Equivalent Stiffness Research Articles

Implicit Low-Rank Riemannian Schemes for the Time Integration of Stiff Partial Differential Equations

We propose two implicit numerical schemes for the low-rank time integration of stiff nonlinear partial differential equations. Our approach uses the preconditioned Riemannian trust-region method of Absil, Baker, and Gallivan, 2007. We demonstrate the efficiency of our method for solving the Allen–Cahn and the Fisher–KPP equations on the manifold of fixed-rank matrices. Our approach allows us to avoid the restriction on the time step typical of methods that use the fixed-point iteration to solve the inner nonlinear equations. Finally, we demonstrate the efficiency of the preconditioner on the same variational problems presented in Sutti and Vandereycken, 2021.

Stiffness optimization design of wheeled-legged rover integrating active and passive compliance capabilities

Compliance capability is one of the most important properties of suspension systems for rough-terrain robots. This imposes specific requirements on system stiffness design, which directly determines the platform's performance in response to external stimuli. To address the challenge of stiffness optimization design in active and passive compliant systems, this paper proposes a novel and practical method for optimizing stiffness for a terrain-adaptive wheel-legged rover. Firstly, the kinematic model of this multi-degree-of-freedom platform is established. Secondly, the deformation capability coefficient, load capacity coefficient, energy efficiency coefficient, and dynamic stability coefficient are derived as performance indices to assess the behavior of the system. By establishing the relationship between joint configuration variation and system stiffness, stiffness parameters could be evaluated through these performance indices. Ultimately, the global optimum stiffness parameters are selected from the refined intersection of the individual performance optimal domains. Thirdly, the optimum parameters are calculated and applicability verified numerically. The designed parameters are verified experimentally on a wheeled-legged rover. The experimental results demonstrate that the proposed algorithm can find the parameter combination that achieves optimal system performance, thereby enhancing the system's terrain adaptability.

Homogenized Modeling of CO2/CO Reduction Catalyst Microenvironments with Intermixed Hydrophobic and Hydrophilic Regions

Electroreduction of CO and CO2 offer a pathway toward renewable-powered synthesis of hydrocarbon chemicals and fuels. Both the composition and the structure of cathodic catalyst microenvironments in gas diffusion electrodes play a dominant role in determining the product composition and efficiency metrics. Porous and hydrophilic copper environments are known to produce multi-carbon species and exhibit large active surface areas, but recent investigations have shown that the inclusion of sporadically-distributed porous hydrophobic regions creates additional pathways for the delivery of gaseous reactants, thereby mitigating transport limitations seen in pure Cu catalysts.As the design space for catalysts has grown to include a wide variety of material and geometric parameters, accurate PDE-based modeling and simulation of such systems has become necessary to understand and optimize the coupled reaction and transport processes that determine cell performance. High fidelity models, however, pose immense computational challenges. Physical and chemical processes occur over a wide variety of spatiotemporal scales, ranging from pore-scale reaction and transport to device-scale gradients in species concentrations. Additionally, the spatial orientation of these features necessitates modeling in multiple dimensions, and transport occurs simultaneously through two phases located within randomly-intermixed porous regions. As a result of all these factors, numerical simulation of high fidelity models is prohibitively expensive.In this work, we develop, numerically simulate, and validate a predictive model that efficiently incorporates a wide range of physical and chemical processes occurring in catalyst microenvironments with intermixed hydrophobic and hydrophilic regions. We employ homogenization as a means of model reduction, constructing a medium fidelity model that captures both microenvironment geometric scales and full device scales in 3D. Our model, coupled with the appropriate numerical methods for treatment of stiff and multi-dimensional problems, permits low-cost exploration of the high-dimensional parameter space associated with recently developed catalysts, offering quantitative insight into the optimal design of microenvironments for CO and CO2 electroreduction.This work is supported by the United States Department of Energy under grant DE-SC0021633.

Study on the allowed maximum amplitudes of low-order polygonal wear on resilient wheels based on operational safety

Following the extensive use of resilient wheels on trams, several subways in China have started pre-launch testing of resilient wheels. While it remains at an early stage, the long-term behavior of the wheel has become a great concern for subway operators and wheel suppliers. To address the concern, this study focuses on derailment risk by evaluating the allowed maximum amplitudes of low-order polygonal wear on resilient wheels. Firstly, a metro vehicle-track dynamic system model equipped with resilient wheels is built. Then, based on the operation safety index and current re-profiling regulations for conventional wheels, the influence of wheel axial and radial stiffness on the radial amplitude limits of resilient wheel polygonal wear is analyzed. To perform the analysis, firstly the commonly-used stiffness for a resilient wheel (300 kN/mm in radial direction and 50 kN/mm in axial direction) is adopted to study the effect of resilient wheel polygonization on wheel load reduction ratio. Then, wheel load reduction ratio is predicted for different radial (up to 600 kN/mm) and axial (up to 100 kN/mm) stiffnesses of the resilient wheel and different orders (up to 10) of wheel polygonization of 1 mm amplitude. A contour plot is provided to illustrate how the wheel load reduction ratio varies with the harmonic order and amplitude of wheel polygonization under different combinations of resilient wheel’s equivalent axial and radial stiffnesses. It is found that, with the increase of the amplitude of the polygonal wear of a certain harmonic order on resilient wheel, the number of the available combinations of the equivalent stiffnesses adopted by the resilient wheel becomes less by considering the operation safety indexed with wheel load reduction ratio. Besides, depending on the stiffness of the resilient wheel, the allowed amplitude corresponding to the polygonization of each order has been suggested with the contour plots.

A Review of Machine Tool Motorized Spindle Variable Pressure Preload Technology Research

High-precision spindles are a vital study topic because of the growing demand for highspeed, high-precision, reliable, and long-lasting machine tools. Bearing preload is the primary means of improving the accuracy of the spindle rotor system. This study aims to summarize the research results, systematically analyze and evaluate the machine tool motorized spindle variable pressure preload technology, and provide a scientific basis for the practical application of the motor spindle variable pressure preload technology. This study is an in-depth analysis of the basic principles of the electric spindle preloading technology, the study of its influence mechanism on the thermal deformation, stiffness, slewing error, and life of the spindle system, and a discussion of the current shortcomings in the field of spindle preloading to provide a reference for the subsequent optimization. In the spindle system, the performance of rolling bearings and the design of bearing preload have an important impact on the spindle's accuracy and stability. The traditional preload method has yet to meet the requirements of modern high-speed machine tools. Real-time controllable preload has become the new direction of development, but the current preload technology still has certain limitations and needs to be further improved. In the future, the spindle bearing variable pressure preload technology will be more efficient and intelligent.

A novel ionic model for matured and paced atrial-like human iPSC-CMs integrating [formula omitted] and [formula omitted] currents

This work introduces the first atrial-specific in-silico human induced pluripotent stem cells-derived cardiomyocytes (hiPSC-CMs) model, based on a set of phenotype-specific IKur,IKCa and IK1 membrane currents. This model is built on novel in-vitro experimental data recently published by some of the co-authors to simulate the paced action potential of matured atrial-like hiPSC-CMs. The model consists of a system of stiff ordinary differential equations depending on several parameters, which have been tuned by automatic optimization techniques to closely match selected experimental biomarkers. The new model effectively simulates the electronic in-vitro hiPSC-CMs maturation process, transitioning from an unstable depolarized membrane diastolic potential to a stable hyperpolarized resting potential, and exhibits spontaneous firing activity in unpaced conditions. Moreover, our model accurately reflects the experimental rate dependence data at different cycle length and demonstrates the expected response to a specific current blocker. This atrial-specific in-silico model provides a novel computational tool for electrophysiological studies of cardiac stem cells and their applications to drug evaluation and atrial fibrillation treatment.

Equivalent stiffness analysis of flexible lithium-ion batteries with repeated unit cell: A computational approach

Flexible batteries have recently developed significant advancements in structural design, diverging substantially from traditional battery architectures. However, conventional mechanical testing methods and metrics, tailored for standard battery structures, prove inadequate when evaluating the flexibility of these innovative designs. How to assess the mechanical performance of diverse structural configurations of flexible batteries poses a considerable challenge. In this study, a general computational approach is proposed to evaluate the equivalent stiffness of flexible lithium ion batteries (FLIBs) by analyzing the force–deformation response of a repeated unit cell (RUC), thereby enabling a comprehensive comparison of different FLIB designs. Moreover, to further enhance their deformability, the interconnected supple components of FLIBs have been optimized. This research lays a critical foundation for comparing the mechanical performance and optimizing the design of flexible batteries in the future.

A study on maglev force and vibration attenuation characteristics of quasi-zero stiffness cruciform maglev isolator.

This paper aims to study the maglev force and vibration attenuation characteristics of quasi-zero stiffness cruciform maglev isolators (CMIs). The maglev force and stiffness of CMIs were analytically computed based on equivalent charge theory, and the transfer function of the system was conducted. The effects of magnet geometry parameters and air gap on the maglev force, stiffness, and vibration transmission characteristics of the CMI system were revealed through parametric analyses. With the increase in magnet length and width, the maximum value of maglev force increases, but the displacement range of near-zero stiffness, amplitude, and phase of the system gradually decrease. With the increase in magnet height, the displacement range of near-zero stiffness increases, while the variation in the amplitude and phase of the system has minimal impact. Meanwhile, in the Halbach array, the height variation of the magnet at different positions has different impacts on the magnetic force. As the air gap increases, the maximum value of maglev force decreases, but the amplitude and phase gradually increase, and the displacement range of near-zero stiffness first rises and then decreases. Finally, an experimental study was carried out to test the vibration attenuation characteristics of CMIs, in which sinusoidal excitation, hammer strike excitation, and random excitation were applied.

The stick-slip bending behavior of the multilevel helical structures: A 3D thin rod model with frictional contact

The multilevel helical structures in various engineering and natural fields offer excellent deformation flexibility and load bearing capabilities. Understanding the interplay between the local frictional contact and the geometric characteristics of the helical structure under complex external loads has attracted considerable interest. In this work, the effect of local frictional contact behaviors on the bending in multilevel helical structures is investigated by using a combination of theoretical modeling, finite element (FE) simulations, and experiments. In the case of pure bending, the kinematic parameters of the bent multi-stage helix are derived concisely by the idea of the kinematic analogy. The bending stiffness of the multi-stage helix is further obtained. In the case of the combined tension/torsion and bending, the 3D thin rod model incorporating Coulomb’s friction is established to describe the mechanical responses. It is found that the relationship between equivalent bending stiffness and the laying angle exhibits nonlinearity. A comparison with the classical Papailiou model reveals that, for helical structures at large laying angles, the influence of friction is primarily determined by the internal force in the tangential direction, which is the core assumption of the Papailiou model. However, in the case of small laying angles, the helical twisting characteristics and the contribution of the internal forces and moments in the other two directions (normal and binormal directions) to the friction cannot be ignored. Subsequently, a multilevel frictional contact transmission formulation is proposed according to the force action–reaction principle. Based on the above formulation, the non-simplified thin rod equations with Coulomb’s friction are extended to describe the multilevel stick-slip bending behaviors of the second stage cable (3*3). The dissipation capacity of helical structures is evaluated quantitatively under the hysteretic bending. Finally, the theoretical model is verified by FE simulations and experimental results. This work provides insights for unveiling the intrinsic relationship between the nonlinear bending and local frictional contact behaviors in the multilevel helical structures.

Acute effects of static stretching exercise-induced decrease in arterial stiffness on maximal aerobic capacity.

We recently have reported that individual day-to-day arterial stiffness variations are associated with maximal aerobic capacity. However, the evidence of this phenomenon was not provided sufficiently. The present study aimed to examine whether a decrease in arterial stiffness through static stretching exercise could enhance maximal aerobic capacity. Twelve healthy young men (age 22±2 years, mean and standard deviation) participated in this study and underwent two separate sessions in a randomized controlled crossover design: a single session of a whole-body static stretching exercise protocol that involved the trunk, upper limb, and lower limb (stretch condition), and sedentary control where they rested in the exercise room. Brachial-ankle pulse wave velocity (baPWV) was measured as an index of systemic arterial stiffness before, immediately after and at 30 min after both conditions. Maximal oxygen uptake (V̇O<inf>2</inf>max) was assessed using a graded power test on an electronically braked cycle ergometer after these measurements. As we expected, there was a significant decrease in the baPWV at 30 min after the stretch trial compared to baseline values (P=0.01). The baPWV in the stretch condition was lower than that of the control condition, while V̇O<inf>2</inf>max in the stretch condition was higher than that of the control condition (P=0.03). Based on these findings, it can be inferred that an acute reduction in arterial stiffness may contribute to change in maximal aerobic capacity.

Systemic hemodynamics and pediatric lung disease: mechanistic links and therapeutic relevance.

Chronic lung disease, also known as bronchopulmonary dysplasia, affects thousands of infants worldwide each year. The impact on resources is second only to bronchial asthma, with lung function affected well into adolescence. Diagnostic and therapeutic constructs have almost exclusively focused on pulmonary architecture (alveoli/airways) and pulmonary hypertension. Information on systemic hemodynamics indicates major artery thickness/stiffness, elevated systemic afterload, and/or primary left ventricular dysfunction may play a part in a subset of infants with severe neonatal-pediatric lung disease. Understanding the underlying principles with attendant effectors would aid in identifying the pathophysiological course where systemic afterload reduction with angiotensin-converting enzyme inhibitors could become the preferred treatment strategy over conventional pulmonary artery vasodilatation.NEW & NOTEWORTHY Extremely preterm infants are at a higher risk of developing severe bronchopulmonary dysplasia. In a subset of infants, diuretic and pulmonary vasodilator therapy is ineffective. Recent information points toward systemic hemodynamic disease (systemic arterial stiffness and left ventricular dysfunction) as a contributor via back-pressure changes. Mechanistic links include heightened renin angiotensin aldosterone system activity, inflammation, and oxygen toxicity. Angiotensin-converting enzyme inhibition may be operationally more suited compared with induced pulmonary artery vasodilatation.

Krylov-based adaptive-rank implicit time integrators for stiff problems with application to nonlinear Fokker-Planck kinetic models

We propose a high order adaptive-rank implicit integrators for stiff time-dependent PDEs, leveraging extended Krylov subspaces to efficiently and adaptively populate low-rank solution bases. This allows for the accurate representation of solutions with significantly reduced computational costs. We further introduce an efficient mechanism for residual evaluation and an adaptive rank-seeking strategy that optimizes low-rank settings based on a comparison between the residual size and the local truncation errors of the time-stepping discretization. We demonstrate our approach with the challenging Lenard-Bernstein Fokker-Planck (LBFP) nonlinear equation, which describes collisional processes in a fully ionized plasma. The preservation of the equilibrium state is achieved through the Chang-Cooper discretization, and strict conservation of mass, momentum and energy via a Locally Macroscopic Conservative (LoMaC) procedure. The development of implicit adaptive-rank integrators, demonstrated here up to third-order temporal accuracy via diagonally implicit Runge-Kutta schemes, showcases superior performance in terms of accuracy, computational efficiency, equilibrium preservation, and conservation of macroscopic moments. This study offers a starting point for developing scalable, efficient, and accurate methods for high-dimensional time-dependent problems.

Deformation Characteristics and Response Factors of Rock Bolt Body in Roadway with Layered Composite Roof

Layered composite roofs are characterized by developed bedding fissures, resulting in severe deformation and damage of rock bolts at the top of the roadway, as well as a poor roadway support effect. Increasing pretension force is an effective way to enhance the stiffness of the rock bolt support system. To clarify the influence and mechanism of the pretension force on the support effect of rock bolts in the layered roof, a roadway model of the layered roof was established using the interface unit of FLAC3D, and the simulation rock bolts were constructed using the pile unit, which can simulate the mechanical behaviors of rock bolts, such as tension, shear, bending, fracture, and anchor failure, and the pretension force was applied. On this basis, the deformation and failure characteristics and influencing factors of rock bolts in the layered roadway roof under different surrounding rock conditions were simulated and analyzed. The research shows the following: ① Field measurements showed minor shear deformation in the rock bolts at the center of the roadway roof, with lateral displacements of 5.7 cm and 5.3 cm. Significant shear deformation occurred in the rock bolts at the roof corners, with lateral displacements of 18.2 cm and 17.6 cm. ② Simulations of rock bolt deformation characteristics matched the field measurements closely, confirming the reliability of the simulation method, parameter selection, and calculation sequence. ③ The primary factors affecting rock bolt deformation are the structural plane strength and surrounding rock strength. Rock bolts are most susceptible to lateral displacement when the structural plane strength is low, the strength difference between rock layers is large, and the weaker layer is below the structural plane. The presented research can provide a reference for the instability mechanism and support treatment of the layered composite roof roadway.

Stability analysis of explicit exponential Rosenbrock methods for stiff differential equations with constant delay

Delay differential equations have been used to model numerous phenomena in nature. We extend the previous work of one of the authors to analyze the stability properties of the explicit exponential Rosenbrock methods for stiff differential equations with constant delay. We first derive sufficient conditions so that the exponential Rosenbrock methods satisfy the desired stability property. We accomplish this without relying on some extreme constraints, which are usually necessary in stability analysis. Then, with the aid of the integral form of the method coefficients, we provide a simple stability criterion that can be easily verified. We also present a theorem on the order barrier for the proposed methods, stating that there is no method of order five or higher that satisfies the simple criterion. Numerical tests are carried out to validate the theoretical results.

Identifying failure connection area on wall for deep excavation based on system stiffness influence factor

In this study, a methodology to identify weak or failure connection area on the wall of deep excavation was proposed based on the system stiffness influence factor (IF), which can be beneficially utilized for wall-collapse prevention and forecasting system. Irregular excavation configuration common in urban areas and various weak-connection locations were considered. Three-dimensional finite element analyses with full consideration of actual staged excavation and strut-waler connection condition were performed. It was found that wall deflection and ground movement increased as the location of weak connection became deeper. It was also found that the influence of weak connection on the wall behavior became more pronounced as it located towards the center of the wall. The effects of weak connection on wall deflection were evaluated and quantified using IF. A modification procedure for IF was introduced to consider the effects of depth and horizontal weak-connection locations. The modified IF was adopted to establish a method for quantifying and identifying weak or failure connection area on the wall based on measured wall deflection from field monitoring. Case examples were selected to check the validity of the proposed method. The compared results showed that monitored and predicted locations of weak connection were in close agreement.

Investigation of a novel hydraulic tunnel composite lining with polyurea coating interlayer

PurposeMultilayer composite liner structures are the primary structural form of hydraulic tunnels. However, the bearing mechanism of multilayer composite liners has not been investigated thoroughly. Many existing design schemes do not properly achieve a balance between structural safety, anti-seepage capacity, and cost effectiveness. Thus, a new composite liner structure type and its theoretical model was proposed.Design/methodology/approachA novel hydraulic tunnel composite liner structure with a polyurea spray coating interlayer was proposed in this study. A theoretical model based on the state-space method was developed and verified using FEM models and existing theoretical models. Parametric analysis was conducted based on the theoretical model to investigate the influence of various variables, including interfacial shear stiffness, inner liner thickness, and outer liner elastic modulus.FindingsIt was concluded that the proposed theoretical model can be used successfully to calculate multilayer composite liner structures with high calculation efficiency. The overall deformation stiffness of the composite liner system increased with the interfacial shear stiffness. The sprayed coating interlayer significantly affects the residual force distribution between the outer and inner liners, which can also be affected by the adjustment of the thickness of the outer and inner liners. Thus, attention should be paid to these factors in the rational design of the proposed composite liner system.Originality/valueWith the development of China’s water conservancy projects, complex geological conditions, high surrounding rock stress, high internal and external water pressures, and other unique application scenarios have gradually increased. This places higher requirements on the bearing performance and impermeability of hydraulic tunnel lining structures. On the other hand, conventional hydraulic tunnel lining structures can hardly achieve a satisfactory balance between economy, structural safety, and impermeability. Thus, the proposed structure has the potential to be used in a wide range of applications.

Photon-beam-inducing synthesis of a tunable porous graphene/Ti3C2T x heterostructure for energy conversion-storage system

Flexible electronic device requires a novel micro-supercapacitors (MSCs) energy conversion-storage system based on two-dimensional (2D) materials to solve the problems of stiffness and complexity. Herein, we report a novel catalytic introduction method of graphene with adjustable porosity by high-energy photon beam. The graphene/Ti3C2T x heterostructure was constructed by electrostatic self-assembly, has a high cycle life (98% after 8000 cycles), energy density (11.02 mWh cm−3), and demonstrate excellent flexible alternating current line-filtering performance. The phase angle of −79.8° at 120 Hz and a resistance-capacitance constant of 0.068 ms. Furthermore, the porous graphene/Ti3C2T x structures produced by multiple catalytic inductions allowed ions to deeply penetrate the electrode, thereby increasing the stacking density. The special ‘pore-layer nesting’ graphene structure with adjustable pores effectively increased the specific surface area, and its superior matching with electrolyte solutions greatly improved surface-active site utilization. This work offers an alternative strategy for fabricating a 2D heterostructure for an MSC.

Quantitative Research on Roof Deformation and Temporary Support Stiffness in Deep-Mine Gob-Side Entry Retaining by Roof Cutting

The important technical process to ensure the success of gob-side entry retaining by roof cutting (GERRC) was the advanced pre-splitting blasting to cut off the mechanical connection between the roadway and working face roof. The whole-cycle roof structure evolution and stress characteristics of GERRC were analyzed. The factors affecting the roof deformation of GERRC were analyzed, and the quantitative relationship between the roof deformation of GERRC and the support stiffness was determined. The results showed that the temporary support stiffness was higher, the support position to the side of the roof cutting was closer, and the roof subsidence deformation of GERRC was smaller. It is proposed to use a single support mass with a high stiffness to control the deformation of the roof, but it also made the support mass and roof elastic potential energy aggregate. To fully utilize the matching of the support stiffness and roof subsidence, improve the stability, and control the subsidence deformation of the roof in GERRC, double-row stacking supports were adopted in the inclination of GERRC, which were used to increase the stiffness of the support system.

Cardiovascular Sequelae of Bronchopulmonary Dysplasia in Preterm Neonates Born before 32 Weeks of Gestational Age: Impact of Associated Pulmonary and Systemic Hypertension.

Bronchopulmonary dysplasia (BPD) remains the most common respiratory disorder of prematurity for infants born before 32 weeks of gestational age (GA). Early and prolonged exposure to chronic hypoxia and inflammation induces pulmonary hypertension (PH) with the characteristic features of a reduced number and increased muscularisation of the pulmonary arteries resulting in an increase in the pulmonary vascular resistance (PVR) and a fall in their compliance. BPD and BPD-associated pulmonary hypertension (BPD-PH) together with systemic hypertension (sHTN) are chronic cardiopulmonary disorders which result in an increased mortality and long-term problems for these infants. Previous studies have predominantly focused on the pulmonary circulation (right ventricle and its function) and developing management strategies accordingly for BPD-PH. However, recent work has drawn attention to the importance of the left-sided cardiac function and its impact on BPD in a subset of infants arising from a unique pathophysiology termed postcapillary PH. BPD infants may have a mechanistic link arising from chronic inflammation, cytokines, oxidative stress, catecholamines, and renin-angiotensin system activation along with systemic arterial stiffness, all of which contribute to the development of BPD-sHTN. The focus for the treatment of BPD-PH has been improvement of the right heart function through pulmonary vasodilators. BPD-sHTN and a subset of postcapillary PH may benefit from afterload reducing agents such as angiotensin converting enzyme inhibitors. Preterm infants with BPD-PH are at risk of later cardiac and respiratory morbidities as young adults. This paper reviews the current knowledge of the pathophysiology, diagnosis, and treatment of BPD-PH and BPD-sHTN. Current knowledge gaps and emerging new therapies will also be discussed.

Role of friction and geometry in tuning the bending stiffness of topologically interlocking materials

Topologically interlocking material (TIM) systems offer adjustable bending stiffness controlled by external pre-stress, as shown in previous studies. This study focuses on a specific TIM system comprised of truncated tetrahedral particles interconnected via tensioned wires. The fabrication process involves weaving nylon wires through 3D printed truncated tetrahedrons that have longitudinal and latitudinal through-holes. By varying the tension applied to the wires, one can systematically control the overall bending stiffness of the TIM system. We change the surface friction and the contact angle between adjacent particles at a fixed wire tension, to study experimentally how they affect the system’s bending response. We inform experiments with Level Set Discrete Element Method (LS-DEM) simulations, to correlate surface friction and contact area changes with the system’s bending modulus. The numerical model is shown to be predictive and could be used in the future to evaluate designs of TIMs.