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...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.展开更多
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 ...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.展开更多
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 o...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.展开更多
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 boun...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.展开更多
As an inverse problem of Hamiltonian mechanics, a new Hamiltonian system inelasticity and its variational principle are derived from the basic equations of 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 co...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.展开更多
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 arriva...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 </span><span style="font-family:Verdana;">speed of throughput reveals a latent capacity, which allows arrival orders </span><span style="font-family:Verdana;">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.展开更多
Respecting the on-time<span><span><span> </span></span></span><span><span><span>delivery (OTD) for manufacturing orders is mandatory. However, for non-JIT Batch &a...Respecting the on-time<span><span><span> </span></span></span><span><span><span>delivery (OTD) for manufacturing orders is mandatory. However, for non-JIT Batch & Queue Push-manufacturing systems, the compliance of OTD is not intrinsically guaranteed.</span></span></span><span><span><span> 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 </span></span></span><span><span><span>by</span></span></span><span><span><span> 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 develo</span></span></span><span><span><span>ping</span></span></span><span><span><span> 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 defin</span></span></span><span><span><span>ing</span></span></span><span><span><span> 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 </span></span></span><span><span><span><span><span style="font-size:10.0pt;font-family:;" "=""><span style="font-size:10.0pt;font-family:;" "=""><img src="Edit_e545052a-10c6-459e-aa8a-2bccefd4a1a7.png" alt="" /></span></span></span><i><span>T</span></i><span> is large enough</span></span></span></span><span><span><span>, </span></span></span><span><span><span>hence the importance of having fast and flexible production lines.</span></span></span>展开更多
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 explo...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.展开更多
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 differe...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.展开更多
The recently experienced hype concerning the so-called “4<sup>th</sup> Industrial Revolution” of production systems has prompted several papers of various subtopics regarding Cyber-Phdysical Production S...The recently experienced hype concerning the so-called “4<sup>th</sup> 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.展开更多
Elastic electronics are increasingly prevalent in information storage,smart sensing and health monitoring due to their softness,stretchability and portability.Wearable electronic devices should possess elasticity and ...Elastic electronics are increasingly prevalent in information storage,smart sensing and health monitoring due to their softness,stretchability and portability.Wearable electronic devices should possess elasticity and stretchability that align with biological tissues.Specifically,their materials should be capable of elastic strain up to 50–80%,while the devices themselves must maintain electric stability under strains that accommodate body movements[1].展开更多
The increasing integration of small-scale structures in engineering,particularly in Micro-Electro-Mechanical Systems(MEMS),necessitates advanced modeling approaches to accurately capture their complex mechanical behav...The increasing integration of small-scale structures in engineering,particularly in Micro-Electro-Mechanical Systems(MEMS),necessitates advanced modeling approaches to accurately capture their complex mechanical behavior.Classical continuum theories are inadequate at micro-and nanoscales,particularly concerning size effects,singularities,and phenomena like strain softening or phase transitions.This limitation follows from their lack of intrinsic length scale parameters,crucial for representingmicrostructural features.Theoretical and experimental findings emphasize the critical role of these parameters on small scales.This review thoroughly examines various strain gradient elasticity(SGE)theories commonly employed in literature to capture these size-dependent effects on the elastic response.Given the complexity arising from numerous SGE frameworks available in the literature,including first-and second-order gradient theories,we conduct a comprehensive and comparative analysis of common SGE models.This analysis highlights their unique physical interpretations and compares their effectiveness in modeling the size-dependent behavior of low-dimensional structures.A brief discussion on estimating additional material constants,such as intrinsic length scales,is also included to improve the practical relevance of SGE.Following this theoretical treatment,the review covers analytical and numerical methods for solving the associated higher-order governing differential equations.Finally,we present a detailed overview of strain gradient applications in multiscale andmultiphysics response of solids.Interesting research on exploring the relevance of SGE for reduced-order modeling of complex macrostructures,a universal multiphysics coupling in low-dimensional structures without being restricted to limited material symmetries(as in the case of microstructures),is also presented here for interested readers.Finally,we briefly discuss alternative nonlocal elasticity approaches(integral and integro-differential)for incorporating size effects,and conclude with some potential areas for future research on strain gradients.This review aims to provide a clear understanding of strain gradient theories and their broad applicability beyond classical elasticity.展开更多
Solids in nano-scales hold the promise to exhibit extreme strength and elasticity due to the absence of interior defects and the designability of micro-arrangements.A nano-scaled bulk sample can be produced by diamond...Solids in nano-scales hold the promise to exhibit extreme strength and elasticity due to the absence of interior defects and the designability of micro-arrangements.A nano-scaled bulk sample can be produced by diamond,ice,metallic twins,high entropy alloy(HEA),or cubic boron nitride(cBN).A loading stage capable of 4-DoF movements was designed and built to achieve multi-axial mechanical loading inside a transmission electronic microscope chamber with sub-nanometer loading precision.For single crystal diamond in the shape of nano-needles,we were able to achieve an extreme bending strength of 125 GPa at the tensile side,approaching the theoretical strength of diamond.For ice fibers of sub-micron radius,an extreme elastic strain of 10.9%was acquired,far exceeding the previous record of 0.3%for the elastic strain achievable by ice.For metallic twin specimens made by nano-welding,a shear strain as large as 364%was recorded parallel to the twin boundary.Cyclic shear loading aligned with the twin boundary would drive an up-and-down sweeping movement of the low-angle grain boundary,as composed by an array of dislocations.The sweep of the grain boundary effectively cleanses the lattice defects and creates a feasible scenario of unlimited cyclic endurance.For a HEA dog-bone specimen in nano-scale,an extreme elastic strain of about 10%was achieved.At this level of mechanical straining,stretch-induced melting for crystalline metals,as envisaged by Lindemann a century ago,was realized.For cBN crystals,a fracture path inclined to the stacking hexagon planes would result in a new failure mechanism of layered decohesion,triggered by the extremely large elastic strain(>7%)along the edge of the submicron-scaled specimen.These results indicate ample room for upgrading the mechanical behaviour of solids in nano-scales.展开更多
Surface energy is essential to the understanding of micro-mechanics for heterogeneous composites.To investigate the effective elasticity and fracture behaviors,we derive an effective surface energy based on Eshelby’s...Surface energy is essential to the understanding of micro-mechanics for heterogeneous composites.To investigate the effective elasticity and fracture behaviors,we derive an effective surface energy based on Eshelby’s equivalent inclusion theory.Within a unified theoretical framework,the effective surface energy predicts the fundamentals from elasticity to fracture,and reproduces classical homogenization methods and phase field models.The influences of elastic heterogeneity and size effects are analyzed in depth.Using the surface energy formulation,a computational model is developed by minimizing the deviation of effective elastic modulus from experimental observation.To validate our theoretical prediction,numerical simulations under tension and shear loadings for monodisperse and bidisperse particulate systems are performed,which agree well with experimental evidences.Local debondings nucleate and initiate at the inclusion-matrix interfaces,then develop into multiple interacting cracks and shear bands,thereby greatly promotes the process of fracture.展开更多
In this study,the sliding friction contact problems associated with the indentation of an elastic half-plane by rigid cylindrical and flat punches were investigated within the context of the micropolar theory.The micr...In this study,the sliding friction contact problems associated with the indentation of an elastic half-plane by rigid cylindrical and flat punches were investigated within the context of the micropolar theory.The micropolar theory of elasticity introduces the characteristic material length and the dimensionless coupling number to describe the size effect.Coulomb’s friction law is satisfied by a punch when it is subjected to both normal and tangential forces.Using the Fourier integral transformation technique,these mixed-boundary value problems were reduced to singular integral equations of the second kind in which the unknown quantity is the contact stress on the contact surface.The collocation method was utilized to solve the integral equations numerically.An extensive parametric study was conducted to investigate the effects of the friction coefficient,the characteristic material length,and the dimensionless coupling number on the normal and in-plane stresses.The results show that the contact stress predicted by the micropolar theory differs significantly from those predicted by the couple stress theory and the classical elasticity theory.展开更多
The identification of the traction acting on a portion of the surface of an anisotropic solid is very important in structural health monitoring and optimal design of structures. The traction can be determined using in...The identification of the traction acting on a portion of the surface of an anisotropic solid is very important in structural health monitoring and optimal design of structures. The traction can be determined using inverse methods in which displacement or strain measurements are taken at several points on the body. This paper presents an inverse method based on the method of fundamental solutions for the traction identification problem in two-dimensional anisotropic elasticity. The method of fundamental solutions is an efficient boundary-type meshless method widely used for analyzing various problems. Since the problem is linear, the sensitivity analysis is simply performed by solving the corresponding direct problem several times with different loads. The effects of important parameters such as the number of measurement data, the position of the measurement points, the amount of measurement error, and the type of measurement, i.e., displacement or strain, on the results are also investigated. The results obtained show that the presented inverse method is suitable for the problem of traction identification. It can be concluded from the results that the use of strain measurements in the inverse analysis leads to more accurate results than the use of displacement measurements. It is also found that measurement points closer to the boundary with unknown traction provide more reliable solutions. Additionally, it is found that increasing the number of measurement points increases the accuracy of the inverse solution. However, in cases with a large number of measurement points, further increasing the number of measurement data has little effect on the results.展开更多
This paper presents a novel surface model based on the Gurtin–Murdoch theory and Kerr-type differential relations,which is established and numerically simulated.By employing the principles of equivalent force and mec...This paper presents a novel surface model based on the Gurtin–Murdoch theory and Kerr-type differential relations,which is established and numerically simulated.By employing the principles of equivalent force and mechanical equilibrium,a differential equation for the contact pressure-deflection relationship between a rigid indenter and an elastic thin beam is derived.The study investigates pressure distribution within the contact area and deformation patterns outside this region.The relationship between indentation parameters is analyzed from two perspectives:clamped and simply-supported boundaries,with a detailed comparison to classical cases.The findings reveal that the normalized contact pressure and load–displacement relationship of elastic thin beams are influenced not only by the half-width ratio and indentation depth but also by the material’s surface elasticity.Similar to classical contact scenarios,an increase in surface elasticity leads to the separation of the indenter from the beam’s center when the contact half-width exceeds a certain threshold(e.g.,a ratio of 4 to the beam thickness).This results in a negative normalized contact pressure and the formation of two independent,symmetric contact strips.Notably,the relationship between displacement and contact half-width remains largely unaffected by surface elasticity,aligning with classical indentation contact results.The methodology and outcomes of this research provide a foundation for analyzing the structures and properties of nanostructured materials,offer insights for the design of future nanostructured devices,and present innovative approaches to addressing practical engineering challenges.展开更多
The precise computation of nanoelectromechanical switches’(NEMS)multi-physical interactions requires advanced numerical models and is a crucial part of the development of micro-and nano-systems.This paper presents a ...The precise computation of nanoelectromechanical switches’(NEMS)multi-physical interactions requires advanced numerical models and is a crucial part of the development of micro-and nano-systems.This paper presents a novel compound numerical method to study the instability of a functionally graded(FG)beam-type NEMS,considering surface elasticity effects as stated by Gurtin-Murdoch theory in an Euler-Bernoulli beam.The presented method is based on a combination of the Method of Adjoints(MoA)together with the Bézier-based multistep technique.By utilizing the MoA,a boundary value problem(BVP)is turned into an initial value problem(IVP).The resulting IVP is then solved by employing a cost-efficient multi-step process.It is demonstrated that the mentioned method can arrive at a high level of accuracy.Furthermore,it is revealed that the stability of the presented methodology is far better than that of other common multi-step methods,such as Adams-Bashforth,particularly at higher step sizes.Finally,the effects of axially functionally graded(FG)properties on the pull-in phenomenon and the main design parameters of NEMS,including the detachment length,are inspected.It was shown that the main parameter of design is the modulus of elasticity of the material,as Silver(Ag),which had better mechanical properties,showed almost a 6%improvement compared to aluminum(Al).However,by applying the correct amount of material with sturdier surface parameters,such as Aluminum(Al),at certain points,the nanobeams’functionality can be improved even further by around 1.5%.展开更多
A new suspension gravity compensation system has been developed to alleviate the gravity effects on a two-dimensional(2D)deployable mechanism for ground verification.Considering the rigid-flexible coupling of both the...A new suspension gravity compensation system has been developed to alleviate the gravity effects on a two-dimensional(2D)deployable mechanism for ground verification.Considering the rigid-flexible coupling of both the rotating servo and the suspension system,a multi-body dynamic model simulating their integration is established using Lagrange’s equation.To mitigate instantaneous impact forces due to significant non-plumb effects from passive following in the horizontal direction,an elastic element is added in series with the rope in the vertical suspension system.The dynamic response of this elastic element relative to the rotating servo system is analyzed by the ADAMS software.Simulation results show that the compensating error decreases significantly from 45%to 0.31%when incorporating elastic elements compared to scenarios without such elements.Additionally,low-stiffness elastic elements demonstrate a higher compensating error than high-stiffness ones.A spring with a stiffness coefficient of 6 N/mm is selected in the experiment,ensuring that compensating error meets the design specification of 5%.展开更多
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10962004 and 11061019)the Doctoral Foundation of Inner Mongolia(Grant Nos.2009BS0101 and 2010MS0110)+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20070126002)the Chunhui Program of the Ministry of Education of China(Grant No.Z2009-1-01010)
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12261064 and 11861048)the Natural Science Foundation of Inner Mongolia,China (Grant Nos.2021MS01004 and 2022QN01008)the High-level Talents Scientific Research Start-up Foundation of Inner Mongolia University (Grant No.10000-21311201/165)。
文摘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.
基金supported by the A3 Foresight Program“Modeling and Computation of Applied Inverse Problems”Japan Society for the Promotion of Science(JSPS)+5 种基金National Natural Science Foundation of China(NSFC)supported by NSFC(No.11971121)partially supported by JSPS KAKENHI Grant Number JP15H05740supported by NSFC(No.11771270)partly supported by NSFC(No.91730303)RUDN University Program5-100。
文摘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.
文摘As an inverse problem of Hamiltonian mechanics, a new Hamiltonian system inelasticity and its variational principle are derived from the basic equations of elasticity.
文摘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.
文摘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 </span><span style="font-family:Verdana;">speed of throughput reveals a latent capacity, which allows arrival orders </span><span style="font-family:Verdana;">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.
文摘Respecting the on-time<span><span><span> </span></span></span><span><span><span>delivery (OTD) for manufacturing orders is mandatory. However, for non-JIT Batch & Queue Push-manufacturing systems, the compliance of OTD is not intrinsically guaranteed.</span></span></span><span><span><span> 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 </span></span></span><span><span><span>by</span></span></span><span><span><span> 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 develo</span></span></span><span><span><span>ping</span></span></span><span><span><span> 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 defin</span></span></span><span><span><span>ing</span></span></span><span><span><span> 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 </span></span></span><span><span><span><span><span style="font-size:10.0pt;font-family:;" "=""><span style="font-size:10.0pt;font-family:;" "=""><img src="Edit_e545052a-10c6-459e-aa8a-2bccefd4a1a7.png" alt="" /></span></span></span><i><span>T</span></i><span> is large enough</span></span></span></span><span><span><span>, </span></span></span><span><span><span>hence the importance of having fast and flexible production lines.</span></span></span>
基金supported by the US National Science Foundation grant EAR 1763215 and EAR 1753125XSEDE facilities(GEO170003)+4 种基金the High-Performance Computing,Research Computing Center,Florida State Universitythe UK’s National Supercomputer Service through the UK CarParrinello Consortium(EPSRC Grant No.EP/P022561/1)and project ID d56"Planetary Interiors"funding from the INSU-CNRSthe French Government Laboratory of Excellence initiative n°ANR-10-LABX-0006,the Région Auvergnethe European Regional Development Fund(Cler Volc contribution number 530).
文摘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.
文摘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.
文摘The recently experienced hype concerning the so-called “4<sup>th</sup> 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.
基金supported by generous grants from the Natural Science Foundation of Zhejiang Province(LR24E030003)Zhejiang Province Qianjiang Talent Program(ZJ-QJRC-2020-32).
文摘Elastic electronics are increasingly prevalent in information storage,smart sensing and health monitoring due to their softness,stretchability and portability.Wearable electronic devices should possess elasticity and stretchability that align with biological tissues.Specifically,their materials should be capable of elastic strain up to 50–80%,while the devices themselves must maintain electric stability under strains that accommodate body movements[1].
基金support from the Anusandhan National Research Foundation(ANRF),erstwhile Science and Engineering Research Board(SERB),India,under the startup research grant program(SRG/2022/000566).
文摘The increasing integration of small-scale structures in engineering,particularly in Micro-Electro-Mechanical Systems(MEMS),necessitates advanced modeling approaches to accurately capture their complex mechanical behavior.Classical continuum theories are inadequate at micro-and nanoscales,particularly concerning size effects,singularities,and phenomena like strain softening or phase transitions.This limitation follows from their lack of intrinsic length scale parameters,crucial for representingmicrostructural features.Theoretical and experimental findings emphasize the critical role of these parameters on small scales.This review thoroughly examines various strain gradient elasticity(SGE)theories commonly employed in literature to capture these size-dependent effects on the elastic response.Given the complexity arising from numerous SGE frameworks available in the literature,including first-and second-order gradient theories,we conduct a comprehensive and comparative analysis of common SGE models.This analysis highlights their unique physical interpretations and compares their effectiveness in modeling the size-dependent behavior of low-dimensional structures.A brief discussion on estimating additional material constants,such as intrinsic length scales,is also included to improve the practical relevance of SGE.Following this theoretical treatment,the review covers analytical and numerical methods for solving the associated higher-order governing differential equations.Finally,we present a detailed overview of strain gradient applications in multiscale andmultiphysics response of solids.Interesting research on exploring the relevance of SGE for reduced-order modeling of complex macrostructures,a universal multiphysics coupling in low-dimensional structures without being restricted to limited material symmetries(as in the case of microstructures),is also presented here for interested readers.Finally,we briefly discuss alternative nonlocal elasticity approaches(integral and integro-differential)for incorporating size effects,and conclude with some potential areas for future research on strain gradients.This review aims to provide a clear understanding of strain gradient theories and their broad applicability beyond classical elasticity.
文摘Solids in nano-scales hold the promise to exhibit extreme strength and elasticity due to the absence of interior defects and the designability of micro-arrangements.A nano-scaled bulk sample can be produced by diamond,ice,metallic twins,high entropy alloy(HEA),or cubic boron nitride(cBN).A loading stage capable of 4-DoF movements was designed and built to achieve multi-axial mechanical loading inside a transmission electronic microscope chamber with sub-nanometer loading precision.For single crystal diamond in the shape of nano-needles,we were able to achieve an extreme bending strength of 125 GPa at the tensile side,approaching the theoretical strength of diamond.For ice fibers of sub-micron radius,an extreme elastic strain of 10.9%was acquired,far exceeding the previous record of 0.3%for the elastic strain achievable by ice.For metallic twin specimens made by nano-welding,a shear strain as large as 364%was recorded parallel to the twin boundary.Cyclic shear loading aligned with the twin boundary would drive an up-and-down sweeping movement of the low-angle grain boundary,as composed by an array of dislocations.The sweep of the grain boundary effectively cleanses the lattice defects and creates a feasible scenario of unlimited cyclic endurance.For a HEA dog-bone specimen in nano-scale,an extreme elastic strain of about 10%was achieved.At this level of mechanical straining,stretch-induced melting for crystalline metals,as envisaged by Lindemann a century ago,was realized.For cBN crystals,a fracture path inclined to the stacking hexagon planes would result in a new failure mechanism of layered decohesion,triggered by the extremely large elastic strain(>7%)along the edge of the submicron-scaled specimen.These results indicate ample room for upgrading the mechanical behaviour of solids in nano-scales.
基金supported by the National Natural Science Foundation of China(Grant Nos.12172062 and 12588201).
文摘Surface energy is essential to the understanding of micro-mechanics for heterogeneous composites.To investigate the effective elasticity and fracture behaviors,we derive an effective surface energy based on Eshelby’s equivalent inclusion theory.Within a unified theoretical framework,the effective surface energy predicts the fundamentals from elasticity to fracture,and reproduces classical homogenization methods and phase field models.The influences of elastic heterogeneity and size effects are analyzed in depth.Using the surface energy formulation,a computational model is developed by minimizing the deviation of effective elastic modulus from experimental observation.To validate our theoretical prediction,numerical simulations under tension and shear loadings for monodisperse and bidisperse particulate systems are performed,which agree well with experimental evidences.Local debondings nucleate and initiate at the inclusion-matrix interfaces,then develop into multiple interacting cracks and shear bands,thereby greatly promotes the process of fracture.
基金supported by the National Natural Science Foundation of China(Grant No.12062019)the Natural Science Foundation of Inner Mongolia(Grant Nos.2024QN01013 and 2024MS01007).
文摘In this study,the sliding friction contact problems associated with the indentation of an elastic half-plane by rigid cylindrical and flat punches were investigated within the context of the micropolar theory.The micropolar theory of elasticity introduces the characteristic material length and the dimensionless coupling number to describe the size effect.Coulomb’s friction law is satisfied by a punch when it is subjected to both normal and tangential forces.Using the Fourier integral transformation technique,these mixed-boundary value problems were reduced to singular integral equations of the second kind in which the unknown quantity is the contact stress on the contact surface.The collocation method was utilized to solve the integral equations numerically.An extensive parametric study was conducted to investigate the effects of the friction coefficient,the characteristic material length,and the dimensionless coupling number on the normal and in-plane stresses.The results show that the contact stress predicted by the micropolar theory differs significantly from those predicted by the couple stress theory and the classical elasticity theory.
基金funded by Vice Chancellor of Research at Shiraz University(grant 3GFU2M1820).
文摘The identification of the traction acting on a portion of the surface of an anisotropic solid is very important in structural health monitoring and optimal design of structures. The traction can be determined using inverse methods in which displacement or strain measurements are taken at several points on the body. This paper presents an inverse method based on the method of fundamental solutions for the traction identification problem in two-dimensional anisotropic elasticity. The method of fundamental solutions is an efficient boundary-type meshless method widely used for analyzing various problems. Since the problem is linear, the sensitivity analysis is simply performed by solving the corresponding direct problem several times with different loads. The effects of important parameters such as the number of measurement data, the position of the measurement points, the amount of measurement error, and the type of measurement, i.e., displacement or strain, on the results are also investigated. The results obtained show that the presented inverse method is suitable for the problem of traction identification. It can be concluded from the results that the use of strain measurements in the inverse analysis leads to more accurate results than the use of displacement measurements. It is also found that measurement points closer to the boundary with unknown traction provide more reliable solutions. Additionally, it is found that increasing the number of measurement points increases the accuracy of the inverse solution. However, in cases with a large number of measurement points, further increasing the number of measurement data has little effect on the results.
基金Natural Science Foundation of Gansu Province,24JRRA182,Liyuan Wang,25JRRA802,zhiying ou。
文摘This paper presents a novel surface model based on the Gurtin–Murdoch theory and Kerr-type differential relations,which is established and numerically simulated.By employing the principles of equivalent force and mechanical equilibrium,a differential equation for the contact pressure-deflection relationship between a rigid indenter and an elastic thin beam is derived.The study investigates pressure distribution within the contact area and deformation patterns outside this region.The relationship between indentation parameters is analyzed from two perspectives:clamped and simply-supported boundaries,with a detailed comparison to classical cases.The findings reveal that the normalized contact pressure and load–displacement relationship of elastic thin beams are influenced not only by the half-width ratio and indentation depth but also by the material’s surface elasticity.Similar to classical contact scenarios,an increase in surface elasticity leads to the separation of the indenter from the beam’s center when the contact half-width exceeds a certain threshold(e.g.,a ratio of 4 to the beam thickness).This results in a negative normalized contact pressure and the formation of two independent,symmetric contact strips.Notably,the relationship between displacement and contact half-width remains largely unaffected by surface elasticity,aligning with classical indentation contact results.The methodology and outcomes of this research provide a foundation for analyzing the structures and properties of nanostructured materials,offer insights for the design of future nanostructured devices,and present innovative approaches to addressing practical engineering challenges.
文摘The precise computation of nanoelectromechanical switches’(NEMS)multi-physical interactions requires advanced numerical models and is a crucial part of the development of micro-and nano-systems.This paper presents a novel compound numerical method to study the instability of a functionally graded(FG)beam-type NEMS,considering surface elasticity effects as stated by Gurtin-Murdoch theory in an Euler-Bernoulli beam.The presented method is based on a combination of the Method of Adjoints(MoA)together with the Bézier-based multistep technique.By utilizing the MoA,a boundary value problem(BVP)is turned into an initial value problem(IVP).The resulting IVP is then solved by employing a cost-efficient multi-step process.It is demonstrated that the mentioned method can arrive at a high level of accuracy.Furthermore,it is revealed that the stability of the presented methodology is far better than that of other common multi-step methods,such as Adams-Bashforth,particularly at higher step sizes.Finally,the effects of axially functionally graded(FG)properties on the pull-in phenomenon and the main design parameters of NEMS,including the detachment length,are inspected.It was shown that the main parameter of design is the modulus of elasticity of the material,as Silver(Ag),which had better mechanical properties,showed almost a 6%improvement compared to aluminum(Al).However,by applying the correct amount of material with sturdier surface parameters,such as Aluminum(Al),at certain points,the nanobeams’functionality can be improved even further by around 1.5%.
文摘A new suspension gravity compensation system has been developed to alleviate the gravity effects on a two-dimensional(2D)deployable mechanism for ground verification.Considering the rigid-flexible coupling of both the rotating servo and the suspension system,a multi-body dynamic model simulating their integration is established using Lagrange’s equation.To mitigate instantaneous impact forces due to significant non-plumb effects from passive following in the horizontal direction,an elastic element is added in series with the rope in the vertical suspension system.The dynamic response of this elastic element relative to the rotating servo system is analyzed by the ADAMS software.Simulation results show that the compensating error decreases significantly from 45%to 0.31%when incorporating elastic elements compared to scenarios without such elements.Additionally,low-stiffness elastic elements demonstrate a higher compensating error than high-stiffness ones.A spring with a stiffness coefficient of 6 N/mm is selected in the experiment,ensuring that compensating error meets the design specification of 5%.
