In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow e...In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow equation.The velocity and pressure are computed simultaneously.The accuracy of velocity is improved one order.The concentration equation is solved by using mixed finite element,multi-step difference and upwind approximation.A multi-step method is used to approximate time derivative for improving the accuracy.The upwind approximation and an expanded mixed finite element are adopted to solve the convection and diffusion,respectively.The composite method could compute the diffusion flux and its gradient.It possibly becomes an eficient tool for solving convection-dominated diffusion problems.Firstly,the conservation of mass holds.Secondly,the multi-step method has high accuracy.Thirdly,the upwind approximation could avoid numerical dispersion.Using numerical analysis of a priori estimates and special techniques of differential equations,we give an error estimates for a positive definite problem.Numerical experiments illustrate its computational efficiency and feasibility of application.展开更多
To overcome the limitations posed by three-dimensional corner separation,this paper proposes a novel flow control technology known as passive End-Wall(EW)self-adaptive jet.Two single EW slotted schemes(EWS1 and EWS2),...To overcome the limitations posed by three-dimensional corner separation,this paper proposes a novel flow control technology known as passive End-Wall(EW)self-adaptive jet.Two single EW slotted schemes(EWS1 and EWS2),alongside a combined(COM)scheme featuring double EW slots,were investigated.The results reveal that the EW slot,driven by pressure differentials between the pressure and suction sides,can generate an adaptive jet with escalating velocity as the operational load increases.This high-speed jet effectively re-excites the local low-energy fluid,thereby mitigating the corner separation.Notably,the EWS1 slot,positioned near the blade leading edge,exhibits relatively low jet velocities at negative incidence angles,causing jet separation and exacerbating the corner separation.Besides,the EWS2 slot is close to the blade trailing edge,resulting in massive low-energy fluid accumulating and separating before the slot outlet at positive incidence angles.In contrast,the COM scheme emerges as the most effective solution for comprehensive corner separation control.It can significantly reduce the total pressure loss and improve the static pressure coefficient for the ORI blade at 0°-4° incidence angles,while causing minimal negative impact on the aerodynamic performance at negative incidence angles.Therefore,the corner stall is delayed,and the available incidence angle range is broadened from -10°--2°to -10°-4°.This holds substantial promise for advancing the aerodynamic performance,operational stability,and load capacity of future highly loaded compressors.展开更多
Damage indices are effective in quantifying structural seismic damage.Numerous response-based damage indices have been developed and validated through the hysteretic response of various experimental specimens.However,...Damage indices are effective in quantifying structural seismic damage.Numerous response-based damage indices have been developed and validated through the hysteretic response of various experimental specimens.However,the accuracy of these indices for evaluating damage of RC columns is challenged by fluctuating axial load and irregular horizontal loading paths from 3-D earthquake excitations.This study introduces D_(iem),a material-based damage model for RC columns under random bidirectional loads and variable axial forces.Section damage indices of the plastic hinge are calculated by integrating the damage indices of concrete and steel fiber elements,considering their distance to the centroid axis.The P-Δeffect index is defined,and the component failure index is calculated using a combination of these indices.A hysteretic simulation and D_(iem)damage analysis program for cantilever RC columns is developed using Fortran.Three RC columns tested under bidirectional hysteretic loading are simulated to calibrate the program.Parameter analysis of 1,638 RC columns is conducted to verify D_(iem)’s applicability.The results demonstrated that D_(iem)’s failure assessment aligns with the 80%residual criterion.D_(iem)analysis of a real seismic damaged RC column shows satisfactory agreement with post-earthquake damage assessment and illustrates significant damage differences between columns with and without axial load fluctuation.展开更多
The dynamic stress intensity factor of a three-dimensionalelliptic crack under impact loading is determined with the finiteelement method. The computation results can take into account theinfluence of time and the rat...The dynamic stress intensity factor of a three-dimensionalelliptic crack under impact loading is determined with the finiteelement method. The computation results can take into account theinfluence of time and the ratio of the wave speeds on the stressintensity factor. The present method is suitable not only forthree-dimensional dynamic crack, but also for three-dimensionaldynamic contact.展开更多
The pinwheel pattern as a suitable and advantageous alternative for the loading implementation of the pallet loading problem （PLP） is identified after a survey on the loading pattern. The definitions, elements, cate...The pinwheel pattern as a suitable and advantageous alternative for the loading implementation of the pallet loading problem （PLP） is identified after a survey on the loading pattern. The definitions, elements, categories, generating algorithms of the pinwheel pattern are discussed and a uniform symmetric pinwheel notation is proposed. Based on the forming geometry of a pinwheel, the pinwheel structure is analyzed in terms of the innate box ratio, the box/block orientation and the box number by combinatorial and geometrical methods. A revised data set for the PLP with an area ratio range from 1 to 76 and a box ratio range from 1 to 10 is proposed. All pinwheel instances with this data set are calculated, and box ratio range is obtained for each possible pinwheel pattern, which can be found for all non-prime numbers of boxes. And a high box ratio makes an optimal pinwheel pattern more likely appear. Results identify the impact of the above pinwheel pattern and the box ratio on the pallet loading problem.展开更多
Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For th...Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhe- sive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regu- lation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason cou- pling constant impact is barely perceptible. The validity of the conclusions is verified.展开更多
A frequency domain analysis method based on the three-dimensional translating-pulsating （3DTP） source Green function is developed to investigate wave loads and free motions of two ships advancing on parallel course ...A frequency domain analysis method based on the three-dimensional translating-pulsating （3DTP） source Green function is developed to investigate wave loads and free motions of two ships advancing on parallel course in waves. Two experiments are carried out respectively to mea- sure the wave loads and the free motions for a pair of side-by- side arranged ship models advancing with an identical speed in head regular waves. For comparison, each model is also tested alone. Predictions obtained by the present solution are found in favorable agreement with the model tests and are more accurate than the traditional method based on the three dimensional pulsating （3DP） source Green function. Numer- ical resonances and peak shift can be found in the 3DP pre- dictions, which result from the wave energy trapped in the gap between two ships and the extremely inhomogeneous wave load distribution on each hull. However, they can be eliminated by 3DTP, in which the speed affects the free sur- face and most of the wave energy can be escaped from the gap. Both the experiment and the present prediction show that hydrodynamic interaction effects on wave loads and free motions are significant. The present solver may serve as a validated tool to predict wave loads and motions of two ves- sels under replenishment at sea, and may help to evaluate the hydrodynamic interaction effects on the ships safety in replenishment operation.展开更多
We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forwa...We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forward scattering dominates. At the same time, this model provides an efficiency gain of an order of magnitude or more over two-way coupled-mode models. This model can be applied to three-dimensional range-dependent problems with a slowly varying bathymetry or internal waves. A numerical example of the latter is demonstrated in this work. Comparisons of both accuracy and efficiency between the present model and a benchmark model are also provided.展开更多
By applying the integral transform method and the inverse transformation technique based upon the two types of integration, the present paper has successfully obtained an exact algebraic solution for a two-dimensional...By applying the integral transform method and the inverse transformation technique based upon the two types of integration, the present paper has successfully obtained an exact algebraic solution for a two-dimensional Lamb＇s problem due to a strip impulse loading for the first time. With the algebraic result, the excitation and propagation processes of stress waves, including the longitudinal wave, the transverse wave, and Rayleigh-wave, are discussed in detail. A few new conclusions have been drawn from currently available integral results or computational results.展开更多
In this paper, we use differential game theory to study the three-dimensional two-aircraft air-to-air combat problem. We give the ways to determine the Capture Ranges (CR) and the Dangerous Ranges (DR) for these two a...In this paper, we use differential game theory to study the three-dimensional two-aircraft air-to-air combat problem. We give the ways to determine the Capture Ranges (CR) and the Dangerous Ranges (DR) for these two aircraft according to the target entry directions, barrier and isochronic lines respectively. The simulations are given by referring to two sets of real aircraft parameters. After discussing the simulation results, we have obtained some conclusions that match the real air-to-air combat situation quite well.展开更多
Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green func...Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.展开更多
The paper discusses the application of three-dimensional textbook in English teaching. The three-dimensional textbook plays an incomparable function than the traditional textbook and thus has an extensive application ...The paper discusses the application of three-dimensional textbook in English teaching. The three-dimensional textbook plays an incomparable function than the traditional textbook and thus has an extensive application in the college English education. It demonstrates the application through the usage of the three-dimensional textbook in the real teaching and shows that excessive usage of sound and pictures or drawings may distract the attention of students. It raises several suggestions at the end.展开更多
The container loading problem (CLP) is a well-known NP-hard problem. Due to the computation complexity, heuristics is an often-sought approach. This article proposes two heuristics to pack homogeneous rectangular boxe...The container loading problem (CLP) is a well-known NP-hard problem. Due to the computation complexity, heuristics is an often-sought approach. This article proposes two heuristics to pack homogeneous rectangular boxes into a single container. Both algorithms adopt the concept of building layers on one face of the container, but the first heuristic determines the layer face once for all, while the second treats the remaining container space as a reduced-sized container after one layer is loaded and, hence, selects the layer face dynamically. To handle the layout design problem at a layer's level, a block-based 2D packing procedure is also developed. Numerical studies demonstrate the efficiency of the heuristics.展开更多
In coal mining,rock strata are fractured under cyclic loading and unloading to form fracture channels.Fracture channels are the main flow narrows for gas.Therefore,expounding the flow conductivity of fracture channels...In coal mining,rock strata are fractured under cyclic loading and unloading to form fracture channels.Fracture channels are the main flow narrows for gas.Therefore,expounding the flow conductivity of fracture channels in rocks on fluids is significant for gas flow in rock strata.In this regard,graded incremental cyclic loading and unloading experiments were conducted on sandstones with different initial stress levels.Then,the three-dimensional models for fracture channels in sandstones were established.Finally,the fracture channel percentages were used to reflect the flow conductivity of fracture channels.The study revealed how the particle size distribution of fractured sandstone affects the formation and expansion of fracture channels.It was found that a smaller proportion of large blocks and a higher proportion of small blocks after sandstone fails contribute more to the formation of fracture channels.The proportion of fracture channels in fractured rock can indicate the flow conductivity of those channels.When the proportion of fracture channels varies gently,fluids flow evenly through those channels.However,if the proportion of fracture channels varies significantly,it can greatly affect the flow rate of fluids.The research results contribute to revealing the morphological evolution and flow conductivity of fracture channels in sandstone and then provide a theoretical basis for clarifying the gas flow pattern in the rock strata of coal mines.展开更多
The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped i...The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.展开更多
Transonic shocks play a pivotal role in designation of supersonic inlets and ramjets.For the three-dimensional steady non-isentropic compressible Euler system with frictions,we constructe a family of transonic shock s...Transonic shocks play a pivotal role in designation of supersonic inlets and ramjets.For the three-dimensional steady non-isentropic compressible Euler system with frictions,we constructe a family of transonic shock solutions in rectilinear ducts with square cross-sections.In this article,we are devoted to proving rigorously that a large class of these transonic shock solutions are stable,under multidimensional small perturbations of the upcoming supersonic flows and back pressures at the exits of ducts in suitable function spaces.This manifests that frictions have a stabilization effect on transonic shocks in ducts,in consideration of previous works which shown that transonic shocks in purely steady Euler flows are not stable in such ducts.Except its implications to applications,because frictions lead to a stronger coupling between the elliptic and hyperbolic parts of the three-dimensional steady subsonic Euler system,we develop the framework established in previous works to study more complex and interesting Venttsel problems of nonlocal elliptic equations.展开更多
We demonstrate the direct loading of cold atoms into a microchip 2-mm Z-trap, where the evaporative cooling can be performed efficiently, from a macroscopic quadrupole magnetic trap with a high loading efficiency. The...We demonstrate the direct loading of cold atoms into a microchip 2-mm Z-trap, where the evaporative cooling can be performed efficiently, from a macroscopic quadrupole magnetic trap with a high loading efficiency. The macroscopic quadrupole magnetic trap potential is designed to be moveable by controlling the currents of the two pairs of anti-Helrnholtz coils. The cold atoms are initially prepared in a standard six-beam magneto-optical trap and loaded into the macroscopic quadrupole magnetic trap, and then transported to the atom chip surface by moving the macroscopic trap potential. By means of a three-dimensional absorption imaging system, we are able to optimize the position alignment of the atom cloud in the macroscopic trap and the microchip Z-shaped wire. Consequently, with a proper magnetic transfer scheme, we load the cold atoms into the microchip Z-trap directly and efficiently. The loading efficiency is measured to be about 50%. This approach can be used to generate appropriate ultracold atoms sources, for example, for a magnetically guided atom interferometer based on atom chip.展开更多
Long-term settlements for underground structures, such as tunnels and pipelines, are generally observed after the completion of construction in soft clay. The soil consolidation characteristic has great influences on ...Long-term settlements for underground structures, such as tunnels and pipelines, are generally observed after the completion of construction in soft clay. The soil consolidation characteristic has great influences on the long-term deformation for underground structures. A three-dimensional consolidation analysis method under the asymmetric loads is developed for porous layered soil based on Biot's classical theory. Time-displacement effects can be fully considered in this work and the analytical solutions are obtained by the state space approach in the Cartesian coordinate. The Laplace and double Fourier integral transform are applied to the state variables in order to reduce the partial differential equations into algebraic differential equations and easily obtain the state space solution. Starting from the governing equations of saturated porous soil, the basic relationship of state space variables is established between the ground surface and the arbitrary depth in the integral transform domain. Based on the continuity conditions and boundary conditions of the multi-layered pore soil model, the multi-layered pore half-space solutions are obtained by means of the transfer matrix method and the inverse integral transforms. The accuracy of proposed method is demonstrated with existing classical solutions. The results indicate that the porous homogenous soils as well as the porous non-homogenous layered soils can be considered in this proposed method. When the consolidation time factor is 0.01, the value of immediate consolidation settlement coefficient calculated by the weighted homogenous solution is 27.4% bigger than the one calculated by the non-homogeneity solution. When the consolidation time factor is 0.05, the value of excess pore water pressure for the weighted homogenous solution is 27.2% bigger than the one for the non-homogeneity solution. It is shown that the material non-homogeneity has a great influence on the long-term settlements and the dissipation process of excess pore water pressure.展开更多
In the repair of peripheral nerve injury using autologous or synthetic nerve grafting, the mag- nitude of tensile forces at the anastomosis affects its response to physiological stress and the ultimate success of the ...In the repair of peripheral nerve injury using autologous or synthetic nerve grafting, the mag- nitude of tensile forces at the anastomosis affects its response to physiological stress and the ultimate success of the treatment. One-dimensional stretching is commonly used to measure changes in tensile stress and strain; however, the accuracy of this simple method is limited. There- fore, in the present study, we established three-dimensional finite element models of sciatic nerve defects repaired by autologous nerve grafts. Using PRO E 5.0 finite element simulation software, we calculated the maximum stress and displacement of an anastomosis under a 5 N load in 10-, 20-, 30-, 40-mm long autologous nerve grafts. We found that maximum displacement increased with graft length, consistent with specimen force. These findings indicate that three-dimensional finite element simulation is a feasible method for analyzing stress and displacement at the anas- tomosis after autologous nerve grafting.展开更多
By making use of the direct integration method,an exact analysis of the general three-dimensional thermoelasticity problem is performed for the case of a transversely isotropic homogeneous half-space subject to local ...By making use of the direct integration method,an exact analysis of the general three-dimensional thermoelasticity problem is performed for the case of a transversely isotropic homogeneous half-space subject to local thermal and force loadings.The material plane of isotropy is assumed to be parallel to the limiting surface of the halfspace.By reducing the original thermoelasticity equations to the governing ones for individual stress-tensor components,the effect of material anisotropy in the stress field is analyzed with regard to the feasibility requirement,i.e.,the finiteness of the stress field at a distance from the disturbed area.As a result,the solution is constructed in the form of explicit analytical dependencies on the force and thermal loadings for various kinds of transversely isotropic materials and agrees with the basic principles of the continua mechanics.The solution can be efficiently used as a benchmark one for the direct computation of temperature and thermal stresses in transversely isotropic semi-infinite domains,as well as for the verification of solutions constructed by different means.展开更多
基金supported by the Natural Science Foundation of Shandong Province(ZR2021MA019)the National Natural Science Foundation of China(11871312)。
文摘In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow equation.The velocity and pressure are computed simultaneously.The accuracy of velocity is improved one order.The concentration equation is solved by using mixed finite element,multi-step difference and upwind approximation.A multi-step method is used to approximate time derivative for improving the accuracy.The upwind approximation and an expanded mixed finite element are adopted to solve the convection and diffusion,respectively.The composite method could compute the diffusion flux and its gradient.It possibly becomes an eficient tool for solving convection-dominated diffusion problems.Firstly,the conservation of mass holds.Secondly,the multi-step method has high accuracy.Thirdly,the upwind approximation could avoid numerical dispersion.Using numerical analysis of a priori estimates and special techniques of differential equations,we give an error estimates for a positive definite problem.Numerical experiments illustrate its computational efficiency and feasibility of application.
基金sponsored by the National Natural Science Foundation of China(No.52106057)the National Major Science and Technology Projects of China(No.2017-Ⅱ-0001-0013)+2 种基金Fundamental Research Funds for the Central Universities of China(No.D5000210483)the Foundation of State Level Key Laboratory of Airfoil and Cascade Aerodynamics of China(Nos.D5150210006 and D5050210015)the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University of China(No.CX2023012).
文摘To overcome the limitations posed by three-dimensional corner separation,this paper proposes a novel flow control technology known as passive End-Wall(EW)self-adaptive jet.Two single EW slotted schemes(EWS1 and EWS2),alongside a combined(COM)scheme featuring double EW slots,were investigated.The results reveal that the EW slot,driven by pressure differentials between the pressure and suction sides,can generate an adaptive jet with escalating velocity as the operational load increases.This high-speed jet effectively re-excites the local low-energy fluid,thereby mitigating the corner separation.Notably,the EWS1 slot,positioned near the blade leading edge,exhibits relatively low jet velocities at negative incidence angles,causing jet separation and exacerbating the corner separation.Besides,the EWS2 slot is close to the blade trailing edge,resulting in massive low-energy fluid accumulating and separating before the slot outlet at positive incidence angles.In contrast,the COM scheme emerges as the most effective solution for comprehensive corner separation control.It can significantly reduce the total pressure loss and improve the static pressure coefficient for the ORI blade at 0°-4° incidence angles,while causing minimal negative impact on the aerodynamic performance at negative incidence angles.Therefore,the corner stall is delayed,and the available incidence angle range is broadened from -10°--2°to -10°-4°.This holds substantial promise for advancing the aerodynamic performance,operational stability,and load capacity of future highly loaded compressors.
基金Scientific Research Fund of Institute of Engineering Mechanics,China Earthquake Administration under Grant No.2019B12National Natural Science Foundation of China Youth Fund under Grant No.51108433National Natural Science Foundation of China under Grant No.51778186。
文摘Damage indices are effective in quantifying structural seismic damage.Numerous response-based damage indices have been developed and validated through the hysteretic response of various experimental specimens.However,the accuracy of these indices for evaluating damage of RC columns is challenged by fluctuating axial load and irregular horizontal loading paths from 3-D earthquake excitations.This study introduces D_(iem),a material-based damage model for RC columns under random bidirectional loads and variable axial forces.Section damage indices of the plastic hinge are calculated by integrating the damage indices of concrete and steel fiber elements,considering their distance to the centroid axis.The P-Δeffect index is defined,and the component failure index is calculated using a combination of these indices.A hysteretic simulation and D_(iem)damage analysis program for cantilever RC columns is developed using Fortran.Three RC columns tested under bidirectional hysteretic loading are simulated to calibrate the program.Parameter analysis of 1,638 RC columns is conducted to verify D_(iem)’s applicability.The results demonstrated that D_(iem)’s failure assessment aligns with the 80%residual criterion.D_(iem)analysis of a real seismic damaged RC column shows satisfactory agreement with post-earthquake damage assessment and illustrates significant damage differences between columns with and without axial load fluctuation.
基金the National Natural Science Foundation of China( No.K19672007)
文摘The dynamic stress intensity factor of a three-dimensionalelliptic crack under impact loading is determined with the finiteelement method. The computation results can take into account theinfluence of time and the ratio of the wave speeds on the stressintensity factor. The present method is suitable not only forthree-dimensional dynamic crack, but also for three-dimensionaldynamic contact.
基金The National Natural Science Foundation of China(No.70571033,70831002)
文摘The pinwheel pattern as a suitable and advantageous alternative for the loading implementation of the pallet loading problem （PLP） is identified after a survey on the loading pattern. The definitions, elements, categories, generating algorithms of the pinwheel pattern are discussed and a uniform symmetric pinwheel notation is proposed. Based on the forming geometry of a pinwheel, the pinwheel structure is analyzed in terms of the innate box ratio, the box/block orientation and the box number by combinatorial and geometrical methods. A revised data set for the PLP with an area ratio range from 1 to 76 and a box ratio range from 1 to 10 is proposed. All pinwheel instances with this data set are calculated, and box ratio range is obtained for each possible pinwheel pattern, which can be found for all non-prime numbers of boxes. And a high box ratio makes an optimal pinwheel pattern more likely appear. Results identify the impact of the above pinwheel pattern and the box ratio on the pallet loading problem.
基金supported by the National Natural Science Foundation of China(Nos.11362018,11261045,and 11261401)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20116401110002)
文摘Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhe- sive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regu- lation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason cou- pling constant impact is barely perceptible. The validity of the conclusions is verified.
基金supported by the National Natural Science Foundation of China(50879090)the Key Research Program of Hydrodynamics of China(9140A14030712JB11044)
文摘A frequency domain analysis method based on the three-dimensional translating-pulsating （3DTP） source Green function is developed to investigate wave loads and free motions of two ships advancing on parallel course in waves. Two experiments are carried out respectively to mea- sure the wave loads and the free motions for a pair of side-by- side arranged ship models advancing with an identical speed in head regular waves. For comparison, each model is also tested alone. Predictions obtained by the present solution are found in favorable agreement with the model tests and are more accurate than the traditional method based on the three dimensional pulsating （3DP） source Green function. Numer- ical resonances and peak shift can be found in the 3DP pre- dictions, which result from the wave energy trapped in the gap between two ships and the extremely inhomogeneous wave load distribution on each hull. However, they can be eliminated by 3DTP, in which the speed affects the free sur- face and most of the wave energy can be escaped from the gap. Both the experiment and the present prediction show that hydrodynamic interaction effects on wave loads and free motions are significant. The present solver may serve as a validated tool to predict wave loads and motions of two ves- sels under replenishment at sea, and may help to evaluate the hydrodynamic interaction effects on the ships safety in replenishment operation.
基金Supported by the National Natural Science Foundation of China under Grant No 11774374the Natural Science Foundation of Shandong Province of China under Grant No ZR2016AL10
文摘We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forward scattering dominates. At the same time, this model provides an efficiency gain of an order of magnitude or more over two-way coupled-mode models. This model can be applied to three-dimensional range-dependent problems with a slowly varying bathymetry or internal waves. A numerical example of the latter is demonstrated in this work. Comparisons of both accuracy and efficiency between the present model and a benchmark model are also provided.
基金Project supported by the National Natural Science Foundation of China(No.10572002).
文摘By applying the integral transform method and the inverse transformation technique based upon the two types of integration, the present paper has successfully obtained an exact algebraic solution for a two-dimensional Lamb＇s problem due to a strip impulse loading for the first time. With the algebraic result, the excitation and propagation processes of stress waves, including the longitudinal wave, the transverse wave, and Rayleigh-wave, are discussed in detail. A few new conclusions have been drawn from currently available integral results or computational results.
基金research was supported by Aviation Science Fund.
文摘In this paper, we use differential game theory to study the three-dimensional two-aircraft air-to-air combat problem. We give the ways to determine the Capture Ranges (CR) and the Dangerous Ranges (DR) for these two aircraft according to the target entry directions, barrier and isochronic lines respectively. The simulations are given by referring to two sets of real aircraft parameters. After discussing the simulation results, we have obtained some conclusions that match the real air-to-air combat situation quite well.
基金Project supported by the National Natural Science Foundation of China (No. 50776097)
文摘Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.
文摘The paper discusses the application of three-dimensional textbook in English teaching. The three-dimensional textbook plays an incomparable function than the traditional textbook and thus has an extensive application in the college English education. It demonstrates the application through the usage of the three-dimensional textbook in the real teaching and shows that excessive usage of sound and pictures or drawings may distract the attention of students. It raises several suggestions at the end.
基金the Natural Sciences and Engineering Research Council of Canada (NSERC) under the Discovery Grant Program
文摘The container loading problem (CLP) is a well-known NP-hard problem. Due to the computation complexity, heuristics is an often-sought approach. This article proposes two heuristics to pack homogeneous rectangular boxes into a single container. Both algorithms adopt the concept of building layers on one face of the container, but the first heuristic determines the layer face once for all, while the second treats the remaining container space as a reduced-sized container after one layer is loaded and, hence, selects the layer face dynamically. To handle the layout design problem at a layer's level, a block-based 2D packing procedure is also developed. Numerical studies demonstrate the efficiency of the heuristics.
基金This work was financially supported by the National Natural Science Foundation of China(No.52074041)the Chongqing Talent Program(No.cstc2022ycjh-bgzxm0077)the Postgraduate Research and Innovation Foundation of Chongqing,China(No.CYS23060).
文摘In coal mining,rock strata are fractured under cyclic loading and unloading to form fracture channels.Fracture channels are the main flow narrows for gas.Therefore,expounding the flow conductivity of fracture channels in rocks on fluids is significant for gas flow in rock strata.In this regard,graded incremental cyclic loading and unloading experiments were conducted on sandstones with different initial stress levels.Then,the three-dimensional models for fracture channels in sandstones were established.Finally,the fracture channel percentages were used to reflect the flow conductivity of fracture channels.The study revealed how the particle size distribution of fractured sandstone affects the formation and expansion of fracture channels.It was found that a smaller proportion of large blocks and a higher proportion of small blocks after sandstone fails contribute more to the formation of fracture channels.The proportion of fracture channels in fractured rock can indicate the flow conductivity of those channels.When the proportion of fracture channels varies gently,fluids flow evenly through those channels.However,if the proportion of fracture channels varies significantly,it can greatly affect the flow rate of fluids.The research results contribute to revealing the morphological evolution and flow conductivity of fracture channels in sandstone and then provide a theoretical basis for clarifying the gas flow pattern in the rock strata of coal mines.
文摘The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.
基金This work was supported in part by National Nature Science Foundation of China(11371141 and 11871218)by Science and Technology Commission of Shanghai Municipality(18dz2271000).
文摘Transonic shocks play a pivotal role in designation of supersonic inlets and ramjets.For the three-dimensional steady non-isentropic compressible Euler system with frictions,we constructe a family of transonic shock solutions in rectilinear ducts with square cross-sections.In this article,we are devoted to proving rigorously that a large class of these transonic shock solutions are stable,under multidimensional small perturbations of the upcoming supersonic flows and back pressures at the exits of ducts in suitable function spaces.This manifests that frictions have a stabilization effect on transonic shocks in ducts,in consideration of previous works which shown that transonic shocks in purely steady Euler flows are not stable in such ducts.Except its implications to applications,because frictions lead to a stronger coupling between the elliptic and hyperbolic parts of the three-dimensional steady subsonic Euler system,we develop the framework established in previous works to study more complex and interesting Venttsel problems of nonlocal elliptic equations.
基金Project supported by the National Natural Science Foundation of China(Grant No.11604348)
文摘We demonstrate the direct loading of cold atoms into a microchip 2-mm Z-trap, where the evaporative cooling can be performed efficiently, from a macroscopic quadrupole magnetic trap with a high loading efficiency. The macroscopic quadrupole magnetic trap potential is designed to be moveable by controlling the currents of the two pairs of anti-Helrnholtz coils. The cold atoms are initially prepared in a standard six-beam magneto-optical trap and loaded into the macroscopic quadrupole magnetic trap, and then transported to the atom chip surface by moving the macroscopic trap potential. By means of a three-dimensional absorption imaging system, we are able to optimize the position alignment of the atom cloud in the macroscopic trap and the microchip Z-shaped wire. Consequently, with a proper magnetic transfer scheme, we load the cold atoms into the microchip Z-trap directly and efficiently. The loading efficiency is measured to be about 50%. This approach can be used to generate appropriate ultracold atoms sources, for example, for a magnetically guided atom interferometer based on atom chip.
基金Project(51008188)supported by National Natural Science Foundation of ChinaProject(KLE-TJGE-B1302)supported by Key Laboratory Fund of Geotechnical and Underground Engineering of Ministry of Education,ChinaProject(SKLGDUEK1205)supported by Open Program of State Key Laboratory for Geomechanics and Deep Underground Engineering,China
文摘Long-term settlements for underground structures, such as tunnels and pipelines, are generally observed after the completion of construction in soft clay. The soil consolidation characteristic has great influences on the long-term deformation for underground structures. A three-dimensional consolidation analysis method under the asymmetric loads is developed for porous layered soil based on Biot's classical theory. Time-displacement effects can be fully considered in this work and the analytical solutions are obtained by the state space approach in the Cartesian coordinate. The Laplace and double Fourier integral transform are applied to the state variables in order to reduce the partial differential equations into algebraic differential equations and easily obtain the state space solution. Starting from the governing equations of saturated porous soil, the basic relationship of state space variables is established between the ground surface and the arbitrary depth in the integral transform domain. Based on the continuity conditions and boundary conditions of the multi-layered pore soil model, the multi-layered pore half-space solutions are obtained by means of the transfer matrix method and the inverse integral transforms. The accuracy of proposed method is demonstrated with existing classical solutions. The results indicate that the porous homogenous soils as well as the porous non-homogenous layered soils can be considered in this proposed method. When the consolidation time factor is 0.01, the value of immediate consolidation settlement coefficient calculated by the weighted homogenous solution is 27.4% bigger than the one calculated by the non-homogeneity solution. When the consolidation time factor is 0.05, the value of excess pore water pressure for the weighted homogenous solution is 27.2% bigger than the one for the non-homogeneity solution. It is shown that the material non-homogeneity has a great influence on the long-term settlements and the dissipation process of excess pore water pressure.
基金supported by the Science and Technology Development Project of Jilin Province in China,No.20110492
文摘In the repair of peripheral nerve injury using autologous or synthetic nerve grafting, the mag- nitude of tensile forces at the anastomosis affects its response to physiological stress and the ultimate success of the treatment. One-dimensional stretching is commonly used to measure changes in tensile stress and strain; however, the accuracy of this simple method is limited. There- fore, in the present study, we established three-dimensional finite element models of sciatic nerve defects repaired by autologous nerve grafts. Using PRO E 5.0 finite element simulation software, we calculated the maximum stress and displacement of an anastomosis under a 5 N load in 10-, 20-, 30-, 40-mm long autologous nerve grafts. We found that maximum displacement increased with graft length, consistent with specimen force. These findings indicate that three-dimensional finite element simulation is a feasible method for analyzing stress and displacement at the anas- tomosis after autologous nerve grafting.
基金supported by Joint Fund of Advanced Aerospace Manufacturing Technology Research(No. U1937601)the partial financial support of this research by the budget program of Ukraine“Support for the Development of Priority Research Areas”(No.CPCEC 6451230)。
文摘By making use of the direct integration method,an exact analysis of the general three-dimensional thermoelasticity problem is performed for the case of a transversely isotropic homogeneous half-space subject to local thermal and force loadings.The material plane of isotropy is assumed to be parallel to the limiting surface of the halfspace.By reducing the original thermoelasticity equations to the governing ones for individual stress-tensor components,the effect of material anisotropy in the stress field is analyzed with regard to the feasibility requirement,i.e.,the finiteness of the stress field at a distance from the disturbed area.As a result,the solution is constructed in the form of explicit analytical dependencies on the force and thermal loadings for various kinds of transversely isotropic materials and agrees with the basic principles of the continua mechanics.The solution can be efficiently used as a benchmark one for the direct computation of temperature and thermal stresses in transversely isotropic semi-infinite domains,as well as for the verification of solutions constructed by different means.
