The symplectic approach was utilized to derive solutions to the orthotropic micropolar plane stress problem.The Hamiltonian canonical equation was first obtained by applying Legendre’s transformation and the Hamilton...The symplectic approach was utilized to derive solutions to the orthotropic micropolar plane stress problem.The Hamiltonian canonical equation was first obtained by applying Legendre’s transformation and the Hamiltonian mixed energy variational principle.Then,by using the method of separation of variables,the eigenproblem of the corresponding homogeneous Hamiltonian canonical equation was derived.Subsequently,the corresponding eigensolutions for three kinds of homogeneous boundary conditions were derived.According to the adjoint symplectic orthogonality of the eigensolutions and expansion theorems,the solutions to this plane stress problem were expressed as a series expansion of these eigensolutions.The numerical results for the orthotropic micropolar plane stress problem under various boundary conditions were presented and validated using the finite element method,which confirmed the convergence and accuracy of the proposed approach.We also investigated the relationship between the size-dependent behaviour and material parameters using the proposed approach.Furthermore,this approach was applied to analyze lattice structures under an equivalent micropolar continuum approximation.展开更多
The impact of longitudinal stiffener configurations on the structural performance of orthotropic steel bridge decks(OSD)was systematically investigated,with emphasis on U-shaped,T-shaped,and rectangular ribs.Finite el...The impact of longitudinal stiffener configurations on the structural performance of orthotropic steel bridge decks(OSD)was systematically investigated,with emphasis on U-shaped,T-shaped,and rectangular ribs.Finite element analysis was employed to evaluate deformation and stress distribution under three critical loading scenarios:vertical uniformload,vertical eccentric load,and lateral uniformload.Equivalentmodels ensuring identical steel usage,moment of inertia,and centroid alignment were established to compare five stiffener configurations.Results demonstrate that U-rib configurations exhibit superior performance in controlling local displacements and minimizing stress concentrations.Under eccentric loading,U-ribs significantly reduce deck displacement andmitigate stress fluctuations at critical junctions compared to alternative stiffeners.Stability analysis further reveals that U-ribs achieve stability coefficients substantially higher than open-section alternatives,particularly excelling under lateral loading due to enhanced torsional rigidity.Parametric optimization identifies key geometric thresholds where U-rib thickness exceeding 6 mm yields diminishing returns in stress reduction and stability enhancement,while deck flange thickness beyond 16 mm provides marginal improvements in displacement control despite increased material usage.An optimized design combining 6-mm U-ribs with 16-mm deck flanges is proposed,balancing structural efficiency with stringent deformation requirements for high-speed rail bridges.These findings provide foundational insights for optimizing stiffener selection and enhancing the longevity of orthotropic steel bridge decks in heavy-load applications.展开更多
This paper studies the vibration responses of porous functionally graded(FG)thin plates with four various types of porous distribution based on the physical neutral plane by employing the peridynamic differential oper...This paper studies the vibration responses of porous functionally graded(FG)thin plates with four various types of porous distribution based on the physical neutral plane by employing the peridynamic differential operator(PDDO).It is assumed that density and elastic modulus continuously vary along the transverse direction following the power law distribution for porous FG plates.The governing differential equation of free vibration for a porous rectangular FG plate and its associated boundary conditions are expressed by a Lévy-type solution based on nonlinear von Karman plate theory.Dimensionless frequencies and mode shapes are obtained after solving the characteristic equations established by PDDO.The results of the current method are validated through comparison with existing literature.The effects of geometric parameters,material properties,elastic foundation,porosity distribution,and boundary conditions on the frequency are investigated and discussed in detail.The highest fundamental dimensionless frequency occurs under SCSC boundary conditions,while the lowest is under SFSF boundary conditions.The porous FG plate with the fourth pore type,featuring high density of porosity at the top and low at the bottom,exhibits the highest fundamental frequency under SSSS,SFSF,and SCSC boundary conditions.The dimensionless frequency increases with an increase in the elastic foundation stiffness coefficient.展开更多
Vertically oriented carbon structures constructed from low-dimen-sional carbon materials are ideal frameworks for high-performance thermal inter-face materials(TIMs).However,improving the interfacial heat-transfer eff...Vertically oriented carbon structures constructed from low-dimen-sional carbon materials are ideal frameworks for high-performance thermal inter-face materials(TIMs).However,improving the interfacial heat-transfer efficiency of vertically oriented carbon structures is a challenging task.Herein,an orthotropic three-dimensional(3D)hybrid carbon network(VSCG)is fabricated by depositing vertically aligned carbon nanotubes(VACNTs)on the surface of a horizontally oriented graphene film(HOGF).The interfacial interaction between the VACNTs and HOGF is then optimized through an annealing strategy.After regulating the orientation structure of the VACNTs and filling the VSCG with polydimethylsi-loxane(PDMS),VSCG/PDMS composites with excellent 3D thermal conductive properties are obtained.The highest in-plane and through-plane thermal conduc-tivities of the composites are 113.61 and 24.37 W m^(-1)K^(-1),respectively.The high contact area of HOGF and good compressibility of VACNTs imbue the VSCG/PDMS composite with low thermal resistance.In addition,the interfacial heat-transfer efficiency of VSCG/PDMS composite in the TIM performance was improved by 71.3%compared to that of a state-of-the-art thermal pad.This new structural design can potentially realize high-performance TIMs that meet the need for high thermal conductivity and low contact thermal resistance in interfacial heat-transfer processes.展开更多
Black phosphorus nanotubes(BPNTs)may have good properties and potential applications.Determining thevibration property of BPNTs is essential for gaining insight into the mechanical behaviour of BPNTs and designingopti...Black phosphorus nanotubes(BPNTs)may have good properties and potential applications.Determining thevibration property of BPNTs is essential for gaining insight into the mechanical behaviour of BPNTs and designingoptimized nanodevices.In this paper,the mechanical behaviour and vibration property of BPNTs are studied viaorthotropic cylindrical shell model and molecular dynamics(MD)simulation.The vibration frequencies of twochiral BPNTs are analysed systematically.According to the results of MD calculations,it is revealed that thenatural frequencies of two BPNTs with approximately equal sizes are unequal at each order,and that the naturalfrequencies of armchair BPNTs are higher than those of zigzag BPNTs.In addition,an armchair BPNTs witha stable structure is considered as the object of research,and the vibration frequencies of BPNTs of differentsizes are analysed.When comparing the MD results,it is found that both the isotropic cylindrical shell modeland orthotropic cylindrical shell model can better predict the thermal vibration of the lower order modes of thelonger BPNTs better.However,for the vibration of shorter and thinner BPNTs,the prediction of the orthotropiccylindrical shell model is obviously superior to the isotropic shell model,thereby further proving the validity ofthe shell model that considers orthotropic for BPNTs.展开更多
To analyze the stress state of steel orthotropic deck pavement and provide reference for the design of the overlay, the inner stress state and strain distribution of surfacing under the load of the deformation of the ...To analyze the stress state of steel orthotropic deck pavement and provide reference for the design of the overlay, the inner stress state and strain distribution of surfacing under the load of the deformation of the whole bridge structure and tyre load are analyzed by the finite element method of submodeling. Influence of surfacing modulus on the strain state of the overlay is analyzed for the purpose of the optimal design of the overlay structure. Analysis results show that the deformation of the whole bridge structure has no evident influence on the stress state of the overlay. The key factor of the overlay design is the transverse tensile strain in the overlay above the upper edge of web plate of rib. The stress state of the overlay is influenced evidently by the modulus of rigidity transform overlay. And the stress state of the overlay can be optimized and lowered by increasing the modulus and thickness of rigidity transform overlay, The fatigue test has been done to evaluate the fatigue performance and modulus of different deck pavement materials such as epoxy asphalt, SBS modified asphalt, rosphalt asphalt which can provide reference for deck pavement structure design.展开更多
In this paper three important characteristics in piezoresistance for the orthotropic material are given and proved theoretically:(1) The piezoresistance on the principal axis of an orthotropic material is independent ...In this paper three important characteristics in piezoresistance for the orthotropic material are given and proved theoretically:(1) The piezoresistance on the principal axis of an orthotropic material is independent of shear strains/stresses, but correlated with the normal strains/stresses only;(2) On the principal axis of material, following relations between piezoconductivity and piezoresistivity exist η iikk =-(γ ii ) -2 ξ iikk =-(ρ ii ) 2ξ iikk λ iikk =-(γ ii ) -2 χ iikk =-(ρ ii ) 2χ iikk (3) A laminate composed of orthotropic laminae in different orientations is orthotropic for its average/effective properties.展开更多
The purpose of the present work is to study the buckling problem with plate/shell topology optimization of orthotropic material. A model of buckling topology optimization is established based on the independent, conti...The purpose of the present work is to study the buckling problem with plate/shell topology optimization of orthotropic material. A model of buckling topology optimization is established based on the independent, continuous, and mapping method, which considers structural mass as objective and buckling critical loads as constraints. Firstly, composite exponential function (CEF) and power function (PF) as filter functions are introduced to recognize the element mass, the element stiffness matrix, and the element geometric stiffness matrix. The filter functions of the orthotropic material stiffness are deduced. Then these filter functions are put into buckling topology optimization of a differential equation to analyze the design sensitivity. Furthermore, the buckling constraints are approximately expressed as explicit functions with respect to the design variables based on the first-order Taylor expansion. The objective function is standardized based on the second-order Taylor expansion. Therefore, the optimization model is translated into a quadratic program. Finally, the dual sequence quadratic programming (DSQP) algorithm and the global convergence method of moving asymptotes algorithm with two different filter functions (CEF and PF) are applied to solve the optimal model. Three numerical results show that DSQP&CEF has the best performance in the view of structural mass and discretion.展开更多
This paper analyses the bending of rectangular orthotropic plates on a Winkler elastic foundation.Appropriate definition of symplectic inner product and symplectic space formed by generalized displacements establish d...This paper analyses the bending of rectangular orthotropic plates on a Winkler elastic foundation.Appropriate definition of symplectic inner product and symplectic space formed by generalized displacements establish dual variables and dual equations in the symplectic space.The operator matrix of the equation set is proven to be a Hamilton operator matrix.Separation of variables and eigenfunction expansion creates a basis for analyzing the bending of rectangular orthotropic plates on Winkler elastic foundation and obtaining solutions for plates having any boundary condition.There is discussion of symplectic eigenvalue problems of orthotropic plates under two typical boundary conditions,with opposite sides simply supported and opposite sides clamped.Transcendental equations of eigenvalues and symplectic eigenvectors in analytical form given.Analytical solutions using two examples are presented to show the use of the new methods described in this paper.To verify the accuracy and convergence,a fully simply supported plate that is fully and simply supported under uniformly distributed load is used to compare the classical Navier method,the Levy method and the new method.Results show that the new technique has good accuracy and better convergence speed than other methods,especially in relation to internal forces.A fully clamped rectangular plate on Winkler foundation is solved to validate application of the new methods,with solutions compared to those produced by the Galerkin method.展开更多
To improve the strength-toughness of traditional U-rib（ TUR） and solve the problem of insufficient penetration between TUR and deckplate,a new local thickened U-rib（ LTUR） has been proposed to improve the fatigue ...To improve the strength-toughness of traditional U-rib（ TUR） and solve the problem of insufficient penetration between TUR and deckplate,a new local thickened U-rib（ LTUR） has been proposed to improve the fatigue resistance of the weld joint under the premise of not increasing thickness and strength of the TUR material. And a hot /warm roll-forming process（ RFP） adopting partially induction heating to 700- 1 000℃ was carried out to fabricate LTUR. The deformation behaviors in the forming process and microstructure of LTUR have been investigated.Mechanical properties and fracture mechanism of the LTUR after hot / warm RFP have been systematically discussed. Moreover,the results are compared with those obtained in cold RFP. Mechanical properties of the LTUR deformed above the critical transformation temperature（ A_（c3）） show high performance characteristics with marked fatigue resistance and superior toughness. Upon increasing the heating temperature from 700 to 900 ℃,the initial coarse ferrite-pearlite structure transform into equiaxed ultrafine ferrite（ 1- 3 μm） and precipitates such as（ Nb,Ti）（ C,N） are uniformly distributed in the matrix. The average dislocation density of the specimens after hot rollforming at heating temperature of 900 ℃ decreases dramatically compared with those of the specimens subjected to the cold RFP. Furthermore,a typical characteristic of ductile fracture mechanism and the high impact energy are more convinced that the specimens deformed above 900 ℃ have obtained an optimal combination of strength and toughness.展开更多
A nonlocal continuum orthotropic plate model is proposed to study the vibration behavior of single-layer graphene sheets (SLGSs) using an analytical symplectic approach. A Hamiltonian system is established by introduc...A nonlocal continuum orthotropic plate model is proposed to study the vibration behavior of single-layer graphene sheets (SLGSs) using an analytical symplectic approach. A Hamiltonian system is established by introducing a total unknown vector consisting of the displacement amplitude, rotation angle, shear force, and bending moment. The high-order governing differential equation of the vibration of SLGSs is transformed into a set of ordinary differential equations in symplectic space. Exact solutions for free vibration are obtianed by the method of separation of variables without any trial shape functions and can be expanded in series of symplectic eigenfunctions. Analytical frequency equations are derived for all six possible boundary conditions. Vibration modes are expressed in terms of the symplectic eigenfunctions. In the numerical examples, comparison is presented to verify the accuracy of the proposed method. Comprehensive numerical examples for graphene sheets with Levy-type boundary conditions are given. A parametric study of the natural frequency is also included.展开更多
When a body consists completely or even partly of viscoelastic materials, its response under static loading will be time-dependent. The adhesives used to glue together single plies in laminates usually exhibit a certa...When a body consists completely or even partly of viscoelastic materials, its response under static loading will be time-dependent. The adhesives used to glue together single plies in laminates usually exhibit a certain viscoelastic characteristic in a high temperature environment. In this paper, a laminated orthotropic rectangular plate with viscoelastic interfaces, described by the Kelvin-Voigt model, is considered. A power series expansion technique is adopted to approximate the time-variation of various field quantities. Results indicate that the response of the laminated plate with viscoelastic interfaces changes remarkably with time, and is much different from that of a plate with spring-like or viscous interfaces.展开更多
Time reversal is a key component of time-reverse migration and source location using wavefield extrapolation.The implementation of time reversal depends on the time symmetry of wave equations in acoustic and elastic m...Time reversal is a key component of time-reverse migration and source location using wavefield extrapolation.The implementation of time reversal depends on the time symmetry of wave equations in acoustic and elastic media.This symmetry in time is no longer valid in attenuative medium.Not only the velocity is anisotropic in shale oil and gas reservoirs,but also the attenuation is usually anisotropic,which can be characterized by viscoelastic orthotropic media.In this paper,the fractional order viscoelastic anisotropic wave equation is used to decouple the energy dissipation and the velocity dispersion.By changing the sign of the dissipation term during backpropagation,the anisotropic attenuation is compensated and the time symmetry is restored.The attenuation compensation time-reverse location algorithm can eff ectively locate the source in viscoelastic orthotropic media.Compared to cases without attenuation compensation or using isotropic attenuation compensation,this method can remove location error caused by anisotropic attenuation and improve the imaging eff ect of the source.This paper verifi es the eff ectiveness of the method through theoretical analysis and model testing.展开更多
Orthotropic materials weakened by a doubly periodic array of cracks under far-field antiplane shear are investigated, where the fundamental cell contains four cracks of unequal size. By applying the mapping technique,...Orthotropic materials weakened by a doubly periodic array of cracks under far-field antiplane shear are investigated, where the fundamental cell contains four cracks of unequal size. By applying the mapping technique, the elliptical function theory and the theory of analytical function boundary value problems, a closed form solution of the whole-field stress is obtained. The exact formulae for the stress intensity factor at the crack tip and the effective antiplane shear modulus of the cracked orthotropic material are derived. A comparison with the finite element method shows the efficiency and accuracy of the present method. Several illustrative examples are provided, and an interesting phenomenon is observed, that is, the stress intensity factor and the dimensionless effective modulus are independent of the material property for a doubly periodic cracked isotropic material, but depend strongly on the material property for the doubly periodic cracked orthotropic material. Such a phenomenon for antiplane problems is similar to that for in-plane problems. The present solution can provide benchmark results for other numerical and approximate methods.展开更多
On the basis of the existing fundamental solutions ofdisplacements, further improvement is made, and then the generalfundamental solutions of both plane elastic and plane plasticproblems for ortho- tropic materials ar...On the basis of the existing fundamental solutions ofdisplacements, further improvement is made, and then the generalfundamental solutions of both plane elastic and plane plasticproblems for ortho- tropic materials are obtained. Two parametersbased on material constants a_1, a_2 are used to derive the rele-vant expressions in a real variable form. Additionally, an analyticalmethod of solving the singular integral for the internal stresses isintroduced, and the corresponding result are given. If a_1=a_2=1, allthe expres- sions obtained for orthotropy can be reduced to thecorresponding ones for isotropy. Because all these expres- sions andresults can be directly used for both isotropic problems andorthotropic problems, it is convenient to use them in engineeringwith the boundary element method (BEM).展开更多
An interaction function was constructed based on the axial compression/tension and shear loads of orthotropic plates.The coefficients of the polynomial function were determined by uniaxial test results.Buckling intera...An interaction function was constructed based on the axial compression/tension and shear loads of orthotropic plates.The coefficients of the polynomial function were determined by uniaxial test results.Buckling interaction and failure interaction formulae under combined axial tension/compression and shear loads were established.Based on the uniaxial load test results of orthotropic plates,the buckling load and bearing capacity under any proportion of the combined loads could be predicted by using the proposed interaction formulae.The buckling interaction curves and failure envelopes predicted by the proposed interaction formulae were in excellent agreement with the test results.展开更多
In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solutio...In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor （SIF）.展开更多
This paper first gives the general solution of two-dimensional orthotropic media expressed with two harmonic displacement functions by using the governing equations. Then, based on the general solution in the case of ...This paper first gives the general solution of two-dimensional orthotropic media expressed with two harmonic displacement functions by using the governing equations. Then, based on the general solution in the case of distinct eigenvalues, a series of beam problems, including the problem of cantilever beam under uniform loads, cantilever beam with axial load and bending moment at the free end, cantilever beam under the first, second, third and fourth power ofx tangential loads, is solved by the superposition principle and the trial-and-error methods.展开更多
Adopting the complex function approach, the paper studies the stress intensity factor in orthotropic bi-material interface cracks under mixed loads. With con- sideration of the boundary conditions, a new stress functi...Adopting the complex function approach, the paper studies the stress intensity factor in orthotropic bi-material interface cracks under mixed loads. With con- sideration of the boundary conditions, a new stress function is introduced to transform the problem of bi-material interface crack into a boundary value problem of partial dif- ferential equations. Two sets of non-homogeneous linear equations with 16 unknowns are constructed. By solving the equations, the expressions for the real bi-material elastic constant εt and the real stress singularity exponents λt are obtained with the bi-material engineering parameters satisfying certain conditions. By the uniqueness theorem of limit, undetermined coefficients are determined, and thus the bi-material stress intensity factor in mixed cracks is obtained. The bi-material stress intensity factor characterizes features of mixed cracks. When orthotropic bi-materials are of the same material, the degenerate solution to the stress intensity factor in mixed bi-material interface cracks is in complete agreement with the present classic conclusion. The relationship between the bi-material stress intensity factor and the ratio of bi-material shear modulus and the relationship be- tween the bi-material stress intensity factor and the ratio of bi-material Young＇s modulus are given in the numerical analysis.展开更多
This paper deals with the mathematical modelling and 3D FEM study of the energy release rate(ERR)in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initial...This paper deals with the mathematical modelling and 3D FEM study of the energy release rate(ERR)in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initially before the loading of the crack's edge planes.The initial stretching or compressing of the plate causes uniformly distributed normal stress to appear acting in the direction which is parallel to the plane on which the band crack is located.After the appearance of the initial stress in the plate it is assumed that the crack's edge planes are loaded with additional uniformly distributed normal forces and the ERR caused with this additional loading is studied.The corresponding boundary value problem is formulated within the scope of the so-called 3D linearized theory of elasticity which allows the initial stress on the values of the ERR to be taken into consideration.Numerical results on the influence of the initial stress,anisotropy properties of the plate material,the crack’s length and its distance from the face planes of the plate on the values of the ERR,are presented and discussed.In particular,it is established that for the relatively greater length of the crack’s band,the initial stretching of the plate causes a decrease,but the initial compression causes an increase in the values of the ERR.展开更多
基金supported by the National Key R&D Program of China (Grant No.2022YFB4201200)Technology Major Project (Grant No.J2019-IV-0019-0087)National Science and Technology Major Project (Grant No.J2019-IV-0019-0087).
文摘The symplectic approach was utilized to derive solutions to the orthotropic micropolar plane stress problem.The Hamiltonian canonical equation was first obtained by applying Legendre’s transformation and the Hamiltonian mixed energy variational principle.Then,by using the method of separation of variables,the eigenproblem of the corresponding homogeneous Hamiltonian canonical equation was derived.Subsequently,the corresponding eigensolutions for three kinds of homogeneous boundary conditions were derived.According to the adjoint symplectic orthogonality of the eigensolutions and expansion theorems,the solutions to this plane stress problem were expressed as a series expansion of these eigensolutions.The numerical results for the orthotropic micropolar plane stress problem under various boundary conditions were presented and validated using the finite element method,which confirmed the convergence and accuracy of the proposed approach.We also investigated the relationship between the size-dependent behaviour and material parameters using the proposed approach.Furthermore,this approach was applied to analyze lattice structures under an equivalent micropolar continuum approximation.
基金supported by the Chongqing Municipal Talent Plan Project(cstc2024ycjh-bgzxm0186).
文摘The impact of longitudinal stiffener configurations on the structural performance of orthotropic steel bridge decks(OSD)was systematically investigated,with emphasis on U-shaped,T-shaped,and rectangular ribs.Finite element analysis was employed to evaluate deformation and stress distribution under three critical loading scenarios:vertical uniformload,vertical eccentric load,and lateral uniformload.Equivalentmodels ensuring identical steel usage,moment of inertia,and centroid alignment were established to compare five stiffener configurations.Results demonstrate that U-rib configurations exhibit superior performance in controlling local displacements and minimizing stress concentrations.Under eccentric loading,U-ribs significantly reduce deck displacement andmitigate stress fluctuations at critical junctions compared to alternative stiffeners.Stability analysis further reveals that U-ribs achieve stability coefficients substantially higher than open-section alternatives,particularly excelling under lateral loading due to enhanced torsional rigidity.Parametric optimization identifies key geometric thresholds where U-rib thickness exceeding 6 mm yields diminishing returns in stress reduction and stability enhancement,while deck flange thickness beyond 16 mm provides marginal improvements in displacement control despite increased material usage.An optimized design combining 6-mm U-ribs with 16-mm deck flanges is proposed,balancing structural efficiency with stringent deformation requirements for high-speed rail bridges.These findings provide foundational insights for optimizing stiffener selection and enhancing the longevity of orthotropic steel bridge decks in heavy-load applications.
基金supported by the Research Start-Up Fund for Introducing Talents from Anhui Polytechnic University(S022023032)the Program for Synergy Innovation in the Anhui Higher Education Institutions of China(GXXT-2021-044 and GXXT-2022-082)+2 种基金the Scientific Research Foundation of Education Department of Anhui Province,China(2022AH040361)the National Natural Science Foundation of China(12172114)the Natural Science Funds for Distinguished Young Scholar of Anhui Province of China(2208085J25).
文摘This paper studies the vibration responses of porous functionally graded(FG)thin plates with four various types of porous distribution based on the physical neutral plane by employing the peridynamic differential operator(PDDO).It is assumed that density and elastic modulus continuously vary along the transverse direction following the power law distribution for porous FG plates.The governing differential equation of free vibration for a porous rectangular FG plate and its associated boundary conditions are expressed by a Lévy-type solution based on nonlinear von Karman plate theory.Dimensionless frequencies and mode shapes are obtained after solving the characteristic equations established by PDDO.The results of the current method are validated through comparison with existing literature.The effects of geometric parameters,material properties,elastic foundation,porosity distribution,and boundary conditions on the frequency are investigated and discussed in detail.The highest fundamental dimensionless frequency occurs under SCSC boundary conditions,while the lowest is under SFSF boundary conditions.The porous FG plate with the fourth pore type,featuring high density of porosity at the top and low at the bottom,exhibits the highest fundamental frequency under SSSS,SFSF,and SCSC boundary conditions.The dimensionless frequency increases with an increase in the elastic foundation stiffness coefficient.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.52130303,52327802,52303101,52173078,51973158)the China Postdoctoral Science Foundation(2023M732579)+2 种基金Young Elite Scientists Sponsorship Program by CAST(No.2022QNRC001)National Key R&D Program of China(No.2022YFB3805702)Joint Funds of Ministry of Education(8091B032218).
文摘Vertically oriented carbon structures constructed from low-dimen-sional carbon materials are ideal frameworks for high-performance thermal inter-face materials(TIMs).However,improving the interfacial heat-transfer efficiency of vertically oriented carbon structures is a challenging task.Herein,an orthotropic three-dimensional(3D)hybrid carbon network(VSCG)is fabricated by depositing vertically aligned carbon nanotubes(VACNTs)on the surface of a horizontally oriented graphene film(HOGF).The interfacial interaction between the VACNTs and HOGF is then optimized through an annealing strategy.After regulating the orientation structure of the VACNTs and filling the VSCG with polydimethylsi-loxane(PDMS),VSCG/PDMS composites with excellent 3D thermal conductive properties are obtained.The highest in-plane and through-plane thermal conduc-tivities of the composites are 113.61 and 24.37 W m^(-1)K^(-1),respectively.The high contact area of HOGF and good compressibility of VACNTs imbue the VSCG/PDMS composite with low thermal resistance.In addition,the interfacial heat-transfer efficiency of VSCG/PDMS composite in the TIM performance was improved by 71.3%compared to that of a state-of-the-art thermal pad.This new structural design can potentially realize high-performance TIMs that meet the need for high thermal conductivity and low contact thermal resistance in interfacial heat-transfer processes.
基金supported by the National Science Fund for Distin-guished Young Scholars(Grants No.11925205)the National Natural Science Foundation of China(Grant Nos.51921003 and U2341230).
文摘Black phosphorus nanotubes(BPNTs)may have good properties and potential applications.Determining thevibration property of BPNTs is essential for gaining insight into the mechanical behaviour of BPNTs and designingoptimized nanodevices.In this paper,the mechanical behaviour and vibration property of BPNTs are studied viaorthotropic cylindrical shell model and molecular dynamics(MD)simulation.The vibration frequencies of twochiral BPNTs are analysed systematically.According to the results of MD calculations,it is revealed that thenatural frequencies of two BPNTs with approximately equal sizes are unequal at each order,and that the naturalfrequencies of armchair BPNTs are higher than those of zigzag BPNTs.In addition,an armchair BPNTs witha stable structure is considered as the object of research,and the vibration frequencies of BPNTs of differentsizes are analysed.When comparing the MD results,it is found that both the isotropic cylindrical shell modeland orthotropic cylindrical shell model can better predict the thermal vibration of the lower order modes of thelonger BPNTs better.However,for the vibration of shorter and thinner BPNTs,the prediction of the orthotropiccylindrical shell model is obviously superior to the isotropic shell model,thereby further proving the validity ofthe shell model that considers orthotropic for BPNTs.
文摘To analyze the stress state of steel orthotropic deck pavement and provide reference for the design of the overlay, the inner stress state and strain distribution of surfacing under the load of the deformation of the whole bridge structure and tyre load are analyzed by the finite element method of submodeling. Influence of surfacing modulus on the strain state of the overlay is analyzed for the purpose of the optimal design of the overlay structure. Analysis results show that the deformation of the whole bridge structure has no evident influence on the stress state of the overlay. The key factor of the overlay design is the transverse tensile strain in the overlay above the upper edge of web plate of rib. The stress state of the overlay is influenced evidently by the modulus of rigidity transform overlay. And the stress state of the overlay can be optimized and lowered by increasing the modulus and thickness of rigidity transform overlay, The fatigue test has been done to evaluate the fatigue performance and modulus of different deck pavement materials such as epoxy asphalt, SBS modified asphalt, rosphalt asphalt which can provide reference for deck pavement structure design.
文摘In this paper three important characteristics in piezoresistance for the orthotropic material are given and proved theoretically:(1) The piezoresistance on the principal axis of an orthotropic material is independent of shear strains/stresses, but correlated with the normal strains/stresses only;(2) On the principal axis of material, following relations between piezoconductivity and piezoresistivity exist η iikk =-(γ ii ) -2 ξ iikk =-(ρ ii ) 2ξ iikk λ iikk =-(γ ii ) -2 χ iikk =-(ρ ii ) 2χ iikk (3) A laminate composed of orthotropic laminae in different orientations is orthotropic for its average/effective properties.
基金supported by the National Natural Science Foundation of China (Grants 11072009, 11172013)the Beijing Education Committee Development Project (Grant SQKM2016100 05001)the Beijing University of Technology Basic Research Fund (Grant 001000514313003)
文摘The purpose of the present work is to study the buckling problem with plate/shell topology optimization of orthotropic material. A model of buckling topology optimization is established based on the independent, continuous, and mapping method, which considers structural mass as objective and buckling critical loads as constraints. Firstly, composite exponential function (CEF) and power function (PF) as filter functions are introduced to recognize the element mass, the element stiffness matrix, and the element geometric stiffness matrix. The filter functions of the orthotropic material stiffness are deduced. Then these filter functions are put into buckling topology optimization of a differential equation to analyze the design sensitivity. Furthermore, the buckling constraints are approximately expressed as explicit functions with respect to the design variables based on the first-order Taylor expansion. The objective function is standardized based on the second-order Taylor expansion. Therefore, the optimization model is translated into a quadratic program. Finally, the dual sequence quadratic programming (DSQP) algorithm and the global convergence method of moving asymptotes algorithm with two different filter functions (CEF and PF) are applied to solve the optimal model. Three numerical results show that DSQP&CEF has the best performance in the view of structural mass and discretion.
基金supported by the National Natural Science Foundation of China (10772039 and 10632030)the National Basic Research Program of China (973 Program) (2010CB832704)
文摘This paper analyses the bending of rectangular orthotropic plates on a Winkler elastic foundation.Appropriate definition of symplectic inner product and symplectic space formed by generalized displacements establish dual variables and dual equations in the symplectic space.The operator matrix of the equation set is proven to be a Hamilton operator matrix.Separation of variables and eigenfunction expansion creates a basis for analyzing the bending of rectangular orthotropic plates on Winkler elastic foundation and obtaining solutions for plates having any boundary condition.There is discussion of symplectic eigenvalue problems of orthotropic plates under two typical boundary conditions,with opposite sides simply supported and opposite sides clamped.Transcendental equations of eigenvalues and symplectic eigenvectors in analytical form given.Analytical solutions using two examples are presented to show the use of the new methods described in this paper.To verify the accuracy and convergence,a fully simply supported plate that is fully and simply supported under uniformly distributed load is used to compare the classical Navier method,the Levy method and the new method.Results show that the new technique has good accuracy and better convergence speed than other methods,especially in relation to internal forces.A fully clamped rectangular plate on Winkler foundation is solved to validate application of the new methods,with solutions compared to those produced by the Galerkin method.
文摘To improve the strength-toughness of traditional U-rib（ TUR） and solve the problem of insufficient penetration between TUR and deckplate,a new local thickened U-rib（ LTUR） has been proposed to improve the fatigue resistance of the weld joint under the premise of not increasing thickness and strength of the TUR material. And a hot /warm roll-forming process（ RFP） adopting partially induction heating to 700- 1 000℃ was carried out to fabricate LTUR. The deformation behaviors in the forming process and microstructure of LTUR have been investigated.Mechanical properties and fracture mechanism of the LTUR after hot / warm RFP have been systematically discussed. Moreover,the results are compared with those obtained in cold RFP. Mechanical properties of the LTUR deformed above the critical transformation temperature（ A_（c3）） show high performance characteristics with marked fatigue resistance and superior toughness. Upon increasing the heating temperature from 700 to 900 ℃,the initial coarse ferrite-pearlite structure transform into equiaxed ultrafine ferrite（ 1- 3 μm） and precipitates such as（ Nb,Ti）（ C,N） are uniformly distributed in the matrix. The average dislocation density of the specimens after hot rollforming at heating temperature of 900 ℃ decreases dramatically compared with those of the specimens subjected to the cold RFP. Furthermore,a typical characteristic of ductile fracture mechanism and the high impact energy are more convinced that the specimens deformed above 900 ℃ have obtained an optimal combination of strength and toughness.
基金support of the National Natural Science Foundation of China (Grant 11672054)the Research Grant Council of Hong Kong (11215415)the National Basic Research Program of China (973 Program) (Grant 2014CB046803)
文摘A nonlocal continuum orthotropic plate model is proposed to study the vibration behavior of single-layer graphene sheets (SLGSs) using an analytical symplectic approach. A Hamiltonian system is established by introducing a total unknown vector consisting of the displacement amplitude, rotation angle, shear force, and bending moment. The high-order governing differential equation of the vibration of SLGSs is transformed into a set of ordinary differential equations in symplectic space. Exact solutions for free vibration are obtianed by the method of separation of variables without any trial shape functions and can be expanded in series of symplectic eigenfunctions. Analytical frequency equations are derived for all six possible boundary conditions. Vibration modes are expressed in terms of the symplectic eigenfunctions. In the numerical examples, comparison is presented to verify the accuracy of the proposed method. Comprehensive numerical examples for graphene sheets with Levy-type boundary conditions are given. A parametric study of the natural frequency is also included.
基金Project supported by the National Natural Science Foundation of China (No. 10432030) and NCET.
文摘When a body consists completely or even partly of viscoelastic materials, its response under static loading will be time-dependent. The adhesives used to glue together single plies in laminates usually exhibit a certain viscoelastic characteristic in a high temperature environment. In this paper, a laminated orthotropic rectangular plate with viscoelastic interfaces, described by the Kelvin-Voigt model, is considered. A power series expansion technique is adopted to approximate the time-variation of various field quantities. Results indicate that the response of the laminated plate with viscoelastic interfaces changes remarkably with time, and is much different from that of a plate with spring-like or viscous interfaces.
基金This work was supported by National Natural Science Foundation of China(No.41504097,41874153).
文摘Time reversal is a key component of time-reverse migration and source location using wavefield extrapolation.The implementation of time reversal depends on the time symmetry of wave equations in acoustic and elastic media.This symmetry in time is no longer valid in attenuative medium.Not only the velocity is anisotropic in shale oil and gas reservoirs,but also the attenuation is usually anisotropic,which can be characterized by viscoelastic orthotropic media.In this paper,the fractional order viscoelastic anisotropic wave equation is used to decouple the energy dissipation and the velocity dispersion.By changing the sign of the dissipation term during backpropagation,the anisotropic attenuation is compensated and the time symmetry is restored.The attenuation compensation time-reverse location algorithm can eff ectively locate the source in viscoelastic orthotropic media.Compared to cases without attenuation compensation or using isotropic attenuation compensation,this method can remove location error caused by anisotropic attenuation and improve the imaging eff ect of the source.This paper verifi es the eff ectiveness of the method through theoretical analysis and model testing.
基金supported by the National Natural Science Foundation of China (No.10672008).
文摘Orthotropic materials weakened by a doubly periodic array of cracks under far-field antiplane shear are investigated, where the fundamental cell contains four cracks of unequal size. By applying the mapping technique, the elliptical function theory and the theory of analytical function boundary value problems, a closed form solution of the whole-field stress is obtained. The exact formulae for the stress intensity factor at the crack tip and the effective antiplane shear modulus of the cracked orthotropic material are derived. A comparison with the finite element method shows the efficiency and accuracy of the present method. Several illustrative examples are provided, and an interesting phenomenon is observed, that is, the stress intensity factor and the dimensionless effective modulus are independent of the material property for a doubly periodic cracked isotropic material, but depend strongly on the material property for the doubly periodic cracked orthotropic material. Such a phenomenon for antiplane problems is similar to that for in-plane problems. The present solution can provide benchmark results for other numerical and approximate methods.
文摘On the basis of the existing fundamental solutions ofdisplacements, further improvement is made, and then the generalfundamental solutions of both plane elastic and plane plasticproblems for ortho- tropic materials are obtained. Two parametersbased on material constants a_1, a_2 are used to derive the rele-vant expressions in a real variable form. Additionally, an analyticalmethod of solving the singular integral for the internal stresses isintroduced, and the corresponding result are given. If a_1=a_2=1, allthe expres- sions obtained for orthotropy can be reduced to thecorresponding ones for isotropy. Because all these expres- sions andresults can be directly used for both isotropic problems andorthotropic problems, it is convenient to use them in engineeringwith the boundary element method (BEM).
文摘An interaction function was constructed based on the axial compression/tension and shear loads of orthotropic plates.The coefficients of the polynomial function were determined by uniaxial test results.Buckling interaction and failure interaction formulae under combined axial tension/compression and shear loads were established.Based on the uniaxial load test results of orthotropic plates,the buckling load and bearing capacity under any proportion of the combined loads could be predicted by using the proposed interaction formulae.The buckling interaction curves and failure envelopes predicted by the proposed interaction formulae were in excellent agreement with the test results.
文摘In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor （SIF）.
文摘This paper first gives the general solution of two-dimensional orthotropic media expressed with two harmonic displacement functions by using the governing equations. Then, based on the general solution in the case of distinct eigenvalues, a series of beam problems, including the problem of cantilever beam under uniform loads, cantilever beam with axial load and bending moment at the free end, cantilever beam under the first, second, third and fourth power ofx tangential loads, is solved by the superposition principle and the trial-and-error methods.
基金supported by the National Key Basic Research Program of China(973 Program)(No.2009CB724201)the Science and Technology Major Project of the Ministry of Education of China(No.208022)+1 种基金the Postgraduate Scientific and Technological Innovation Project of Taiyuan University of Science and Technology(No.20125027)the Scientific Research Funds for Doctoral Students of Taiyuan University of Science and Technology(No.20122005)
文摘Adopting the complex function approach, the paper studies the stress intensity factor in orthotropic bi-material interface cracks under mixed loads. With con- sideration of the boundary conditions, a new stress function is introduced to transform the problem of bi-material interface crack into a boundary value problem of partial dif- ferential equations. Two sets of non-homogeneous linear equations with 16 unknowns are constructed. By solving the equations, the expressions for the real bi-material elastic constant εt and the real stress singularity exponents λt are obtained with the bi-material engineering parameters satisfying certain conditions. By the uniqueness theorem of limit, undetermined coefficients are determined, and thus the bi-material stress intensity factor in mixed cracks is obtained. The bi-material stress intensity factor characterizes features of mixed cracks. When orthotropic bi-materials are of the same material, the degenerate solution to the stress intensity factor in mixed bi-material interface cracks is in complete agreement with the present classic conclusion. The relationship between the bi-material stress intensity factor and the ratio of bi-material shear modulus and the relationship be- tween the bi-material stress intensity factor and the ratio of bi-material Young＇s modulus are given in the numerical analysis.
文摘This paper deals with the mathematical modelling and 3D FEM study of the energy release rate(ERR)in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initially before the loading of the crack's edge planes.The initial stretching or compressing of the plate causes uniformly distributed normal stress to appear acting in the direction which is parallel to the plane on which the band crack is located.After the appearance of the initial stress in the plate it is assumed that the crack's edge planes are loaded with additional uniformly distributed normal forces and the ERR caused with this additional loading is studied.The corresponding boundary value problem is formulated within the scope of the so-called 3D linearized theory of elasticity which allows the initial stress on the values of the ERR to be taken into consideration.Numerical results on the influence of the initial stress,anisotropy properties of the plate material,the crack’s length and its distance from the face planes of the plate on the values of the ERR,are presented and discussed.In particular,it is established that for the relatively greater length of the crack’s band,the initial stretching of the plate causes a decrease,but the initial compression causes an increase in the values of the ERR.
