Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

E-Cervix imaging displaying cervical elasticity characteristics of healthy adult nulliparous women at different age groups and different menstrual cycle stages

Objective To observe the cervical elasticity of healthy adult nulliparous women at different age groups and different stages of menstrual cycle with E-Cervix imaging technology.Methods A total of 218 healthy adult nulliparous women who underwent transvaginal ultrasound examination for routine physical examination were retrospectively enrolled,including 103 in follicular phase,78 in ovulation phase and 37 in luteal phase.Cervical canal length(CL)and E-Cervix elasticity parameters were compared among different age groups and different stages of menstrual cycle,including elasticity contrast index(ECI),hardness ratio(HR),cervical internal and external orifice strain values(IOS and EOS)and IOS/EOS ratio.Results No significant difference of CL nor cervical elasticity parameters was detected among healthy adult nulliparous women at different age groups(all P>0.05).There were significant differences of ECI,HR and IOS among different menstrual cycle stages(all P<0.05),among which women in follicular phase had higher ECI and IOS but lower HR than those in luteal phase(all P<0.05).Conclusion No significant difference of cervical elasticity existed among healthy adult nulliparous women at different age groups.Meanwhile,cervical elasticity of healthy adult nulliparous women changed during menstrual cycle,in follicular phase had higher ECI and IOS but lower HR than in luteal phase.

Publisher Correction to:Highly Elastic,Bioresorbable Polymeric Materials for Stretchable,Transient Electronic Systems

Due to typesetting mistake,Hanul Min was missed to be denoted as a corresponding author in the article.The type-setter apologizes for this.The original article has been corrected.Open Access This article is licensed under a Creative Commons Attribution 4.0 International License,which permits use,sharing,adaptation,distribution and reproduction in any medium or format,as long as you give appropriate credit to the original author(s)and the source,provide a link to the Creative Commons licence,and indicate if changes were made.The images or other third party material in this article are included in the article’s Creative Commons licence,unless indicated otherwise in a credit line to the material.If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use,you will need to obtain permission directly from the copyright holder.

Trajectory compensation for multi-robot coordinated lifting system considering elastic catenary of the rope

The multi-robot coordinated lifting system is an unconstrained system with a rigid and flexible coupling.The deformation of the flexible rope causes errors in the movement trajectory of the lifting system.Based on the kinematic and dynamic analysis of the lifting system,the elastic catenary mod-el considering the elasticity and mass of the flexible rope is established,and the effect of the deform-ation of the flexible rope on the position and posture of the suspended object is analyzed.According to the deformation of flexible rope,a real-time trajectory compensation method is proposed based on the compensation principle of position and posture.Under the lifting task of the low-speed move-ment,this is compared with that of the system which neglects the deformation of the flexible rope.The trajectoy of the lifting system considering the deformation of flexible rope.The results show that the mass and elasticity of the flexible rope can not be neglected.Meanwhile,the proposed trajectory compensation method can improve the movement accuracy of the lifting system,which verifies the ef-fectiveness of this compensation method.The research results provide the basis for trajectory plan-ning and coordinated control of the lifting system。

The Fictitious Domain Method with Sharp Interface for Elasticity Systems with General Jump Embedded Boundary Conditions

In framework of the fictitious domain methods with immersed interfaces for the elasticity problem,the present contribution is to study and numerically validate the jump-integrated boundary conditions method with sharp interface for the vector elasticity system discretized by a proposed finite volume method.The main idea of the fictitious domain approach consists in embedding the original domain of study into a geometrically larger and simpler one called the fictitious domain.Here,we present a cell-centered finite volume method to discretize the fictitious domain problem.The proposed method is numerically validated for different test cases.This work can be considered as a first step before more challenging problems such as fluid-structure interactions or moving interface problems.

Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory

This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.

Unique Continuation Property with Partial Information for Two-Dimensional Anisotropic Elasticity Systems

In this paper,we establish a novel unique continuation property for two-dimensional anisotropic elasticity systems with partial information.More precisely,given a homogeneous elasticity system in a connected open bounded domain,we investigate the unique continuation by assuming only the vanishing of one component of the solution in a subdomain.Using the corresponding Riemann function,we prove that the solution vanishes in the whole domain provided that the other component vanishes at one point up to its second derivatives.Further,we construct several examples showing the possibility of further reducing the additional information of the other component.This result possesses remarkable significance in both theoretical and practical aspects because the required data are almost halved for the unique determination of the whole solution.

Hamiltonian Systems in Elasticity and Their Variational Principles

As an inverse problem of Hamiltonian mechanics, a new Hamiltonian system inelasticity and its variational principle are derived from the basic equations of elasticity.

HAMILTONIAN SYSTEM AND THE SAINT VENANT PROBLEM IN ELASTICITY

The traditional semi-inverse solution method of the Saint Venant problem, which is described in the Euclidian space under the Lagrangian system formulation, is updated to be solved in the symplectic space under the conservative hamiltonian system. It was proved in the present paper that all the Saint Venant solutions can be obtained directly via the zero eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian operator matrix.

Exploiting Virtual Elasticity of Production Systems for Respecting OTD-Part 1: Post-Optimality Conditions for Ergodic Order Arrivals in Fixed Capacity Regimes

Respecting the on-time-delivery (OTD) for manufacturing orders is mandatory. This depends, however, on the probability distribution of incoming order rate. The case of non-equal distribution, such as aggregated arrivals, may compromise the observance of on-time supplies for some orders. The purpose of this paper is to evaluate the conditions of post-optimality for stochastic order rate governed production systems in order to observe OTD. Instead of a heuristic or a simulative exploration, a Cartesian-based approach is applied to developing the necessary and sufficient mathematical condition to solve the problem statement. The research result demonstrates that increasing speed of throughput reveals a latent capacity, which allows arrival orders above capacity limits to be backlog-buffered and rescheduled for OTD, exploiting the virtual manufacturing elasticity inherent to all production systems to increase OTD reliability of non JIT-based production systems.

Exploiting Virtual Elasticity of Manufacturing Systems to Respect OTD—Part 2: Post-Optimality Conditions for the Cases of Ergodic and Non-Ergodic Order Rate with Deterministic Product-Mix

Respecting the on-time delivery (OTD) for manufacturing orders is mandatory. However, for non-JIT Batch & Queue Push-manufacturing systems, the compliance of OTD is not intrinsically guaranteed. As an OTD related manufacturing theory is largely missing it is crucial to understand and formalize the necessary conditions of OTD compliance for complex production environments for maximum exploitation of the production capacity. This paper evaluates the conditions of post-optimality while being OTD compliant for production systems, which are characterized by stochastic order rate and a deterministic product-mix. Instead of applying discrete event simulation to explore the real case-by-case order scheduling optimization for OTD compliance, a Cartesian approach is followed. This enables to define theoretically the solution space of order backlog for OTD, which contributes to developing further manufacturing theory. At the base stands the recently defined new concept of virtual manufacturing elasticity by reducing lead-time to increase virtually production capacity. The result has led to defining additional two corollaries to the OTD theorem, which sets up basic OTD theory. Apart from defining the post-optimal requirements to guarantee for orders at least a weak solution for OTD compliance, this paper reveals that for a deterministic product-mix a non-ergodic order arrival rate can be rescheduled into an ergodic order input rate to the shopfloor if the virtual elasticity T is large enough, hence the importance of having fast and flexible production lines.

Monitoring the change in horizontal stress with multi-wave time-lapse seismic response based on nonlinear elasticity theory

Monitoring the change in horizontal stress from the geophysical data is a tough challenge, and it has a crucial impact on broad practical scenarios which involve reservoir exploration and development, carbon dioxide (CO_(2)) injection and storage, shallow surface prospecting and deep-earth structure description. The change in in-situ stress induced by hydrocarbon production and localized tectonic movements causes the changes in rock mechanic properties (e.g. wave velocities, density and anisotropy) and further causes the changes in seismic amplitudes, phases and travel times. In this study, the nonlinear elasticity theory that regards the rock skeleton (solid phase) and pore fluid as an effective whole is used to characterize the effect of horizontal principal stress on rock overall elastic properties and the stress-dependent anisotropy parameters are therefore formulated. Then the approximate P-wave, SV-wave and SH-wave angle-dependent reflection coefficient equations for the horizontal-stress-induced anisotropic media are proposed. It is shown that, on the different reflectors, the stress-induced relative changes in reflectivities (i.e., relative difference) of elastic parameters (i.e., P- and S-wave velocities and density) are much less than the changes in contrasts of anisotropy parameters. Therefore, the effects of stress change on the reflectivities of three elastic parameters are reasonably neglected to further propose an AVO inversion approach incorporating P-, SH- and SV-wave information to estimate the change in horizontal principal stress from the corresponding time-lapse seismic data. Compared with the existing methods, our method eliminates the need for man-made rock-physical or fitting parameters, providing more stable predictive power. 1D test illustrates that the estimated result from time-lapse P-wave reflection data shows the most reasonable agreement with the real model, while the estimated result from SH-wave reflection data shows the largest bias. 2D test illustrates the feasibility of the proposed inversion method for estimating the change in horizontal stress from P-wave time-lapse seismic data.

Anomalous elasticity of talc at high pressures:Implications for subduction systems

Talc is a layered hydrous silicate mineral that plays a vital role in transporting water into Earth’s interior and is crucial for explaining geophysical observations in subduction zone settings.In this study,we explored the structure,equation of state,and elasticity of both triclinic and monoclinic talc under high pressures up to 18 GPa using first principles simulations based on density functional theory corrected for dispersive forces.Our results indicate that principal components of the full elastic constant tensor C_(11) and C_(22),shear components C_(66),and several off-diagonal components show anomalous pressure dependence.This non-monotonic pressure dependence of elastic constant components is likely related to the structural changes and is often manifested in a polytypic transition from a low-pressure polytype talc-I to a high-pressure polytype talc-Ⅱ.The polytypic transition of talc occurs at pressures within its thermodynamic stability.However,the bulk and shear elastic moduli show no anomalous softening.Our study also shows that talc has low velocity,extremely high anisotropy,and anomalously high V_(P)/V_(S) ratio,thus making it a potential candidate mineral phase that could readily explain unusually high V_(P)/V_(S) ratio and large shear wave splitting delays as observed from seismological studies in many subduction systems.

RESEARCH ON A SYSTEMATIC METHODOLOGY FOR THEORY OF ELASTICITY

The equivalence between differential form and integral form of a systematic methodology for theory of elasticity is proved. A uniform framework of the systematic methodology is established. New system includes differential form, integral form and mixed form. All kinds of variational principle are proved by the equivalence between differential form and integral form. The idea for generalized virtual work and virtual function is presented.

Ni-P-SBR composite-electroless-plating enables Si anode with high conductivity and elasticity for high performance Li-ion batteries application

Silica-based anode is widely employed for high energy density Li-ion batteries owing to their high theoretical specific capacity(4200 m A h g-1).However,it is always accompanied by a huge volume expansion(300%)and shrinks during the lithiation/delithiation process,further leading to low cycle stability.Efforts to mitigate the adverse effects caused by volume expansion such as robust binder matrix,Coreshell structure,etc.,inevitably affect the electronic conductivity within the electrode.Herein,a high conductivity and elasticity Si anode(Ni-P-SBR(styrene-butadiene rubber)@Si)was designed and fabricated via the Ni-P-SBR composite-electroless-plating process.In this design,the Si particles are surrounded by SBR polymer and Ni particles,where the SBR can adapt to the volume change and Ni particles can provide the electrode with high electronic conductivity.Therefore,the Ni-P-SBR@Si delivers a high initial capacity of 3470 m A h g-1and presents capacity retention of 49.4%within 200 cycles at 600 m A g-1.Additionally,a high capacity of 1153 m A h g-1can be achieved at 2000 m A g-1and can be cycled stably under bending conditions.This strategy provides feasible ideas to solve the key issues that limit the practical application of Si anodes.

Low-frequency laboratory measurements of the elastic properties of solids using a distributed acoustic sensing system

In recent decades,low-frequency(LF)experiments based on the forced-oscillation(FO)method have become common practice in many rock physics laboratories for measuring the elastic and anelastic properties of rocks.However,the use of the electronic displacement sensors in traditional acquisition systems of FO devices such as conventional capacitive transducers or strain gauges seriously limits both the efficiency and productivity of LF measurements,and,due to the limited contact area of the displacement sensors with a sample under test,increases the requirements for sample homogeneity.In this paper,we present the first results obtained in the development of a new laboratory method elaborated to measure the elastic properties of solids.The method is a further development of the FO method where traditional data acquisition is replaced by acquisition based on fiber-optic distributed acoustic sensing(DAS)technology.The new method was tested in a laboratory study using two FO setups designed for measurements under uniaxial and confining pressures.The study was carried out on a sample made from polymethyl methacrylate(PMMA)and an aluminium standard,first under uniaxial pressure at FO frequencies of 1,10,30,60 and 100 Hz,and then under confining pressure at an FO frequency of 1 Hz.Both uniaxial and confining pressures were equal to 10 MPa,and the strain in the PMMA sample in all measurements did not exceed 4×10^(-8).The performance of DAS acquisition was compared with the measurements conducted at a strain of 1×10^(-6) using the traditional FO method based on the use of semiconductor strain gauges and the ultrasonic method.The results of the DAS measurements are in good agreement with the FO measurements carried out using semiconductor strain gauges and with the literature data.

Data envelopment analysis for scale elasticity measurement in the stochastic case:with an application to Indian banking

In the nonparametric data envelopment analysis literature,scale elasticity is evaluated in two alternative ways:using either the technical efficiency model or the cost efficiency model.This evaluation becomes problematic in several situations,for example(a)when input proportions change in the long run,(b)when inputs are heterogeneous,and(c)when firms face ex-ante price uncertainty in making their production decisions.To address these situations,a scale elasticity evaluation was performed using a value-based cost efficiency model.However,this alternative value-based scale elasticity evaluation is sensitive to the uncertainty and variability underlying input and output data.Therefore,in this study,we introduce a stochastic cost-efficiency model based on chance-constrained programming to develop a value-based measure of the scale elasticity of firms facing data uncertainty.An illustrative empirical application to the Indian banking industry comprising 71 banks for eight years(1998–2005)was made to compare inferences about their efficiency and scale properties.The key findings are as follows:First,both the deterministic model and our proposed stochastic model yield distinctly different results concerning the efficiency and scale elasticity scores at various tolerance levels of chance constraints.However,both models yield the same results at a tolerance level of 0.5,implying that the deterministic model is a special case of the stochastic model in that it reveals the same efficiency and returns to scale characterizations of banks.Second,the stochastic model generates higher efficiency scores for inefficient banks than its deterministic counterpart.Third,public banks exhibit higher efficiency than private and foreign banks.Finally,public and old private banks mostly exhibit either decreasing or constant returns to scale,whereas foreign and new private banks experience either increasing or decreasing returns to scale.Although the application of our proposed stochastic model is illustrative,it can be potentially applied to all firms in the information and distribution-intensive industry with high fixed costs,which have ample potential for reaping scale and scope benefits.

A Wire-Driven Series Elastic Mechanism Based on Ultrasonic Motor for Walking Assistive System

In order to improve the elderly people's quality of life,supporting their walking behaviors is a promising technology.Therefore,based on one ultrasonic motor,a wire-driven series elastic mechanism for walking assistive system is proposed and investigated in this research.In contrast to tradition,it innovatively utilizes an ultrasonic motor and a wire-driven series elastic mechanism to achieve superior system performances in aspects of simple structure,high torque/weight ratio,quiet operation,quick response,favorable electromagnetic compatibility,strong shock resistance,better safety,and accurately stable force control.The proposed device is mainly composed of an ultrasonic motor,a linear spring,a steel wire,four pulleys and one rotating part.To overcome the ultrasonic motor's insufficient output torque,a steel wire and pulleys are smartly combined to directly magnify the torque instead of using a conventional gear reducer.Among the pulleys,there is one tailored pulley playing an important role to keep the reduction ratio as 4.5 constantly.Meanwhile,the prototype is manufactured and its actual performance is verified by experimental results.In a one-second operating cycle,it only takes 86 ms for this mechanism to output an assistive torque of 1.6 N·m.At this torque,the ultrasonic motor's speed is around 4.1 rad/s.Moreover,experiments with different operation periods have been conducted for different application scenarios.This study provides a useful idea for the application of ultrasonic motor in walking assistance system.

Exploiting Virtual Elasticity of Production Systems to Respect OTD—Part 3: Basic Considerations for Modelling CPPS Characterized by Non-Ergodic Order Entry and Non-Deterministic Product-Mix for Fully Flexible Addressable Workstations

The recently experienced hype concerning the so-called “4th Industrial Revolution” of production systems has prompted several papers of various subtopics regarding Cyber-Phdysical Production Systems (CPPS). However, important aspects such as the modelling of CPPS to understand the theory regarding the performance of highly non-ergodic and non-deterministic flexible manufacturing systems in terms of Exit Rate (ER), Manufacturing Lead Time (MLT), and On-Time Delivery (OTD) have not yet been examined systematically and even less modeled analytically. To develop the topic, in this paper, the prerequisites for modelling such systems are defined in order to be able to derive an explicit and dedicated production mathematics-based understanding of CPPS and its dynamics: switching from explorative simulation to rational modelling of the manufacturing “physics” led to an own and specific manufacturing theory. The findings have led to enouncing, among others, the Theorem of Non-Ergodicity as well as the Batch Cycle Time Deviation Function giving important insights to model digital twin-based CPPS for complying with the mandatory OTD.

Two-Stage Low-Carbon Economic Dispatch of Integrated Demand Response-Enabled Integrated Energy System with Ladder-Type Carbon Trading

Driven by the goal of“carbon neutrality”and“emission peak”,effectively controlling system carbon emissions has become significantly important to governments around the world.To this end,a novel two-stage low-carbon economic scheduling framework that considers the coordinated optimization of ladder-type carbon trading and integrated demand response(IDR)is proposed in this paper for the integrated energy system(IES),where the first stage determines the energy consumption plan of users by leveraging the price-based electrical-heat IDR.In contrast,the second stage minimizes the system total cost to optimize the outputs of generations with consideration of the uncertainty of renewables.In addition,to fully exploit the system’s emission reduction potential,a carbon trading cost model with segmented CO_(2) emission intervals is built by introducing a reward-penalty ladder-type carbon trading mechanism,and the flexible thermal comfort elasticity of customers is taken into account by putting forward a predicted mean vote index on the load side.The CPLEX optimizer resolves the two-stage model,and the study results on a modified IES situated in North China show the proposed model can effectively reduce carbon emissions and guarantee economical efficiency operation of the system.