffness and frequency on swimming speed is investigated based on the identified dynamic model. At each frequency, the optimal joint stiffness distribution is one that reduces the stiffness from the front to the rear. At the maximum driving frequency of 2.5 Hz, the optimal swimming speed is 0.3 body lengths per second, higher than that when rigid joints are used.

Novel Rubber Composites Based on Copper Particles, Multi-Wall Carbon Nanotubes and Their Hybrid for Stretchable Devices.

New technologies are constantly addressed in the scientific community for updating novel stretchable devices, such as flexible electronics, electronic packaging, and piezo-electric energy-harvesting devices. The device promoted in the present work was found to generate promising ~6V and durability of >0.4 million cycles. This stretchable device was based on rubber composites. These rubber composites were developed by solution mixing of room temperature silicone rubber (RTV-SR) and nanofiller, such as multi-wall carbon nanotube (MWCNT) and micron-sized copper particles and their hybrid. The hybrid composite consists of 50:50 of both fillers. The mechanical stretchability and compressive modulus of the composites were studied in detail. For example, the compressive modulus was 1.82 MPa (virgin) and increased at 3 per hundred parts of rubber (phr) to 3.75 MPa (MWCNT), 2.2 MPa (copper particles) and 2.75 MPa (hybrid). Similarly, the stretching ability for the composites used in fabricating devices was 148% (virgin) and changes at 3 phr to 144% (MWCNT), 230% (copper particles) and 199% (hybrid). Hence, the hybrid composite was found suitable with optimum stiffness and robust stretching ability to be useful for stretching electronic devices explored in this work. These improved properties were tested for a real-time stretchable device, such as a piezoelectric energy-harvesting device and their improved voltage output and durability were reported. In the end, a series of experiments conducted were summarized and a discussion on the best candidate with higher properties useful for prospective applications was reported.

Design of a More Efficient Rotating-EM Energy Floor with Lead-Screw and Clutch Mechanism

There is an interest in harvesting energy from people’s footsteps in crowded areas to power smart electronic devices with low consumption. The average power consumption of these devices is approximately 10 μW. The energy from our footsteps is green and free, because walking is a routine activity in everyday life. The energy floor is one of the most efficient pieces of equipment in vibration-based energy harvesting. The paper aims to improve the previous design of the energy floor—called Genpath—which uses a rotational electromagnetic (EM) technique to generate electricity from human footsteps. The design consists of two main parts of (1) the EM generator, including the lead-screw mechanism for translation-to-rotation conversion, and (2) the Power Management and Storage (PMS) circuit. The improvement was focused on the part of the EM generator. A thorough investigation of the design components reveals that the EM generator shaft in the previous Genpath design cannot continuously rotate when the floor-tile reaches the bottom end, resulting in no energy gain. Therefore, a one-way clutch is implemented to the system to disengage the generator shaft from the lead-screw motion when the floor-tile reaches the allowable displacement. During the disengagement, the EM generator shaft still proceeds with a free rotation and could generate more power. In our analysis, the dynamic model of the electro-mechanical systems with the one-way clutch was successfully developed and used to predict the energy performances of the VEH floors and fine-tune the design parameters. The analytical result is shown that the spring stiffness mainly affects the force transmitted to the EM generator, and then the induced voltage and power of the generator, thus, the value of the stiffness is one of the critical design parameters to optimize. Finally, the new prototype consisting of 12-V-DC generator, mechanisms of lead-screw and clutch, as well as coil springs with the optimal stiffness of 1700 N/m was built and tested. The average energy produced by the new prototype is 3637 mJ (or average power of 3219 mW), per footstep which is 2935 mJ greater than that of the previous design. Moreover, to raise the social awareness about energy usage, the sets of Genpath have been used to organize an exhibition, “Genpath Empower our Journey”. The people who stroll forward on the paths can realize how much energy they gain from their footsteps.

Evaluation of Lower Limb Exoskeleton for Improving Balance during Squatting Exercise using Center of Pressure Metrics

The foot center of pressure (COP) variability is an important indicator of balance, particularly relevant for rehabilitation and training using wearable lower limb exoskeletons. This study aimed to evaluate the effectiveness of our exoskeleton in assisting squatting motion using the COP variability as a metric. Six human subjects performed alternate squatting and standing movements while their foot pressure and COP trajectories were recorded using insole pressure sensors. The exercises were performed under three conditions: i) no device, ii) unpowered device, and iii) device with optimal stiffness. Results showed that the variability of the COP trajectory in the anterior-posterior direction of the foot during squatting tended to be lower for the optimal stiffness condition than the no device and unpowered device conditions, indicating the potential usefulness of the device in improving balance during squatting. This study has implications for human-inthe-loop optimization and balance control of the exoskeleton based on COP.

The effect of subject characteristics and walking speed on optimal ankle foot orthosis stiffness– a predictive simulation study

The effect of subject characteristics and walking speed on optimal ankle foot orthosis stiffness– a predictive simulation study

Relationship between Joint Stiffness, Limb Stiffness and Whole–Body Center of Mass Mechanical Work across Running Speeds

The lower–extremity system acts like a spring in the running stance phase. Vertical stiffness (Kvert) and leg stiffness (Kleg) reflect the whole–body center of mass (COM) and leg–spring system loading and response in running, while joint stiffness (Kjoint) represents joint–level dynamic loading and response. This study aimed to investigate whether Kjoint is associated with Kvert and Kleg across different running speeds. Twenty healthy subjects were recruited into a treadmill running study (1.8 to 3.8 m/s, with 0.4 m/s intervals). We found that Kjoint accounted for 38.4% of the variance in Kvert (p = 0.046) and 42.4% of the variance in Kleg (p = 0.028) at 1.8 m/s; Kjoint also accounted for 49.8% of the variance in Kvert (p = 0.014) and 79.3% of the variance in Kleg (p < 0.0001) at 2.2 m/s. Kknee had the strongest unique association with Kvert and Kleg at 1.8 and 2.2 m/s. Kjoint was associated with Kleg at a wider range of speeds. These findings built a connection between joint stiffness and limb stiffness within a certain range of running speeds. Kknee may need to be considered as an important factor in future limb stiffness optimization and general running performance enhancement.

Aeroelastic method to investigate nonlinear elastic wing structures

Stiffness directions of wing structures are already part of the optimisation in aircraft design. Aircraft like the A350 XWB and the Boeing 787 mainly consist of such composite material, whose stiffness directions can be optimised. To proceed with this stiffness optimisation, the aim of this work is to modify and optimise also the linear stress-strain relation. On that account, the Hooke’s law is exchanged by a multi-linear formulation to analyse any nonlinear elastic structural technology on wing structures. The wing structures, which are used to investigate the nonlinear behaviour, are deduced from a mid-range and a long-range aircraft configuration. These wings are analysed with an extended beam method and coupled with a VLM solution to calculate the aeroelastical loading. The proposed beam method is capable of analysing any multi-linear wing structure technology. A degressive structural behaviour shows up a good potential to reduce the bending moment which is one of the main drivers of the structural weight.

Variable stiffness locomotion with guaranteed stability for quadruped robots traversing uneven terrains.

Quadruped robots are widely applied in real-world environments where they have to face the challenges of walking on unknown rough terrains. This paper presents a control pipeline that generates robust and compliant legged locomotion for torque-controlled quadruped robots on uneven terrains. The Cartesian motion planner is designed to be reactive to unexpected early and late contacts using the estimated contact forces. Moreover, we present a novel scheme of optimal stiffness modulation that aims to coordinate desired compliance and tracking performance. It optimizes joint stiffness and contact forces coordinately in a quadratic programming (QP) formulation, where the constraints of non-slipping contacts and torque limits are imposed as well. In addition, the issue of stability under variable stiffness control is solved by imposing a tank-based passivity constraint explicitly. We finally validate the proposed control pipeline on our quadruped robot CENTAURO in experiments on uneven terrains and, through comparative tests, demonstrate the improvements of the variable stiffness locomotion.

Enhancing the ride comfort of off-road vibratory rollers with seat suspension using optimal quasi-zero stiffness

The research proposes a new design of the seat suspension equipped with the quasi-zero stiffness (QZS) and hydraulic mount (HM) of the cab isolation system to improve the ride comfort of off-road vibratory rollers. To assess the ride comfort of the vehicle using the QZS and the HM, a dynamic model of the off-road vibratory roller is built and researched under various interactions of the drum/wheel and off-road terrain. Based on the multi-objective genetic algorithms, the design parameters of the QZS are also optimized to further enhance the vehicle’s ride comfort. The QZS optimized (QZSO)’s efficiency and the ride comfort of the off-road vibratory roller are analyzed based on the indexes of the seat displacement and acceleration; and the cab’s pitching and rolling acceleration. The experimental investigation is then carried out to verify the accuracy of the mathematical model and research result. The investigation result indicates that with the QZSO applied on the seat isolation, the Root-Mean-Square and Power-Spectral-Density of the acceleration responses of the seat and cab are greatly decreased compared to the seat isolation without the QZS in both the time and frequency regions. Particularly, the Root-Mean-Square acceleration of the seat is remarkably decreased by 61.7% when the vehicle is moving and 67.5% when the vehicle is working. Consequently, this research can provide a valuable reference and knowledge for the application of the QZSO on the driver’s seat suspension of off-road vehicles to optimize ride comfort.

A compact inchworm piezoelectric actuator with high speed: Design, modeling, and experimental evaluation

Inchworm piezoelectric actuators are usually composed of three or more piezoelectric stacks, which makes their structures and circuits sophisticated. Although a variety of inchworm piezoelectric actuators driven by fewer piezoelectric stacks have been proposed to realize the simplification of the traditional structures. It is still difficult to inherit the advantage of large output force and achieve high output speed without backward motion for a simplified inchworm actuator. Here, we present a compact inchworm piezoelectric actuator with two multi-function driving feet, in which only two piezoelectric stacks are utilized. The deformations of the driving feet are utilized efficiently by the proposed working principle, and four steps in each cycle are realized, which improve the output speed of the proposed actuator. The stiffness optimization is carried out to obtain a stable step characteristic and a high output force. Under a voltage of 150 V and a frequency of 50 Hz, the actuator achieved a maximum speed of 2081.16 μm/s, a carrying load larger than 6.442 kg and an output force of 14 N. Furthermore, this actuator also achieved a stable step process without backward motion under a carrying load of 6.442 kg.

Enhanced DC power delivery from a rotational tristable energy harvester driven by colored noise under various constant speeds

This paper investigates the DC power delivery from a rotational tristable energy harvester (TEH) interfaced with a rectifier circuit driven by colored noise. The nonlinear electromechanical coupling equation of the rotational TEH under colored noise is derived, where the mutual coupling behavior caused by the rectifier circuit is also included. Then, the analytical expressions of the joint probability density function (JPDF) and mean DC power are derived under different constant speeds by using the stochastic averaging based on energy-dependent frequency. In order to enhance the DC power delivery, the effects of colored noise, rotational constant speed and structural parameters on dynamical behaviors and harvesting performance are analyzed. The obtained results suggest that by choosing an appropriate rotational speed or electromechanical coupling coefficient, the rectified voltage can reach the maximum while the JPDF has a symmetric tristable structure. The optimal nonlinear stiffness coefficients can be obtained by adjusting the position of the magnets to maximize the DC power. Unlike the monotonically decreasing rectification efficiency, the power conversion efficiency is approximately proportional to the time constant ratio. Therefore, a proper choice of time constant ratio is very important for the optimal design of the harvester. Finally, the numerical simulation and experimental results verify the effectiveness of the theoretical analysis.

Stiffness optimization design for TPMS architected cellular materials

The unique topology-driven versatility of natural biological systems has motivated the material science research community to design and synthesize architected cellular materials for different engineering disciplines. However, the lattice cell design of architected cellular materials is highly arbitrary, making the design of architected cellular materials very difficult. In order to overcome these problems, an innovative triple period minimal surface (TPMS) lattice type distribution algorithm based on the maximum strain energy principle is proposed in this paper to optimize the stiffness of the structure. The algorithm establishes the mapping relationship between the relative density of TPMS lattice cells and the surface bias parameter t by generating a voxel model, obtains the equivalent mechanical properties of lattice cells as a function of relative density by homogenization algorithm and function fitting, establishes a TPMS lattice database, and innovatively distributes the TPMS lattice types by selecting the maximum strain energy lattice cells on the basis of the topology optimization results. The experimental results show that the stiffness of the multi-TPMS lattice structure is improved by 55.89% and 30.15%, respectively, compared with the two single lattice structures.

Unified multiscale theory of cellular mechanical adaptations to substrate stiffness

Rigidity of the extracellular matrix markedly regulates many cellular processes. However, how cells detect and respond to matrix rigidity remains incompletely understood. Here, we propose a unified two-dimensional multiscale framework accounting for the chemomechanical feedback to explore the interrelated cellular mechanosensing, polarization, and migration, which constitute the dynamic cascade in cellular response to matrix stiffness but are often modeled separately in previous theories. By combining integrin dynamics and intracellular force transduction, we show that substrate stiffness can act as a switch to activate or deactivate cell polarization. Our theory quantitatively reproduces rich stiffness-dependent cellular dynamics, including spreading, polarity selection, migration pattern, durotaxis, and even negative durotaxis, reported in a wide spectrum of cell types, and reconciles some inconsistent experimental observations. We find that a specific bipolarized mode can determine the optimal substrate stiffness, which enables the fastest cell migration rather than the largest traction forces that cells apply on the substrate. We identify that such a mechanical adaptation stems from the force balance across the whole cell. These findings could yield universal insights into various stiffness-mediated cellular processes within the context of tissue morphogenesis, wound healing, and cancer invasion.

진동을 고려한 보빈 홀더의 전산모사 모델의 개발

The goal of this study is to develop an FE model for bobbin holders which wind the fiber. It comprised 25 components. Under mechanical assumption, it was simplified and approximated to 8 components. The equivalent stiffness of three types of bearings in a bobbin holder were obtained using compression tests. The main natural frequency of a precision model without a chuck was 17.82 ㎐ in mode 1 and 102.95 ㎐ in mode 3. The results of simulation and experimental analysis by modal testing were very similar within 2%. To obtain a more precise FE model, optimization for equivalent stiffness of the 6011 bearing was applied to modal analysis in the ANSYS. Finally, an FE model of a bobbin holder considering vibrations was developed.

Customized Multifunctional Peptide Hydrogel Scaffolds for CAR-T-Cell Rapid Proliferation and Solid Tumor Immunotherapy.

CAR-T-cell therapies must be expanded to obtain a large number of effector cells quickly, and the current technology cannot address this challenge. A longer operational time would lose or alter the function and phenotype of CAR-T cells in response to therapy, and it also causes a loss in the optimal treatment time for patients. At present, lower survival time and homing efficiency reduce the antitumor effect of CAR-T in vivo. But nobody has solved these two issues in one system, which has a similar microenvironment of lymphoid organs to activate/expand cell delivery for immunotherapy. Here, we generated artificial, customized immune cell matrix scaffolds based on a self-assembling peptide to preserve and augment the cell phenotype in light of the characteristics of CAR-T. The all-in-one nanoscale matrix scaffolds reduced the processing time of CAR-T to 3 days and resulted in over a 10-fold increase compared with the traditional protocol. The cells were combined to modulate mechanotransduction and chemical signals, and the mimic matrix scaffolds showed optimal stiffness and adhesive ligand density, thereby accelerating CAR-T-cell proliferation. Meanwhile, engineering CAR-T-secreted intrinsic PD-1 blocking single-chain variable fragments (scFv) further increased cell proliferation and cytotoxicity by resisting the self and tumor microenvironment in a paracrine and autocrine manner. Local delivery of CAR-T cells from the scaffolds significantly enabled long-term retention, suppressed tumor growth, and increased infiltration of effector T cells compared with traditional CAR-T treatment. The application of bioengineering and genetic engineering approaches has led to the development of rapid culture environments that can control matrix scaffold properties for CAR-T-cell and cancer immunotherapies.

Semi-Physical Simulation Optimization Method for Bolt Tightening Process Based on Reinforcement Learning

Bolted connections are the main method of connecting the components of an aero-engine low pressure rotor. Due to the influence of the elastic interaction relationship, it is easy to cause uneven distribution of the preload force of the bolt group, although it can meet the stiffness needs; however, it may lead to the deflection of the spatial relative position of the components, which is can easily cause coaxiality overrun. In view of the contradictory problem of optimization between coaxiality and stiffness of rotor assembly, this paper proposes a semi-physical simulation optimization method for the bolt tightening process based on reinforcement learning. Firstly, by studying the elastic interaction mechanism between the bolts, the elastic interaction matrix was established using finite element simulation data. On this basis, a coaxiality prediction model for the bolt tightening process was established using a GRU (gate recurrent unit) network to realize the prediction of coaxiality in the bolt tightening process. Then, through the analysis of the bolt connection stiffness, a stiffness calculation model containing the bolt stiffness, the stiffness of the connected parts, and the contact stiffness of the joint surface in series was constructed to realize the calculation of the stiffness during the bolt tightening process. Finally, with the bolt preload force as the optimization variable, coaxiality and stiffness as the optimization target, and the tightening torque and preload force of the installed bolts in the actual assembly process as the constraints, a semi-physical simulation optimization model of the bolt tightening process was established using reinforcement learning to realize the optimization of the bolt tightening process. Moreover, through the semi-physical simulation optimization method, the bolt tightening process can be installed and adjusted at the same time.