Lightweight,high-strength,and heat-resistant protective structures have consistently been crucial for applications in extreme environments,such as aerospace,semiconductors,and nuclear power industries.Multilayered TC4...Lightweight,high-strength,and heat-resistant protective structures have consistently been crucial for applications in extreme environments,such as aerospace,semiconductors,and nuclear power industries.Multilayered TC4/TB8 titanium(Ti)laminates,inspired by theheterostructures of natural biological shells,were fabricated using a hybrid diffusion bonding-hot rolling process followed by an aging treatment,resulting in an architected micro structure.The laminate achieves an ultra-high yield stress of 1020 MPa and proper uniform elongation of 4.2%at 500℃.The TB8 layers with high-density nano-precipitates and dislocations act as hard zone,contributing to high strength.The TC4 layers,with their bimodal structure consisting of coarse and fine grains characterized by equiaxed and lamellar structures,experience more plastic strain than the TB8 layers.The hetero deformation associated with the detwinning ofαgrains in the TC4 layer induces toughening at high temperatures.展开更多
The vascular network is integral to the developmental and metabolic processes of various tissues and functions as a systemic circulatory system that also interconnects organs throughout the body.In this study,we descr...The vascular network is integral to the developmental and metabolic processes of various tissues and functions as a systemic circulatory system that also interconnects organs throughout the body.In this study,we describe a multilayered microfluidic organ-on-a-chip platform designed for reproducing various three-dimensional(3D)vascularized microtissue models for biological applications.This platform utilizes a porous membrane as a physical barrier and leverages capillary action for hydrogel self-filling.Its high flow resistance mitigates the risk of gel bursting into the medium channels and facilitates the delivery of substances to generate a wide range of interstitial flow and biochemical factor concentration gradients.This study demonstrated that this platform can be used to accurately replicate 3D microenvironments for vasculogenesis,angiogenesis,and vascularized tumor modeling.We also investigated the critical role of multiple microenvironmental regulations in vascular formation on a chip.Moreover,we reproduced the process of tumor angiogenesis,including primary solid tumor features and the inhibitory effects of antitumor drugs on tumor growth and tumor vasculature before and after angiogenesis.Hence,our multilayered microfluidic platform is valuable for exploring multiple vascular mechanisms and constructing specific microtissues that closely mimic in vivo physiological conditions,providing new strategies for cancer research.Furthermore,the multilayered configuration improves design flexibility and scalability,providing the potential for a multi-organ interconnected platform for high-throughput drug screening.展开更多
Heat transfers at the interface of adjacent saturated soil primarily through the soil particles and the water in the voids.The presence of water induces the contraction of heat flow lines at the interface,leading to t...Heat transfers at the interface of adjacent saturated soil primarily through the soil particles and the water in the voids.The presence of water induces the contraction of heat flow lines at the interface,leading to the emergence of the thermal contact resistance effect.In this paper,four thermal contact models were developed to predict the thermal contact resistance at the interface of multilayered saturated soils.Based on the theory of thermal-hydro-mechanical coupling,semi-analytical solutions of thermal consolidation subjected to time-dependent heating and loading were obtained by employing Laplace transform and its inverse transformation.Thermal consolidation characteristics of multilayered saturated soils under four different thermal contact models were discussed,and the effects of thermal resistance coefficient,partition thermal contact coefficient,and temperature amplitude on the thermal consolidation process were investigated.The outcomes indicate that the general thermal contact model results in the most pronounced thermal gradient at the interface,which can be degenerated to the other three thermal contact models.The perfect thermal contact model overestimates the deformation of the saturated soil during the thermal consolidation.Moreover,the effect of temperature on consolidation properties decreases gradually with increasing interfacial contact thermal resistance.展开更多
When the interface of a multilayered saturated soil is rough with noticeable gaps, heat flow lines converge towards the actual contact points, causing thermal flow contraction. Conversely, in the interface between two...When the interface of a multilayered saturated soil is rough with noticeable gaps, heat flow lines converge towards the actual contact points, causing thermal flow contraction. Conversely, in the interface between two layers of soil with different properties, pore water flows slowly along the pore channels, demonstrating laminar flow phenomenon. To predict the thermal contact resistance and flow contact resistance at the interface, this paper constructs general imperfect thermal contact model and general imperfect flow contact model, respectively. Utilizing a thermo-hydro- mechanical coupling model, the thermal consolidation behavior of multilayered saturated soil under two-dimensional conditions is investigated. Fourier and Laplace transformations are applied to decouple the governing equations, yielding expressions for the temperature increment, pore water pressure, and displacement in multilayered saturated soil. The inverse Fourier-Laplace transformation is then used to obtain numerical solutions, which are compared with degeneration solutions to validate the computational accuracy. The differences in the thermal consolidation process under various thermal contact and flow contact resistance models are discussed. Furthermore, the impact of parameters such as the thermal resistance coefficient, partition thermal contact coefficient, flow contact resistance coefficient, and partition flow contact coefficient on thermal consolidation are investigated. Results indicate that thermal contact resistance creates a relative thermal gradient at the interface, leading to increased pore water pressure and reduced displacement nearby. In contrast, flow contact resistance generates a relative pore pressure gradient at the interface, resulting in increased displacement within the saturated soil with minimal effect on temperature increment distribution.展开更多
The effects of accumulative hot rolling followed by solution treatment on the microstructural evolution and fracture behavior of 30CrMo/316L multilayered composites have been investigated.A scanning electron microscop...The effects of accumulative hot rolling followed by solution treatment on the microstructural evolution and fracture behavior of 30CrMo/316L multilayered composites have been investigated.A scanning electron microscope equipped with an electron backscatter diffraction probe,a laser confocal microscope,an electron probe microanalysis,and a universal testing machine were employed to characterize the microstructures and mechanical properties.The results indicate that solution treatment transformed the microstructure of the 30CrMo layer from ferrite to martensite,while the 316L layer remained austenitic but transitioned from the rolled to the recrystallized state.Additionally,solution treatment significantly enhanced the mechanical properties of the composite,leading to an increase in yield strength and ultimate tensile strength to 744 and 1106 MPa,respectively—258 and 276 MPa higher than those of the hot-rolled plate.The enhancement in strength is primarily attributed to the formation of high-strength martensite in the 30CrMo layer.During deformation,the composite interface effectively impeded crack propagation and induced step-like deflection.However,the formation of cross-layer grains facilitated crack nucleation at grain boundaries,leading to rapid crack propagation and instantaneous fracture.Therefore,preventing the formation of cross-layer grains during the heat treatment process is crucial,as their presence weakens the interfacial strengthening effect of the composite plate.This study provides valuable insights for the design and development of multi-layered steels.展开更多
This study proposes a three-dimensional(3D)coupled magneto-electro-elastic problem for the static analysis of multilayered plates embedding piezomagnetic and piezoelectric layers by considering both sensor and actuato...This study proposes a three-dimensional(3D)coupled magneto-electro-elastic problem for the static analysis of multilayered plates embedding piezomagnetic and piezoelectric layers by considering both sensor and actuator configurations.The 3D governing equations for the magneto-electro-elastic static behavior of plates are explicitly show that are made by the three 3D equilibrium equations,the 3D divergence equation for magnetic induction,and the 3D divergence equation for the electric displacement.The proposed solution involves the exponential matrix in the thickness direction and primary variables’harmonic forms in the in-plane ones.A closed-form solution is performed considering simply-supported boundary conditions.Interlaminar continuity conditions are imposed for displacements,magnetic potential,electric potential,transverse shear/normal stresses,transverse normal magnetic induction and transverse normal electric displacement.Therefore,a layerwise approach is adopted.The results section is composed of an assessment part,where the present model is compared to past 3D electro-elastic or magneto-elastic formulations and a new benchmark part.Benchmarks consider sensor and actuator plate configurations for the fully coupled magneto-electro-elastic cases for different thickness ratios.Tabular and graphical results are presented for displacements,stresses,magnetic potential,electric potential,transverse normal magnetic induction and transverse normal electric displacement.For each presented benchmark,magneto-electro-elastic coupling and thickness and material layer effects are discussed in depth.展开更多
Tin dioxide(SnO_(2))with a high theoretical specific capacity of 1494 mAh g^(-1)is a promising candidate anode material for lithium storage.However,the shortcomings of serious volume expansion and low conductivity lim...Tin dioxide(SnO_(2))with a high theoretical specific capacity of 1494 mAh g^(-1)is a promising candidate anode material for lithium storage.However,the shortcomings of serious volume expansion and low conductivity limit its wide application.Herein,coaxial nano-multilayered C/SnO_(2)/TiO_(2)composites were fabricated via layerby-layer self-assembly of TiO_(2)and SnO_(2)-gel layers on the natural cellulose filter paper,followed by thermal treatment under a nitrogen atmosphere.Through engineering design of the assembly process,the optimal C/SinO_(2)/TiO_(2)composite features five alternating SnO_(2)and TiO_(2)nanolayers,with TiO_(2)as the outside shell(denoted as C/TSTST).This unique structure endows the C/TSTST with excellent structural stability and electrochemical kinetics,making it a high-performance anode for lithium-ion batteries(LIBs).The C/TSTST composite delivers a high reversible capacity of 676 mAh g^(-1)at 0.1 A g^(-1)after 200 cycles and retains a capacity of 504 mAh g^(-1)at 1.0 A g^(-1),which can be recovered to 781 mAh g^(-1)at 0.1 A g^(-1)The significantly enhanced electrochemical performance is attributed to the hierarchical hybrid structure,where the carbon core combined with coaxial TiO_(2)nanolayers serves as a structural scaffold,ameliorating volume change of SnO_(2)while creating abundant interfacial defects for enhanced lithium storage and rapid charge transport.These findings are further demonstrated by the density functional theory(DFT)calculations.This work provides an efficient strategy for designing coaxial nano-multilayered transition metal oxide-related electrode materials,offering new insights into high-performance LIBs anodes.展开更多
Multilayered Ti-Al based intermetallic sheets were fabricated by sintering alternately layered titanium and aluminum foils.The microstructure and phase formation of the obtained sheets under different sintering condit...Multilayered Ti-Al based intermetallic sheets were fabricated by sintering alternately layered titanium and aluminum foils.The microstructure and phase formation of the obtained sheets under different sintering conditions were evaluated by various techniques.The results reveal that when the sintering temperature is above the melting point of aluminum,the self-propagating high-temperature synthesis reaction occurs between Ti and Al,and forms various phases of Ti-based solid solutions including α-Ti Ti3Al,TiAl,TiAl2 and α-Ti including TiAl3,etc.When the sintering time increased,Ti-based solid solution,TiAl2 and TiAl3 disappeared gradually,and the sheet containing Ti3Al and TiAl phases in a multilayered structure formed finally.A lot of voids were also observed in the sintered structures,which were caused by the melting Al,Kirkendall effect and the difference of molar volumes between reactants and products.The voids were eliminated and a dense sample was obtained by the following hot press.展开更多
Ti O2-organic multilayered nanocomposite films were deposited on a self-assembled monolayer-coated silicon substrate based on layer-by-layer technique and chemical bath deposition method by a hydrolysis of Ti Cl4 in a...Ti O2-organic multilayered nanocomposite films were deposited on a self-assembled monolayer-coated silicon substrate based on layer-by-layer technique and chemical bath deposition method by a hydrolysis of Ti Cl4 in an acid aqueous solution. The chemical compositions, surface morphologies and mechanical properties of the films were investigated by X-ray photoelectron spectrometer(XPS), scanning electron microscopy(SEM) and nanoindentation depth-sensing technique, respectively. The results indicate that the major chemical compositions of the films are Ti and O. The principal mechanism for the nucleation and growth of the films is homogeneous nucleation, and the layer number of films has great influence on the surface morphology and roughness of the films. In addition, mechanical nanoindentation testing presents a significant increase in hardness and fracture toughness of titanium dioxide multilayered films compared with single-layer titanium dioxide thin film.展开更多
The ultrastructure of the blepharoplast and the multilayered structure (MLS) in the fern Osmunda cinnamomea var. asiatica Fernald have been studied by electron microscopy with respect to spermatogenesis. The blepharop...The ultrastructure of the blepharoplast and the multilayered structure (MLS) in the fern Osmunda cinnamomea var. asiatica Fernald have been studied by electron microscopy with respect to spermatogenesis. The blepharoplast appears in the young spermatid. The differentiating blepharoplast is approximately a spherical body, which is composed of densely stained granular material in the center and some cylinders outside of it. The differentiated blepharoplast is also a sphere, but without the densely stained material in the center, consisting of scattered or radially arranged cylinders. The MLS seen in the spermatid lies between the basal bodies and the giant mitochondrion. In the early developmental stage, the MLS only consists of lamellar layers, each of which runs parallel to one another and forms a strip. In the mid stage, the MLS is composed of the microtubular ribbon (MTr), the lamellar layers and a layer of plaque. In the late stage, the MLS forms accessory band, osmiophilic crest and a layer of osmiophilic material. The MTr grows out from the MLS and extends along the surface of the nucleus to unite with the nuclear envelope in a complex. The basal body coming from the cylinder produces the axoneme of the flagella in the distal end and the wedge-shaped structure in the proximal end, respectively. In the present study, the ultrastructural features of blepharoplast and the MLS of the protoleptosporangiopsida fern, O. cinnamomea var. asiatica, have been described and compared with those of other kinds of pteridophytes in detail. The lamellar layers appearing before the formation of the MTr was found and reported for the first time.展开更多
In this paper,we theoretically study the Lamb wave in a multilayered piezoelectric semiconductor(PSC)plate,where each layer is an n-type PSC with the symmetry of transverse isotropy.Based on the extended Stroh formali...In this paper,we theoretically study the Lamb wave in a multilayered piezoelectric semiconductor(PSC)plate,where each layer is an n-type PSC with the symmetry of transverse isotropy.Based on the extended Stroh formalism and dual-variable and position(DVP)method,the general solution of the coupled fields for the Lamb wave is derived,and then the dispersion equation is obtained by the application of the boundary conditions.First,the influence of semiconducting properties on the dispersion behavior of the Lamb wave in a single-layer PSC plate is analyzed.Then,the propagation characteristics of the Lamb wave in a sandwich plate are investigated in detail.The numerical results show that the wave speed and attenuation depend on the stacking sequence,layer thickness,and initial carrier density,the Lamb wave can propagate without a cut-off frequency in both the homogeneous and multilayer PSC plates due to the semiconducting properties,and the Lamb wave without attenuation can be achieved by carefully selecting the semiconductor property in the upper and lower layers.These new features could be very helpful as theoretical guidance for the design and performance optimization of PSC devices.展开更多
In rotationally extruded fittings,high-density polyethylene(HDPE)pipes prepared using conventional processing methods often suffer from poor pressure resistance and low toughness.This study introduces an innovative ro...In rotationally extruded fittings,high-density polyethylene(HDPE)pipes prepared using conventional processing methods often suffer from poor pressure resistance and low toughness.This study introduces an innovative rotary shear system(RSS)to address these deficiencies through controlled mandrel rotation and cooling rates.We successfully prepared self-reinforced HDPE pipes with a three-layer structure combining spherical and shish-kebab crystals.Rotational processing aligned the molecular chains in the ring direction and formed shish-kebab crystals.As a result,the annular tensile strength of the rotationally processed three-layer shish-kebab structure(TSK)pipe increased from 26.7 MPa to 76.3 MPa,an enhancement of 185.8%.Notably,while maintaining excellent tensile strength(73.4 MPa),the elongation at break of the spherulite shishkebab spherulite(SKS)tubes was improved to 50.1%,as compared to 33.8%in the case of shish-kebab spherulite shish-kebab(KSK)tubes.This improvement can be attributed to the changes in the micro-morphology and polymer structure within the SKS tubes,specifically due to the formation of small-sized shish-kebab crystals and the low degrees of interlocking.In addition,2D-SAXS analysis revealed that KSK tubes have higher tensile strength due to smaller crystal sizes and larger shish dimensions,forming dense interlocking structures.In contrast,the SKS and TSK tubes had thicker amorphous regions and smaller shish sizes,resulting in reduced interlocking and mechanical performance.展开更多
Al/Mg alloy multilayered composites were produced successfully at the lower temperature（280 C） by accumulative roll bonding（ARB） processing technique.The microstructures of Al and Mg alloy layers were characterize...Al/Mg alloy multilayered composites were produced successfully at the lower temperature（280 C） by accumulative roll bonding（ARB） processing technique.The microstructures of Al and Mg alloy layers were characterized by scanning electron microscopy and transmission electron microscopy.Vickers hardness and three-point bending tests were conducted to investigate mechanical properties of the composites.It is found that Vickers hardness,bending strength and stiffness modulus of the Al/Mg alloy multilayered composite increase with increasing the ARB pass.Delamination and crack propagation along the interface are the two main failure modes of the multilayered composite subjected to bending load.Strengthening and fracture mechanisms of the composite are analyzed.展开更多
Ti/Cu multilayered composites were fabricated via accumulative roll bonding(ARB). During codeformation of the constituent metals, the hard Ti layers necked preferentially and then fragmented with the development of sh...Ti/Cu multilayered composites were fabricated via accumulative roll bonding(ARB). During codeformation of the constituent metals, the hard Ti layers necked preferentially and then fragmented with the development of shear bands. Transmission electron microscopy showed that with increasing ARB cycles, grains in Ti were significantly refined even though dynamic recrystallization has occurred. For Cu the significant grain refinement was only found within the shear banded region when the composite was processed after five ARB cycles. Due to the diffusion of Cu atoms into Ti at the heterophase interfaces, amorphization with a width less than 10 nm was identified even in the composite processed by one cycle. At higher ARB cycles, the width of amorphous region increased and intermetallic compounds CuTi appeared from the region. The lattice defects introduced at the heterophase interfaces under roll bonding was responsible for the formation of the nano-scaled compounds. X-ray diffraction showed that an abnormal {1120} fiber texture was developed in Ti layers, while significant brass-type textures were developed in Cu layers. Some orientations along the {1120} fiber favored the prismatic < a> slip for Ti.Tensile tests revealed the elevated strength without a substantial sacrifice of ductility in the composites during ARB. The unique mechanical properties were attributed to the significantly refined grains in individual metals, the good bonding between the constituent metals, as well as the development of an abnormal {1120} fiber texture in Ti layers.展开更多
The study of transient heat conduction in multilayered slabs is widely used in various engineering fields. In this paper, the transient heat conduction in multilayered slabs with general boundary conditions and arbitr...The study of transient heat conduction in multilayered slabs is widely used in various engineering fields. In this paper, the transient heat conduction in multilayered slabs with general boundary conditions and arbitrary heat generations is analysed. The boundary conditions are general and include various combinations of Dirichlet, Neumann or Robin boundary conditions at either surface. Moreover, arbitrary heat generations in the slabs are taken into account. The solutions are derived by basic methods, including the superposition method, separation variable method and orthogonal expansion method. The simplified double-layered analytical solution is validated by a numerical method and applied to predicting the temporal and spatial distribution of the temperature inside a landfill. It indicates the ability of the proposed analytical solutions for solving the wide range of applied transient heat conduction problems.展开更多
There has been much interest in developing multilayered or nanolayered physical vapor deposition（PVD） coatings identified as a group of promising protective coatings for their excellent mechanical properties and cor...There has been much interest in developing multilayered or nanolayered physical vapor deposition（PVD） coatings identified as a group of promising protective coatings for their excellent mechanical properties and corrosion resistance. In this study, the multilayered Cr N/Cr2O3 coatings with different bilayer periods（L） were synthesized on the polished high speed steel substrates from a Cr target with the alternative atmosphere of pure nitrogen and pure oxygen by arc ion plating（AIP） technique. The results revealed that the microstructure,morphologies and properties of the multilayered coatings were strongly influenced by the bilayer period（L）.There were two kinds of interfaces in the multilayered Cr N/Cr2O3coatings： the sharp ones and the blurry ones. With reducing the value of L, the macro-particles densities decreased gradually, whereas the coating microhardness, adhesive strength and wear resistance first increased, and then decreased slightly or remained stable as the bilayer period L 〈 590 nm. The multilayered Cr N/Cr2O3 coating with the bilayer period L of 590 nm possessed the best comprehensive properties, namely the highest microhardness, the strongest adhesion, and the lowest wear rate.展开更多
Quasicrystals （QCs） are sensitive to the piezoelectric （PE） effect. This paper studies static deformation of a multilayered one-dimensional （1D） hexagonal QC plate with the PE effect. The exact closed-form solut...Quasicrystals （QCs） are sensitive to the piezoelectric （PE） effect. This paper studies static deformation of a multilayered one-dimensional （1D） hexagonal QC plate with the PE effect. The exact closed-form solutions of the extended displacement and traction for a homogeneous piezoelectric quasicrystal （PQC）plate are derived from an eigensystem. The general solutions for multilayered PQC plates are then obtained using the propagator matrix method when mechanical and electrical loads are applied on the top surface of the plate. Numerical examples for several sandwich plates made up of PQC, PE, and QC materials are provided to show the effect of stacking sequence on phonon, phason, and electric fields under mechanical and electrical loads, which is useful in designing new composites for engineering structures.展开更多
A self-adaptive differential evolution neutron spectrum unfolding algorithm(SDENUA)is established in this study to unfold the neutron spectra obtained from a water-pumping-injection multilayered concentric sphere neut...A self-adaptive differential evolution neutron spectrum unfolding algorithm(SDENUA)is established in this study to unfold the neutron spectra obtained from a water-pumping-injection multilayered concentric sphere neutron spectrometer(WMNS).Specifically,the neutron fluence bounds are estimated to accelerate the algorithm convergence,and the minimum error between the optimal solution and input neutron counts with relative uncertainties is limited to 10^(-6)to avoid unnecessary calculations.Furthermore,the crossover probability and scaling factor are self-adaptively controlled.FLUKA Monte Carlo is used to simulate the readings of the WMNS under(1)a spectrum of Cf-252 and(2)its spectrum after being moderated,(3)a spectrum used for boron neutron capture therapy,and(4)a reactor spectrum.Subsequently,the measured neutron counts are unfolded using the SDENUA.The uncertainties of the measured neutron count and the response matrix are considered in the SDENUA,which does not require complex parameter tuning or an a priori default spectrum.The results indicate that the solutions of the SDENUA agree better with the IAEA spectra than those of MAXED and GRAVEL in UMG 3.1,and the errors of the final results calculated using the SDENUA are less than 12%.The established SDENUA can be used to unfold spectra from the WMNS.展开更多
Coalbed methane(CBM)is an important unconventional natural gas.Exploitation of multilayered CBM reservoir is still facing the challenge of low production rate.Radial borehole fracturing,which integrates radial jet dri...Coalbed methane(CBM)is an important unconventional natural gas.Exploitation of multilayered CBM reservoir is still facing the challenge of low production rate.Radial borehole fracturing,which integrates radial jet drilling and hydraulic fracturing,is expected to create complex fracture networks in multilayers and enhance CBM recovery.The main purpose of this paper is to investigate the mechanisms and efficacy of radial borehole fracturing in increasing CBM production in multiple layers.First,a two-phase flow and multi-scale 3 D fracture network including radial laterals,hydraulic fractures and face/butt cleats model is established,and embedded discrete fracture model(EDFM)is applied to handle the complex fracture networks.Then,effects of natural-fracture nonuniform distribution are investigated to show the advantages of targeted stimulation for radial borehole fracturing.Finally,two field CBM wells located in eastern Yunnan-western Guizhou,China were presented to illuminate the stimulation efficiency by radial borehole fracturing.The results indicated that compared with vertical well fracturing,radial borehole fracturing can achieve higher gas/water daily production rate and cumulative gas/water production,approximately 2 times higher.Targeted communications to cleats and sweet spots and flexibility in designing radial borehole parameters in different layers so as to increase fracture-network complexity and connectivity are the major reasons for production enhancement of radial borehole fracturing.Furthermore,the integration of geology-engineering is vital for the decision of radial borehole fracturing designing scheme.The key findings of this paper could provide useful insights towards understanding the capability of radial borehole fracturing in developing CBM and coal-measure gas in multiple-thin layers.展开更多
Conventional orthogonal polynomial approach can solve the multilayered plate only when the material properties of two adjacent layers do not change significantly. This paper de- veloped an improved orthogonal polynomi...Conventional orthogonal polynomial approach can solve the multilayered plate only when the material properties of two adjacent layers do not change significantly. This paper de- veloped an improved orthogonal polynomial approach to solve wave propagation in multilayered plates with very dissimilar material properties. Through numerical comparisons among the exact solution, the results from the conventional polynomial approach and from the improved poly- nomial approach, the validity of the improved polynomial approach is illustrated. Finally, it is shown that the conventional polynomial approach can not yield correct continuous normal stress profiles. The improved orthogonul polynomial approach has overcome this drawback.展开更多
基金financially supported by the Natural Science Foundation of Changsha,China(No.kq2402015)the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIP)(Nos.NRF-2021R1A2C3006662 and NRF-2022R1A5A1030054)supported by Brain Pool Program through the NRF of Korea,funded by the Ministry of Science and ICT(No.NRF-RS_(2)02300263999)
文摘Lightweight,high-strength,and heat-resistant protective structures have consistently been crucial for applications in extreme environments,such as aerospace,semiconductors,and nuclear power industries.Multilayered TC4/TB8 titanium(Ti)laminates,inspired by theheterostructures of natural biological shells,were fabricated using a hybrid diffusion bonding-hot rolling process followed by an aging treatment,resulting in an architected micro structure.The laminate achieves an ultra-high yield stress of 1020 MPa and proper uniform elongation of 4.2%at 500℃.The TB8 layers with high-density nano-precipitates and dislocations act as hard zone,contributing to high strength.The TC4 layers,with their bimodal structure consisting of coarse and fine grains characterized by equiaxed and lamellar structures,experience more plastic strain than the TB8 layers.The hetero deformation associated with the detwinning ofαgrains in the TC4 layer induces toughening at high temperatures.
基金supported by grants from the Interdisciplinary Program of Shanghai Jiao Tong University(No.YG2023LC04)the National Natural Science Foundation of China(Nos.32471473,62231025,and 82171011)+1 种基金the Research Program of Shanghai Science and Technology Committee(Nos.24141900900 and 25JC3201100)Chongqing Natural Science Foundation(No.CSTB2022NSCQ-MSX0767)
文摘The vascular network is integral to the developmental and metabolic processes of various tissues and functions as a systemic circulatory system that also interconnects organs throughout the body.In this study,we describe a multilayered microfluidic organ-on-a-chip platform designed for reproducing various three-dimensional(3D)vascularized microtissue models for biological applications.This platform utilizes a porous membrane as a physical barrier and leverages capillary action for hydrogel self-filling.Its high flow resistance mitigates the risk of gel bursting into the medium channels and facilitates the delivery of substances to generate a wide range of interstitial flow and biochemical factor concentration gradients.This study demonstrated that this platform can be used to accurately replicate 3D microenvironments for vasculogenesis,angiogenesis,and vascularized tumor modeling.We also investigated the critical role of multiple microenvironmental regulations in vascular formation on a chip.Moreover,we reproduced the process of tumor angiogenesis,including primary solid tumor features and the inhibitory effects of antitumor drugs on tumor growth and tumor vasculature before and after angiogenesis.Hence,our multilayered microfluidic platform is valuable for exploring multiple vascular mechanisms and constructing specific microtissues that closely mimic in vivo physiological conditions,providing new strategies for cancer research.Furthermore,the multilayered configuration improves design flexibility and scalability,providing the potential for a multi-organ interconnected platform for high-throughput drug screening.
基金Projects(U24B20113,42477162) supported by the National Natural Science Foundation of ChinaProject(2025C02228) supported by the Primary Research and Development Plan of Zhejiang Province,China。
文摘Heat transfers at the interface of adjacent saturated soil primarily through the soil particles and the water in the voids.The presence of water induces the contraction of heat flow lines at the interface,leading to the emergence of the thermal contact resistance effect.In this paper,four thermal contact models were developed to predict the thermal contact resistance at the interface of multilayered saturated soils.Based on the theory of thermal-hydro-mechanical coupling,semi-analytical solutions of thermal consolidation subjected to time-dependent heating and loading were obtained by employing Laplace transform and its inverse transformation.Thermal consolidation characteristics of multilayered saturated soils under four different thermal contact models were discussed,and the effects of thermal resistance coefficient,partition thermal contact coefficient,and temperature amplitude on the thermal consolidation process were investigated.The outcomes indicate that the general thermal contact model results in the most pronounced thermal gradient at the interface,which can be degenerated to the other three thermal contact models.The perfect thermal contact model overestimates the deformation of the saturated soil during the thermal consolidation.Moreover,the effect of temperature on consolidation properties decreases gradually with increasing interfacial contact thermal resistance.
基金Projects(52108347, 52179112, 52178371) supported by the National Natural Science Foundation of ChinaProjects(2020C01147, 2023C01165) supported by the Primary Research and Development Plan of Zhejiang Province,ChinaProject(LQ22E080010) supported by the Outstanding Youth Project of Natural Science Foundation of Zhejiang Province,China。
文摘When the interface of a multilayered saturated soil is rough with noticeable gaps, heat flow lines converge towards the actual contact points, causing thermal flow contraction. Conversely, in the interface between two layers of soil with different properties, pore water flows slowly along the pore channels, demonstrating laminar flow phenomenon. To predict the thermal contact resistance and flow contact resistance at the interface, this paper constructs general imperfect thermal contact model and general imperfect flow contact model, respectively. Utilizing a thermo-hydro- mechanical coupling model, the thermal consolidation behavior of multilayered saturated soil under two-dimensional conditions is investigated. Fourier and Laplace transformations are applied to decouple the governing equations, yielding expressions for the temperature increment, pore water pressure, and displacement in multilayered saturated soil. The inverse Fourier-Laplace transformation is then used to obtain numerical solutions, which are compared with degeneration solutions to validate the computational accuracy. The differences in the thermal consolidation process under various thermal contact and flow contact resistance models are discussed. Furthermore, the impact of parameters such as the thermal resistance coefficient, partition thermal contact coefficient, flow contact resistance coefficient, and partition flow contact coefficient on thermal consolidation are investigated. Results indicate that thermal contact resistance creates a relative thermal gradient at the interface, leading to increased pore water pressure and reduced displacement nearby. In contrast, flow contact resistance generates a relative pore pressure gradient at the interface, resulting in increased displacement within the saturated soil with minimal effect on temperature increment distribution.
基金supported by the National Key Research and Development Program of China(No.2018YFA0707304).
文摘The effects of accumulative hot rolling followed by solution treatment on the microstructural evolution and fracture behavior of 30CrMo/316L multilayered composites have been investigated.A scanning electron microscope equipped with an electron backscatter diffraction probe,a laser confocal microscope,an electron probe microanalysis,and a universal testing machine were employed to characterize the microstructures and mechanical properties.The results indicate that solution treatment transformed the microstructure of the 30CrMo layer from ferrite to martensite,while the 316L layer remained austenitic but transitioned from the rolled to the recrystallized state.Additionally,solution treatment significantly enhanced the mechanical properties of the composite,leading to an increase in yield strength and ultimate tensile strength to 744 and 1106 MPa,respectively—258 and 276 MPa higher than those of the hot-rolled plate.The enhancement in strength is primarily attributed to the formation of high-strength martensite in the 30CrMo layer.During deformation,the composite interface effectively impeded crack propagation and induced step-like deflection.However,the formation of cross-layer grains facilitated crack nucleation at grain boundaries,leading to rapid crack propagation and instantaneous fracture.Therefore,preventing the formation of cross-layer grains during the heat treatment process is crucial,as their presence weakens the interfacial strengthening effect of the composite plate.This study provides valuable insights for the design and development of multi-layered steels.
文摘This study proposes a three-dimensional(3D)coupled magneto-electro-elastic problem for the static analysis of multilayered plates embedding piezomagnetic and piezoelectric layers by considering both sensor and actuator configurations.The 3D governing equations for the magneto-electro-elastic static behavior of plates are explicitly show that are made by the three 3D equilibrium equations,the 3D divergence equation for magnetic induction,and the 3D divergence equation for the electric displacement.The proposed solution involves the exponential matrix in the thickness direction and primary variables’harmonic forms in the in-plane ones.A closed-form solution is performed considering simply-supported boundary conditions.Interlaminar continuity conditions are imposed for displacements,magnetic potential,electric potential,transverse shear/normal stresses,transverse normal magnetic induction and transverse normal electric displacement.Therefore,a layerwise approach is adopted.The results section is composed of an assessment part,where the present model is compared to past 3D electro-elastic or magneto-elastic formulations and a new benchmark part.Benchmarks consider sensor and actuator plate configurations for the fully coupled magneto-electro-elastic cases for different thickness ratios.Tabular and graphical results are presented for displacements,stresses,magnetic potential,electric potential,transverse normal magnetic induction and transverse normal electric displacement.For each presented benchmark,magneto-electro-elastic coupling and thickness and material layer effects are discussed in depth.
基金financially supported by the National Natural Science Foundation of China(Nos.22302133 and 22405161)Central Guidance on Local Science and Technology Development Fund of Hebei Province,China(No.236Z4406G)+5 种基金the Natural Science Foundation of Hebei Education Department,China(No.BJ2025100)the Natural Science Foundation of Hebei Province,China(No.B2021210001)the Natural Science Foundation of Xinjiang Uygur Autonomous Region(No.2024D01A157)the Key R&D Plan of Karamay(No.2024zdyf0009)Karamay Innovation Environment Construction Plan(Innovative Talents)Project(No.2024hjcxrc0029)the Research Foundation of China University of Petroleum-Beijing at Karamay(No.XQZX20240023)
文摘Tin dioxide(SnO_(2))with a high theoretical specific capacity of 1494 mAh g^(-1)is a promising candidate anode material for lithium storage.However,the shortcomings of serious volume expansion and low conductivity limit its wide application.Herein,coaxial nano-multilayered C/SnO_(2)/TiO_(2)composites were fabricated via layerby-layer self-assembly of TiO_(2)and SnO_(2)-gel layers on the natural cellulose filter paper,followed by thermal treatment under a nitrogen atmosphere.Through engineering design of the assembly process,the optimal C/SinO_(2)/TiO_(2)composite features five alternating SnO_(2)and TiO_(2)nanolayers,with TiO_(2)as the outside shell(denoted as C/TSTST).This unique structure endows the C/TSTST with excellent structural stability and electrochemical kinetics,making it a high-performance anode for lithium-ion batteries(LIBs).The C/TSTST composite delivers a high reversible capacity of 676 mAh g^(-1)at 0.1 A g^(-1)after 200 cycles and retains a capacity of 504 mAh g^(-1)at 1.0 A g^(-1),which can be recovered to 781 mAh g^(-1)at 0.1 A g^(-1)The significantly enhanced electrochemical performance is attributed to the hierarchical hybrid structure,where the carbon core combined with coaxial TiO_(2)nanolayers serves as a structural scaffold,ameliorating volume change of SnO_(2)while creating abundant interfacial defects for enhanced lithium storage and rapid charge transport.These findings are further demonstrated by the density functional theory(DFT)calculations.This work provides an efficient strategy for designing coaxial nano-multilayered transition metal oxide-related electrode materials,offering new insights into high-performance LIBs anodes.
基金Project (2010DFA51650) supported by the Ministry of Science and Technology of China
文摘Multilayered Ti-Al based intermetallic sheets were fabricated by sintering alternately layered titanium and aluminum foils.The microstructure and phase formation of the obtained sheets under different sintering conditions were evaluated by various techniques.The results reveal that when the sintering temperature is above the melting point of aluminum,the self-propagating high-temperature synthesis reaction occurs between Ti and Al,and forms various phases of Ti-based solid solutions including α-Ti Ti3Al,TiAl,TiAl2 and α-Ti including TiAl3,etc.When the sintering time increased,Ti-based solid solution,TiAl2 and TiAl3 disappeared gradually,and the sheet containing Ti3Al and TiAl phases in a multilayered structure formed finally.A lot of voids were also observed in the sintered structures,which were caused by the melting Al,Kirkendall effect and the difference of molar volumes between reactants and products.The voids were eliminated and a dense sample was obtained by the following hot press.
基金Projects(51204036,51234009)supported by the National Natural Science Foundation of ChinaProject(2014CB643405)supported by the National Basic Research Program of China
文摘Ti O2-organic multilayered nanocomposite films were deposited on a self-assembled monolayer-coated silicon substrate based on layer-by-layer technique and chemical bath deposition method by a hydrolysis of Ti Cl4 in an acid aqueous solution. The chemical compositions, surface morphologies and mechanical properties of the films were investigated by X-ray photoelectron spectrometer(XPS), scanning electron microscopy(SEM) and nanoindentation depth-sensing technique, respectively. The results indicate that the major chemical compositions of the films are Ti and O. The principal mechanism for the nucleation and growth of the films is homogeneous nucleation, and the layer number of films has great influence on the surface morphology and roughness of the films. In addition, mechanical nanoindentation testing presents a significant increase in hardness and fracture toughness of titanium dioxide multilayered films compared with single-layer titanium dioxide thin film.
文摘The ultrastructure of the blepharoplast and the multilayered structure (MLS) in the fern Osmunda cinnamomea var. asiatica Fernald have been studied by electron microscopy with respect to spermatogenesis. The blepharoplast appears in the young spermatid. The differentiating blepharoplast is approximately a spherical body, which is composed of densely stained granular material in the center and some cylinders outside of it. The differentiated blepharoplast is also a sphere, but without the densely stained material in the center, consisting of scattered or radially arranged cylinders. The MLS seen in the spermatid lies between the basal bodies and the giant mitochondrion. In the early developmental stage, the MLS only consists of lamellar layers, each of which runs parallel to one another and forms a strip. In the mid stage, the MLS is composed of the microtubular ribbon (MTr), the lamellar layers and a layer of plaque. In the late stage, the MLS forms accessory band, osmiophilic crest and a layer of osmiophilic material. The MTr grows out from the MLS and extends along the surface of the nucleus to unite with the nuclear envelope in a complex. The basal body coming from the cylinder produces the axoneme of the flagella in the distal end and the wedge-shaped structure in the proximal end, respectively. In the present study, the ultrastructural features of blepharoplast and the MLS of the protoleptosporangiopsida fern, O. cinnamomea var. asiatica, have been described and compared with those of other kinds of pteridophytes in detail. The lamellar layers appearing before the formation of the MTr was found and reported for the first time.
基金Project supported by the National Natural Science Foundation of China(Nos.U21A20430 and 12302202)the Hebei Natural Science Foundation of China(No.A2023210040)+1 种基金the Science and Technology Project of Hebei Education Department of China(No.BJ2025005)the Hebei Provincial Department of Human Resources and Social Security of China(No.C20220324)。
文摘In this paper,we theoretically study the Lamb wave in a multilayered piezoelectric semiconductor(PSC)plate,where each layer is an n-type PSC with the symmetry of transverse isotropy.Based on the extended Stroh formalism and dual-variable and position(DVP)method,the general solution of the coupled fields for the Lamb wave is derived,and then the dispersion equation is obtained by the application of the boundary conditions.First,the influence of semiconducting properties on the dispersion behavior of the Lamb wave in a single-layer PSC plate is analyzed.Then,the propagation characteristics of the Lamb wave in a sandwich plate are investigated in detail.The numerical results show that the wave speed and attenuation depend on the stacking sequence,layer thickness,and initial carrier density,the Lamb wave can propagate without a cut-off frequency in both the homogeneous and multilayer PSC plates due to the semiconducting properties,and the Lamb wave without attenuation can be achieved by carefully selecting the semiconductor property in the upper and lower layers.These new features could be very helpful as theoretical guidance for the design and performance optimization of PSC devices.
基金supported by the National Natural Science Foundation of China(Nos.52373045 and 52033005).
文摘In rotationally extruded fittings,high-density polyethylene(HDPE)pipes prepared using conventional processing methods often suffer from poor pressure resistance and low toughness.This study introduces an innovative rotary shear system(RSS)to address these deficiencies through controlled mandrel rotation and cooling rates.We successfully prepared self-reinforced HDPE pipes with a three-layer structure combining spherical and shish-kebab crystals.Rotational processing aligned the molecular chains in the ring direction and formed shish-kebab crystals.As a result,the annular tensile strength of the rotationally processed three-layer shish-kebab structure(TSK)pipe increased from 26.7 MPa to 76.3 MPa,an enhancement of 185.8%.Notably,while maintaining excellent tensile strength(73.4 MPa),the elongation at break of the spherulite shishkebab spherulite(SKS)tubes was improved to 50.1%,as compared to 33.8%in the case of shish-kebab spherulite shish-kebab(KSK)tubes.This improvement can be attributed to the changes in the micro-morphology and polymer structure within the SKS tubes,specifically due to the formation of small-sized shish-kebab crystals and the low degrees of interlocking.In addition,2D-SAXS analysis revealed that KSK tubes have higher tensile strength due to smaller crystal sizes and larger shish dimensions,forming dense interlocking structures.In contrast,the SKS and TSK tubes had thicker amorphous regions and smaller shish sizes,resulting in reduced interlocking and mechanical performance.
基金supported by the National Natural Science Foundation of China (Grant No. 50890173)
文摘Al/Mg alloy multilayered composites were produced successfully at the lower temperature（280 C） by accumulative roll bonding（ARB） processing technique.The microstructures of Al and Mg alloy layers were characterized by scanning electron microscopy and transmission electron microscopy.Vickers hardness and three-point bending tests were conducted to investigate mechanical properties of the composites.It is found that Vickers hardness,bending strength and stiffness modulus of the Al/Mg alloy multilayered composite increase with increasing the ARB pass.Delamination and crack propagation along the interface are the two main failure modes of the multilayered composite subjected to bending load.Strengthening and fracture mechanisms of the composite are analyzed.
基金financially supported by the National Natural Science Foundation of China(No.51571057)the Fundamental Research Funds for the Central Universities(No.N170204012)
文摘Ti/Cu multilayered composites were fabricated via accumulative roll bonding(ARB). During codeformation of the constituent metals, the hard Ti layers necked preferentially and then fragmented with the development of shear bands. Transmission electron microscopy showed that with increasing ARB cycles, grains in Ti were significantly refined even though dynamic recrystallization has occurred. For Cu the significant grain refinement was only found within the shear banded region when the composite was processed after five ARB cycles. Due to the diffusion of Cu atoms into Ti at the heterophase interfaces, amorphization with a width less than 10 nm was identified even in the composite processed by one cycle. At higher ARB cycles, the width of amorphous region increased and intermetallic compounds CuTi appeared from the region. The lattice defects introduced at the heterophase interfaces under roll bonding was responsible for the formation of the nano-scaled compounds. X-ray diffraction showed that an abnormal {1120} fiber texture was developed in Ti layers, while significant brass-type textures were developed in Cu layers. Some orientations along the {1120} fiber favored the prismatic < a> slip for Ti.Tensile tests revealed the elevated strength without a substantial sacrifice of ductility in the composites during ARB. The unique mechanical properties were attributed to the significantly refined grains in individual metals, the good bonding between the constituent metals, as well as the development of an abnormal {1120} fiber texture in Ti layers.
基金Projects(41530637,41877222,41702290)supported by the National Natural Science Foundation of China
文摘The study of transient heat conduction in multilayered slabs is widely used in various engineering fields. In this paper, the transient heat conduction in multilayered slabs with general boundary conditions and arbitrary heat generations is analysed. The boundary conditions are general and include various combinations of Dirichlet, Neumann or Robin boundary conditions at either surface. Moreover, arbitrary heat generations in the slabs are taken into account. The solutions are derived by basic methods, including the superposition method, separation variable method and orthogonal expansion method. The simplified double-layered analytical solution is validated by a numerical method and applied to predicting the temporal and spatial distribution of the temperature inside a landfill. It indicates the ability of the proposed analytical solutions for solving the wide range of applied transient heat conduction problems.
基金financial supports from the National Key Basic Research Program of China (973 Program, No. 2012CB625100)the National Natural Science Foundation of China (Nos. 51001106 and 51301181)the Doctoral Starting up Foundation of Liaoning Province Science and Technology Agency, China (No. 20131118)
文摘There has been much interest in developing multilayered or nanolayered physical vapor deposition（PVD） coatings identified as a group of promising protective coatings for their excellent mechanical properties and corrosion resistance. In this study, the multilayered Cr N/Cr2O3 coatings with different bilayer periods（L） were synthesized on the polished high speed steel substrates from a Cr target with the alternative atmosphere of pure nitrogen and pure oxygen by arc ion plating（AIP） technique. The results revealed that the microstructure,morphologies and properties of the multilayered coatings were strongly influenced by the bilayer period（L）.There were two kinds of interfaces in the multilayered Cr N/Cr2O3coatings： the sharp ones and the blurry ones. With reducing the value of L, the macro-particles densities decreased gradually, whereas the coating microhardness, adhesive strength and wear resistance first increased, and then decreased slightly or remained stable as the bilayer period L 〈 590 nm. The multilayered Cr N/Cr2O3 coating with the bilayer period L of 590 nm possessed the best comprehensive properties, namely the highest microhardness, the strongest adhesion, and the lowest wear rate.
基金Project supported by the National Natural Science Foundation of China(Nos.11502123 and11262012)the Natural Science Foundation of Inner Mongolia Autonomous Region of China(No.2015JQ01)
文摘Quasicrystals （QCs） are sensitive to the piezoelectric （PE） effect. This paper studies static deformation of a multilayered one-dimensional （1D） hexagonal QC plate with the PE effect. The exact closed-form solutions of the extended displacement and traction for a homogeneous piezoelectric quasicrystal （PQC）plate are derived from an eigensystem. The general solutions for multilayered PQC plates are then obtained using the propagator matrix method when mechanical and electrical loads are applied on the top surface of the plate. Numerical examples for several sandwich plates made up of PQC, PE, and QC materials are provided to show the effect of stacking sequence on phonon, phason, and electric fields under mechanical and electrical loads, which is useful in designing new composites for engineering structures.
基金supported by the National Key R&D Program of the MOST of China(No.2016YFA0300204)the National Natural Science Foundation of China(Nos.11227902)as part of the Si PáME2beamline project+1 种基金supported by the National Natural Science Foundation of China(No.41774120)the Sichuan Science and Technology Program(No.2021YJ0329)。
文摘A self-adaptive differential evolution neutron spectrum unfolding algorithm(SDENUA)is established in this study to unfold the neutron spectra obtained from a water-pumping-injection multilayered concentric sphere neutron spectrometer(WMNS).Specifically,the neutron fluence bounds are estimated to accelerate the algorithm convergence,and the minimum error between the optimal solution and input neutron counts with relative uncertainties is limited to 10^(-6)to avoid unnecessary calculations.Furthermore,the crossover probability and scaling factor are self-adaptively controlled.FLUKA Monte Carlo is used to simulate the readings of the WMNS under(1)a spectrum of Cf-252 and(2)its spectrum after being moderated,(3)a spectrum used for boron neutron capture therapy,and(4)a reactor spectrum.Subsequently,the measured neutron counts are unfolded using the SDENUA.The uncertainties of the measured neutron count and the response matrix are considered in the SDENUA,which does not require complex parameter tuning or an a priori default spectrum.The results indicate that the solutions of the SDENUA agree better with the IAEA spectra than those of MAXED and GRAVEL in UMG 3.1,and the errors of the final results calculated using the SDENUA are less than 12%.The established SDENUA can be used to unfold spectra from the WMNS.
基金supported by the National Natural Science Foundation of China(National R&D Program for Major Research Instruments,51827804)Youth Program of National Natural Science Foundation of China(52004299)National Science Foundation for Distinguished Young Scholars(51725404)
文摘Coalbed methane(CBM)is an important unconventional natural gas.Exploitation of multilayered CBM reservoir is still facing the challenge of low production rate.Radial borehole fracturing,which integrates radial jet drilling and hydraulic fracturing,is expected to create complex fracture networks in multilayers and enhance CBM recovery.The main purpose of this paper is to investigate the mechanisms and efficacy of radial borehole fracturing in increasing CBM production in multiple layers.First,a two-phase flow and multi-scale 3 D fracture network including radial laterals,hydraulic fractures and face/butt cleats model is established,and embedded discrete fracture model(EDFM)is applied to handle the complex fracture networks.Then,effects of natural-fracture nonuniform distribution are investigated to show the advantages of targeted stimulation for radial borehole fracturing.Finally,two field CBM wells located in eastern Yunnan-western Guizhou,China were presented to illuminate the stimulation efficiency by radial borehole fracturing.The results indicated that compared with vertical well fracturing,radial borehole fracturing can achieve higher gas/water daily production rate and cumulative gas/water production,approximately 2 times higher.Targeted communications to cleats and sweet spots and flexibility in designing radial borehole parameters in different layers so as to increase fracture-network complexity and connectivity are the major reasons for production enhancement of radial borehole fracturing.Furthermore,the integration of geology-engineering is vital for the decision of radial borehole fracturing designing scheme.The key findings of this paper could provide useful insights towards understanding the capability of radial borehole fracturing in developing CBM and coal-measure gas in multiple-thin layers.
基金supported by the National Natural Science Foundation of China(No.11272115)
文摘Conventional orthogonal polynomial approach can solve the multilayered plate only when the material properties of two adjacent layers do not change significantly. This paper de- veloped an improved orthogonal polynomial approach to solve wave propagation in multilayered plates with very dissimilar material properties. Through numerical comparisons among the exact solution, the results from the conventional polynomial approach and from the improved poly- nomial approach, the validity of the improved polynomial approach is illustrated. Finally, it is shown that the conventional polynomial approach can not yield correct continuous normal stress profiles. The improved orthogonul polynomial approach has overcome this drawback.
