The singular hybrid boundary node method （SHBNM） is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and ...The singular hybrid boundary node method （SHBNM） is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares （MLS） approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The ＇boundary layer effect＇, which is the main drawback of the original Hybrid BNM, was overcome by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method （RHBNM） can be avoided. Numerical examples for some 3D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.展开更多
In the present paper, bending and stress analyses of two-directional functionally graded （FG） annular plates resting on non-uniform two-parameter Winkler-Pasternak founda- tions and subjected to normal and in-plane-...In the present paper, bending and stress analyses of two-directional functionally graded （FG） annular plates resting on non-uniform two-parameter Winkler-Pasternak founda- tions and subjected to normal and in-plane-shear tractions is investigated using the exact three- dimensional theory of elasticity. Neither the in-plane shear loading nor the influence of the two- directional material heterogeneity has been investigated by the researchers before. The solution is obtained by employing the state space and differential quadrature methods. The material proper- ties are assumed to vary in both transverse and radial directions. Three different types of variations of the stiffness of the foundation are considered in the radial direction： linear, parabolic, and sinu- soidal. The convergence analysis and the comparative studies demonstrate the high accuracy and high convergence rate of the present approach. A parametric study consisting of evaluating effects of different parameters （e.g., exponents of the material properties laws, the thickness to radius ratio, trends of variations of the foundation stiffness, and different edge conditions） is carried out. The results are reported for the first time and are discussed in detail.展开更多
Three-dimensional elasticity solutions for static bending of thick functionally graded plates are presented using a hybrid semi-analytical approach-the state-space based differential quadrature method （SSDQM）. The p...Three-dimensional elasticity solutions for static bending of thick functionally graded plates are presented using a hybrid semi-analytical approach-the state-space based differential quadrature method （SSDQM）. The plate is generally supported at four edges for which the two-way differential quadrature method is used to solve the in-plane variations of the stress and displacement fields numerically. An approximate laminate model （ALM） is exploited to reduce the inhomogeneous plate into a multi-layered laminate, thus applying the state space method to solve analytically in the thickness direction. Both the convergence properties of SSDQM and ALM are examined. The SSDQM is validated by comparing the numerical results with the exact solutions reported in the literature. As an example, the Mori-Tanaka model is used to predict the effective bulk and shear moduli. Effects of gradient index and aspect ratios on the bending behavior of functionally graded thick plates are investigated.展开更多
This paper studies the bending of simple-supported rectangular plate on point supports,line supports and elastic foundation.On the basis of three-dimensional elasticity theory,the exact expressions of the displacement...This paper studies the bending of simple-supported rectangular plate on point supports,line supports and elastic foundation.On the basis of three-dimensional elasticity theory,the exact expressions of the displacement functions,which satisfy the governing differential equations and the simply supported boundary conditions at four edges of the plate,are analytically derived.The reaction forces of the in-termediate supports are regarded as the unknown external forces acting on the lower surface of the plate.The unknown coefficients are then determined by the boundary conditions on the upper and lower surfaces of the plate.Comparing the numerical results obtained from the proposed method to those obtained from Kirchhoff plate theory,Mindlin plate theory and those obtained from the commer-cial finite element software ANSYS,the high accuracy of the present method has been demonstrated.展开更多
According to the Mindlin plate theory and the first-order piston theory,this work obtains accurate closed-form eigensolutions for the flutter problem of three-dimensional(3D)rectangular laminated panels.The governing ...According to the Mindlin plate theory and the first-order piston theory,this work obtains accurate closed-form eigensolutions for the flutter problem of three-dimensional(3D)rectangular laminated panels.The governing differential equations are derived by the Hamilton's variational principle,and then solved by the iterative Separation-of-Variable(i SOV)method,which are applicable to arbitrary combinations of homogeneous Boundary Conditions(BCs).However,only the simply-support,clamped and cantilever panels are considered in this work for the sake of clarity.With the closed-form eigensolutions,the flutter frequency,flutter mode and flutter boundary are presented,and the effect of shear deformation and aerodynamic damping on flutter frequencies is investigated.Besides,the relation between panel energy and the work of aerodynamic load is discussed.The numerical comparisons reveal the following.(A)The flutter eigenvalues obtained by the present method are accurate,validated by the Finite Element Method(FEM)and the Galerkin method.(B)When the span-chord ratio is larger than 3,simplifying a 3D panel to 2D(two-dimensional)panel is reasonable and the relative differences of the flutter points predicted by the two models are less than one percent.(C)The reciprocal relationship between the mechanical energy of the panel and the work done by aerodynamic load is verified by using the present flutter eigenvalues and modes,further indicating the high accuracy of the present solutions.(D)The coupling of shear deformation and aerodynamic damping prevents frequency coalescing.展开更多
Weak solution （or generalized solution） for the boundary-value problems of partial differential equations of elasticity of 3D （three-dimensional） quasicrystals is given, in which the matrix expression is used. In ...Weak solution （or generalized solution） for the boundary-value problems of partial differential equations of elasticity of 3D （three-dimensional） quasicrystals is given, in which the matrix expression is used. In terms of Korn inequality and theory of function space, we prove the uniqueness of the weak solution. This gives an extension of existence theorem of solution for classical elasticity to that of quasicrystals, and develops the weak solution theory of elasticity of 2D quasicrystals given by the second author of the paper and his students.展开更多
A localized version of the method of fundamental solution(LMFS)is devised in this paper for the numerical solutions of three-dimensional(3D)elasticity problems.The present method combines the advantages of high comput...A localized version of the method of fundamental solution(LMFS)is devised in this paper for the numerical solutions of three-dimensional(3D)elasticity problems.The present method combines the advantages of high computational efficiency of localized discretization schemes and the pseudo-spectral convergence rate of the classical MFS formulation.Such a combination will be an important improvement to the classical MFS for complicated and large-scale engineering simulations.Numerical examples with up to 100,000 unknowns can be solved without any difficulty on a personal computer using the developed methodologies.The advantages,disadvantages and potential applications of the proposed method,as compared with the classical MFS and boundary element method(BEM),are discussed.展开更多
Objective: To analyze the biomechanical elements of Nitinol Patellar Concentrator (NT-PC) in heating commi nuted patellar fractures. Methods: The epoxy resin three dimensional photoelasticity pobal model was loaded wi...Objective: To analyze the biomechanical elements of Nitinol Patellar Concentrator (NT-PC) in heating commi nuted patellar fractures. Methods: The epoxy resin three dimensional photoelasticity pobal model was loaded with Nitinol Patellar Connector and frozen. After dividing layer, photographing and tracing, iterative method was used to calculate the stress value of every tuteed node. Rasults: Stress values of 1 262 nodes scattered in 12 layers were obtained The stress distribution indicated that an overall stress field was yield when the NT-PC fixated the patellar model, and there existed fixative stress in the facies articularis and distal pole of the patellar model. Conclusion: The NT-PC has evident therapeutic effect for the comminuted patellar fractures. The existing stress is helpful in maintaining anatomical reduction and enhancing fracture healing.展开更多
A three-dimensional(3D)asymptotic theory is reformulated for the static analysis of simply-supported,isotropic and orthotropic single-layered nanoplates and graphene sheets(GSs),in which Eringen’s nonlocal elasticity...A three-dimensional(3D)asymptotic theory is reformulated for the static analysis of simply-supported,isotropic and orthotropic single-layered nanoplates and graphene sheets(GSs),in which Eringen’s nonlocal elasticity theory is used to capture the small length scale effect on the static behaviors of these.The perturbation method is used to expand the 3D nonlocal elasticity problems as a series of two-dimensional(2D)nonlocal plate problems,the governing equations of which for various order problems retain the same differential operators as those of the nonlocal classical plate theory(CST),although with different nonhomogeneous terms.Expanding the primary field variables of each order as the double Fourier series functions in the in-plane directions,we can obtain the Navier solutions of the leading-order problem,and the higher-order modifications can then be determined in a hierarchic and consistent manner.Some benchmark solutions for the static analysis of isotropic and orthotropic nanoplates and GSs subjected to sinusoidally and uniformly distributed loads are given to demonstrate the performance of the 3D nonlocal asymptotic theory.展开更多
The reflection of three-dimensional(3D) plane waves in a highly anisotropic(triclinic) medium under the context of generalized thermoelasticity is studied. The thermoelastic nature of the 3D plane waves in an anisotro...The reflection of three-dimensional(3D) plane waves in a highly anisotropic(triclinic) medium under the context of generalized thermoelasticity is studied. The thermoelastic nature of the 3D plane waves in an anisotropic medium is investigated in the perspective of the three-phase-lag(TPL), dual-phase-lag(DPL), Green-Naghdi-III(GNIII), Lord-Shulman(LS), and classical coupled(CL) theories. The reflection coefficients and energy ratios for all the reflected waves are obtained in a mathematical form. The rotational effects on the reflection characteristics of the 3D waves are discussed under the context of generalized thermoelasticity. Comparative analyses for the reflection coefficients of the waves among these generalized thermoelastic theories are performed. The energy ratios for each of the reflected waves establish the energy conservation law in the reflection phenomena of the plane waves. The highly anisotropic materials along with the rotation may have a significant role in the phenomenon of the reflection behavior of the 3D waves. Numerical computations are performed for the graphical representation of the study.展开更多
In this paper, the displacement discontinu ity fundamental solution (DDFS) corresponding to the unit concentrated displacem ent discontinuity for three dimensional (3D) non_local elasticity under symmetri cal conditio...In this paper, the displacement discontinu ity fundamental solution (DDFS) corresponding to the unit concentrated displacem ent discontinuity for three dimensional (3D) non_local elasticity under symmetri cal condition is obtained. Based on the displacement discontinuity boundary inte gralequation (DDBIE) and boundary_element method (DDBEM) of local (classical) e lasticity, a method of analysis of crack in 3D non_local elasticity with wide ap plication is proposed with the DDFS. Through the method, several import ant problems of fracture mechanics are analysed.展开更多
Unified way for dealing with the problems of three dimensional solid, each type of plates and shells etc. was presented with the virtual boundary element least, squares method(VBEM). It proceeded from the differential...Unified way for dealing with the problems of three dimensional solid, each type of plates and shells etc. was presented with the virtual boundary element least, squares method(VBEM). It proceeded from the differential equations of three-dimensional theory of elasticity and employs the Kelvin solution and the least squares method, It is advantageous to the establishment of the models of a software for general application to calculate each type of three-dimensional problems of elasticity. Owing to directly employing the Kelvin solution and not citing any hypothesis, the numerical results of the method should be better than any others. The merits of the method are highlighted in comparison with the direct formulation of boundary element method (BEM). It is shown that coefficient matrix is symmetric and the treatment of singular integration is rendered unnecessary in the presented method. The examples prove the efficiency and calculating precision of the method.展开更多
Here,we describe the robust and efficient application of the conventional 3D BEM in solving elasticity problems. We have focused on the precise computation of weakly singular integrals. The conformal Duffy-distance tr...Here,we describe the robust and efficient application of the conventional 3D BEM in solving elasticity problems. We have focused on the precise computation of weakly singular integrals. The conformal Duffy-distance transformation was employed to alleviate near singularities caused from two aspects:(1) the large aspect ratio of elements,i.e.,element shape distortions;and(2)the closeness of element boundaries to field points,i.e.,ill-shaped patches. Then,the rigid body motion method was employed to evaluate strongly singular integrals. Numerical solutions of 3D elastostatic problems demonstrated the high accuracy of the proposed method with coarse meshes and high convergence rates with mesh refinement. Compared with the Duffy transformation and original polar coordinate transformations,the proposed method is insensitive to element shapes.展开更多
In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and ...In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP)and quasi-shear(qS_(1) and qS_(2))modes are derived.Based on the transfer and stiffness matrices,band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap property,and the tunability of the nonreciprocal transmission by the initial stress is discussed.This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.展开更多
AIM: To evaluate the usefulness of three-dimensional (3D) shear-wave elastography (SWE) in assessing the liver ablation volume after radiofrequency (RF) ablation.
Using bathymetry and altimetric gravity anomalies, a 1°×9 1° lithospheric effective elastic thickness（Te） model over the Louisville Ridge and its adjacent regions is calculated using the moving window...Using bathymetry and altimetric gravity anomalies, a 1°×9 1° lithospheric effective elastic thickness（Te） model over the Louisville Ridge and its adjacent regions is calculated using the moving window admittance technique. For comparison, three bathymetry models are used： general bathymetric charts of the oceans, SIO V15.1,and BAT_VGG. The results show that BAT_VGG is more suitable for calculating T e than the other two models. T e along the Louisville Ridge was re-evaluated. The southeast of the ridge has a medium Te of 10–20 km, while Te increases dramatically seaward of the Tonga-Kermadec trench as a result of the collision of the Pacific and IndoAustralian plates.展开更多
The dynamic behavior of a rectangular crack in a three-dimensional （3D） orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional （2D） Fourier trans...The dynamic behavior of a rectangular crack in a three-dimensional （3D） orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional （2D） Fourier transform is applied, and the mixed- boundary value problems are converted into three pairs of dual integral equations with the unknown variables being the displacement jumps across the crack surfaces. The effects of the geometric shape of the rectangular crack, the circular frequency of the incident waves, and the lattice parameter of the orthotropic elastic medium on the dynamic stress field near the crack edges are analyzed. The present solution exhibits no stress singularity at the rectangular crack edges, and the dynamic stress field near the rectangular crack edges is finite.展开更多
To address the problem of multi-missile cooperative interception against maneuvering targets at a prespecified impact time and desired Line-of-Sight(LOS)angles in ThreeDimensional(3D)space,this paper proposes a 3D lea...To address the problem of multi-missile cooperative interception against maneuvering targets at a prespecified impact time and desired Line-of-Sight(LOS)angles in ThreeDimensional(3D)space,this paper proposes a 3D leader-following cooperative interception guidance law.First,in the LOS direction of the leader,an impact time-controlled guidance law is derived based on the fixed-time stability theory,which enables the leader to complete the interception task at a prespecified impact time.Next,in the LOS direction of the followers,by introducing a time consensus tracking error function,a fixed-time consensus tracking guidance law is investigated to guarantee the consensus tracking convergence of the time-to-go.Then,in the direction normal to the LOS,by combining the designed global integral sliding mode surface and the second-order Sliding Mode Control(SMC)theory,an innovative 3D LOS-angle-constrained interception guidance law is developed,which eliminates the reaching phase in the traditional sliding mode guidance laws and effectively saves energy consumption.Moreover,it effectively suppresses the chattering phenomenon while avoiding the singularity issue,and compensates for unknown interference caused by target maneuvering online,making it convenient for practical engineering applications.Finally,theoretical proof analysis and multiple sets of numerical simulation results verify the effectiveness,superiority,and robustness of the investigated guidance law.展开更多
This work develops a three-dimensional(3D) multiscale model to analyze a complex carbon dioxide(CO_2) faulted reservoir that includes some key geologic features of the San Andreas and nearby faults southwest of the Ki...This work develops a three-dimensional(3D) multiscale model to analyze a complex carbon dioxide(CO_2) faulted reservoir that includes some key geologic features of the San Andreas and nearby faults southwest of the Kimberlina site.The model uses the STOMP-CO2 code for flow modeling that is coupled to the ABAQUS~ finite element package for geomechanical analysis.A 3D ABAQUS~ finite element model is developed that contains a large number of 3D solid elements with two nearly parallel faults whose damage zones and cores are discretized using the same continuum elements.Five zones with different mineral compositions are considered:shale,sandstone,fault damaged sandstone,fault damaged shale,and fault core.Rocks' elastic properties that govern their poroelastic behavior are modeled by an Eshelby-Mori-Tanaka approach(EMTA).which can account for up to 15 mineral phases.The permeability of fault damage zones affected by crack density and orientations is also predicted by an EMTA formulation.A STOMP-CO2 grid that exactly maps the ABAQUS~ finite element model is built for coupled hydromechanical analyses.Simulations of the reservoir assuming three different crack pattern situations(including crack volume fraction and orientation) for the fault damage zones are performed to predict the potential leakage of CO_2 due to cracks that enhance the permeability of the fault damage zones.The results illustrate the important effect of the crack orientation on fault permeability that can lead to substantial leakage along the fault attained by the expansion of the CO_2 plume.Potential hydraulic fracture and tendency for the faults to slip are also examined and discussed in terms of stress distributions and geomechanical properties.展开更多
Three-dimensional(3D)urban structures play a critical role in informing climate mitigation strategies aimed at the built environment and facilitating sustainable urban development.Regrettably,there exists a significan...Three-dimensional(3D)urban structures play a critical role in informing climate mitigation strategies aimed at the built environment and facilitating sustainable urban development.Regrettably,there exists a significant gap in detailed and consistent data on 3D building space structures with global coverage due to the challenges inherent in the data collection and model calibration processes.In this study,we constructed a global urban structure(GUS-3D)dataset,including building volume,height,and footprint information,at a 500 m spatial resolution using extensive satellite observation products and numerous reference building samples.Our analysis indicated that the total volume of buildings worldwide in2015 exceeded 1×10^(12)m^(3).Over the 1985 to 2015 period,we observed a slight increase in the magnitude of 3D building volume growth(i.e.,it increased from 166.02 km3 during the 1985–2000 period to 175.08km3 during the 2000–2015 period),while the expansion magnitudes of the two-dimensional(2D)building footprint(22.51×10^(3) vs 13.29×10^(3)km^(2))and urban extent(157×10^(3) vs 133.8×10^(3)km^(2))notably decreased.This trend highlights the significant increase in intensive vertical utilization of urban land.Furthermore,we identified significant heterogeneity in building space provision and inequality across cities worldwide.This inequality is particularly pronounced in many populous Asian cities,which has been overlooked in previous studies on economic inequality.The GUS-3D dataset shows great potential to deepen our understanding of the urban environment and creates new horizons for numerous 3D urban studies.展开更多
基金Project supported by the Program of the Key Laboratory of Rock and Soil Mechanics of Chinese Academy of Sciences (No.Z110507)
文摘The singular hybrid boundary node method （SHBNM） is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares （MLS） approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The ＇boundary layer effect＇, which is the main drawback of the original Hybrid BNM, was overcome by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method （RHBNM） can be avoided. Numerical examples for some 3D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.
文摘In the present paper, bending and stress analyses of two-directional functionally graded （FG） annular plates resting on non-uniform two-parameter Winkler-Pasternak founda- tions and subjected to normal and in-plane-shear tractions is investigated using the exact three- dimensional theory of elasticity. Neither the in-plane shear loading nor the influence of the two- directional material heterogeneity has been investigated by the researchers before. The solution is obtained by employing the state space and differential quadrature methods. The material proper- ties are assumed to vary in both transverse and radial directions. Three different types of variations of the stiffness of the foundation are considered in the radial direction： linear, parabolic, and sinu- soidal. The convergence analysis and the comparative studies demonstrate the high accuracy and high convergence rate of the present approach. A parametric study consisting of evaluating effects of different parameters （e.g., exponents of the material properties laws, the thickness to radius ratio, trends of variations of the foundation stiffness, and different edge conditions） is carried out. The results are reported for the first time and are discussed in detail.
基金Project supported by the National Natural Science Foundation of China(Nos.51108412,11472244,and 11202186)the National Basic Research Program of China(973 Program)(No.2013CB035901)+1 种基金the Fundamental Research Funds for the Central Universities(No.2014QNA4017)the Zhejiang Provincial Natural Science Foundation of China(No.LR13A020001)
文摘Three-dimensional elasticity solutions for static bending of thick functionally graded plates are presented using a hybrid semi-analytical approach-the state-space based differential quadrature method （SSDQM）. The plate is generally supported at four edges for which the two-way differential quadrature method is used to solve the in-plane variations of the stress and displacement fields numerically. An approximate laminate model （ALM） is exploited to reduce the inhomogeneous plate into a multi-layered laminate, thus applying the state space method to solve analytically in the thickness direction. Both the convergence properties of SSDQM and ALM are examined. The SSDQM is validated by comparing the numerical results with the exact solutions reported in the literature. As an example, the Mori-Tanaka model is used to predict the effective bulk and shear moduli. Effects of gradient index and aspect ratios on the bending behavior of functionally graded thick plates are investigated.
基金Supported by the Innovation Foundation of Nanjing University of Science and Technology for PhD Graduates
文摘This paper studies the bending of simple-supported rectangular plate on point supports,line supports and elastic foundation.On the basis of three-dimensional elasticity theory,the exact expressions of the displacement functions,which satisfy the governing differential equations and the simply supported boundary conditions at four edges of the plate,are analytically derived.The reaction forces of the in-termediate supports are regarded as the unknown external forces acting on the lower surface of the plate.The unknown coefficients are then determined by the boundary conditions on the upper and lower surfaces of the plate.Comparing the numerical results obtained from the proposed method to those obtained from Kirchhoff plate theory,Mindlin plate theory and those obtained from the commer-cial finite element software ANSYS,the high accuracy of the present method has been demonstrated.
基金support of the National Natural Science Foundation of China(No.12172023)。
文摘According to the Mindlin plate theory and the first-order piston theory,this work obtains accurate closed-form eigensolutions for the flutter problem of three-dimensional(3D)rectangular laminated panels.The governing differential equations are derived by the Hamilton's variational principle,and then solved by the iterative Separation-of-Variable(i SOV)method,which are applicable to arbitrary combinations of homogeneous Boundary Conditions(BCs).However,only the simply-support,clamped and cantilever panels are considered in this work for the sake of clarity.With the closed-form eigensolutions,the flutter frequency,flutter mode and flutter boundary are presented,and the effect of shear deformation and aerodynamic damping on flutter frequencies is investigated.Besides,the relation between panel energy and the work of aerodynamic load is discussed.The numerical comparisons reveal the following.(A)The flutter eigenvalues obtained by the present method are accurate,validated by the Finite Element Method(FEM)and the Galerkin method.(B)When the span-chord ratio is larger than 3,simplifying a 3D panel to 2D(two-dimensional)panel is reasonable and the relative differences of the flutter points predicted by the two models are less than one percent.(C)The reciprocal relationship between the mechanical energy of the panel and the work done by aerodynamic load is verified by using the present flutter eigenvalues and modes,further indicating the high accuracy of the present solutions.(D)The coupling of shear deformation and aerodynamic damping prevents frequency coalescing.
基金Project supported by the National Natural Science Foundation of China (Nos.10372016 and 10672022)
文摘Weak solution （or generalized solution） for the boundary-value problems of partial differential equations of elasticity of 3D （three-dimensional） quasicrystals is given, in which the matrix expression is used. In terms of Korn inequality and theory of function space, we prove the uniqueness of the weak solution. This gives an extension of existence theorem of solution for classical elasticity to that of quasicrystals, and develops the weak solution theory of elasticity of 2D quasicrystals given by the second author of the paper and his students.
基金supported by the National Natural Science Foundation of China(Nos.11872220,11772119)the Natural Science Foundation of Shandong Province of China(Nos.ZR2017JL004,2019KJI009)。
文摘A localized version of the method of fundamental solution(LMFS)is devised in this paper for the numerical solutions of three-dimensional(3D)elasticity problems.The present method combines the advantages of high computational efficiency of localized discretization schemes and the pseudo-spectral convergence rate of the classical MFS formulation.Such a combination will be an important improvement to the classical MFS for complicated and large-scale engineering simulations.Numerical examples with up to 100,000 unknowns can be solved without any difficulty on a personal computer using the developed methodologies.The advantages,disadvantages and potential applications of the proposed method,as compared with the classical MFS and boundary element method(BEM),are discussed.
文摘Objective: To analyze the biomechanical elements of Nitinol Patellar Concentrator (NT-PC) in heating commi nuted patellar fractures. Methods: The epoxy resin three dimensional photoelasticity pobal model was loaded with Nitinol Patellar Connector and frozen. After dividing layer, photographing and tracing, iterative method was used to calculate the stress value of every tuteed node. Rasults: Stress values of 1 262 nodes scattered in 12 layers were obtained The stress distribution indicated that an overall stress field was yield when the NT-PC fixated the patellar model, and there existed fixative stress in the facies articularis and distal pole of the patellar model. Conclusion: The NT-PC has evident therapeutic effect for the comminuted patellar fractures. The existing stress is helpful in maintaining anatomical reduction and enhancing fracture healing.
文摘A three-dimensional(3D)asymptotic theory is reformulated for the static analysis of simply-supported,isotropic and orthotropic single-layered nanoplates and graphene sheets(GSs),in which Eringen’s nonlocal elasticity theory is used to capture the small length scale effect on the static behaviors of these.The perturbation method is used to expand the 3D nonlocal elasticity problems as a series of two-dimensional(2D)nonlocal plate problems,the governing equations of which for various order problems retain the same differential operators as those of the nonlocal classical plate theory(CST),although with different nonhomogeneous terms.Expanding the primary field variables of each order as the double Fourier series functions in the in-plane directions,we can obtain the Navier solutions of the leading-order problem,and the higher-order modifications can then be determined in a hierarchic and consistent manner.Some benchmark solutions for the static analysis of isotropic and orthotropic nanoplates and GSs subjected to sinusoidally and uniformly distributed loads are given to demonstrate the performance of the 3D nonlocal asymptotic theory.
基金the National Board for Higher Mathematics of India(NBHM)(No.2/48(3)/2016/NBHM(R.P)/R D Ⅱ/4528)。
文摘The reflection of three-dimensional(3D) plane waves in a highly anisotropic(triclinic) medium under the context of generalized thermoelasticity is studied. The thermoelastic nature of the 3D plane waves in an anisotropic medium is investigated in the perspective of the three-phase-lag(TPL), dual-phase-lag(DPL), Green-Naghdi-III(GNIII), Lord-Shulman(LS), and classical coupled(CL) theories. The reflection coefficients and energy ratios for all the reflected waves are obtained in a mathematical form. The rotational effects on the reflection characteristics of the 3D waves are discussed under the context of generalized thermoelasticity. Comparative analyses for the reflection coefficients of the waves among these generalized thermoelastic theories are performed. The energy ratios for each of the reflected waves establish the energy conservation law in the reflection phenomena of the plane waves. The highly anisotropic materials along with the rotation may have a significant role in the phenomenon of the reflection behavior of the 3D waves. Numerical computations are performed for the graphical representation of the study.
文摘In this paper, the displacement discontinu ity fundamental solution (DDFS) corresponding to the unit concentrated displacem ent discontinuity for three dimensional (3D) non_local elasticity under symmetri cal condition is obtained. Based on the displacement discontinuity boundary inte gralequation (DDBIE) and boundary_element method (DDBEM) of local (classical) e lasticity, a method of analysis of crack in 3D non_local elasticity with wide ap plication is proposed with the DDFS. Through the method, several import ant problems of fracture mechanics are analysed.
文摘Unified way for dealing with the problems of three dimensional solid, each type of plates and shells etc. was presented with the virtual boundary element least, squares method(VBEM). It proceeded from the differential equations of three-dimensional theory of elasticity and employs the Kelvin solution and the least squares method, It is advantageous to the establishment of the models of a software for general application to calculate each type of three-dimensional problems of elasticity. Owing to directly employing the Kelvin solution and not citing any hypothesis, the numerical results of the method should be better than any others. The merits of the method are highlighted in comparison with the direct formulation of boundary element method (BEM). It is shown that coefficient matrix is symmetric and the treatment of singular integration is rendered unnecessary in the presented method. The examples prove the efficiency and calculating precision of the method.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.51879245,41731284&11672360)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(Grant Nos.CUGCJ1821&CUG170645)。
文摘Here,we describe the robust and efficient application of the conventional 3D BEM in solving elasticity problems. We have focused on the precise computation of weakly singular integrals. The conformal Duffy-distance transformation was employed to alleviate near singularities caused from two aspects:(1) the large aspect ratio of elements,i.e.,element shape distortions;and(2)the closeness of element boundaries to field points,i.e.,ill-shaped patches. Then,the rigid body motion method was employed to evaluate strongly singular integrals. Numerical solutions of 3D elastostatic problems demonstrated the high accuracy of the proposed method with coarse meshes and high convergence rates with mesh refinement. Compared with the Duffy transformation and original polar coordinate transformations,the proposed method is insensitive to element shapes.
基金Project supported by the National Natural Science Foundation of China(Nos.11922209,11991031 and 12021002)。
文摘In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP)and quasi-shear(qS_(1) and qS_(2))modes are derived.Based on the transfer and stiffness matrices,band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap property,and the tunability of the nonreciprocal transmission by the initial stress is discussed.This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.
文摘AIM: To evaluate the usefulness of three-dimensional (3D) shear-wave elastography (SWE) in assessing the liver ablation volume after radiofrequency (RF) ablation.
基金supported financially by the Key Foundation of the Institute of Seismology,China Earthquake Administration (No. IS201506205)the National Natural Science Foundation of China (Nos. 41504017, 41204019, 41304003)
文摘Using bathymetry and altimetric gravity anomalies, a 1°×9 1° lithospheric effective elastic thickness（Te） model over the Louisville Ridge and its adjacent regions is calculated using the moving window admittance technique. For comparison, three bathymetry models are used： general bathymetric charts of the oceans, SIO V15.1,and BAT_VGG. The results show that BAT_VGG is more suitable for calculating T e than the other two models. T e along the Louisville Ridge was re-evaluated. The southeast of the ridge has a medium Te of 10–20 km, while Te increases dramatically seaward of the Tonga-Kermadec trench as a result of the collision of the Pacific and IndoAustralian plates.
基金Project supported by the National Natural Science Foundation of China(Nos.11272105 and 11572101)
文摘The dynamic behavior of a rectangular crack in a three-dimensional （3D） orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional （2D） Fourier transform is applied, and the mixed- boundary value problems are converted into three pairs of dual integral equations with the unknown variables being the displacement jumps across the crack surfaces. The effects of the geometric shape of the rectangular crack, the circular frequency of the incident waves, and the lattice parameter of the orthotropic elastic medium on the dynamic stress field near the crack edges are analyzed. The present solution exhibits no stress singularity at the rectangular crack edges, and the dynamic stress field near the rectangular crack edges is finite.
文摘To address the problem of multi-missile cooperative interception against maneuvering targets at a prespecified impact time and desired Line-of-Sight(LOS)angles in ThreeDimensional(3D)space,this paper proposes a 3D leader-following cooperative interception guidance law.First,in the LOS direction of the leader,an impact time-controlled guidance law is derived based on the fixed-time stability theory,which enables the leader to complete the interception task at a prespecified impact time.Next,in the LOS direction of the followers,by introducing a time consensus tracking error function,a fixed-time consensus tracking guidance law is investigated to guarantee the consensus tracking convergence of the time-to-go.Then,in the direction normal to the LOS,by combining the designed global integral sliding mode surface and the second-order Sliding Mode Control(SMC)theory,an innovative 3D LOS-angle-constrained interception guidance law is developed,which eliminates the reaching phase in the traditional sliding mode guidance laws and effectively saves energy consumption.Moreover,it effectively suppresses the chattering phenomenon while avoiding the singularity issue,and compensates for unknown interference caused by target maneuvering online,making it convenient for practical engineering applications.Finally,theoretical proof analysis and multiple sets of numerical simulation results verify the effectiveness,superiority,and robustness of the investigated guidance law.
基金provided by the National Energy Technology Laboratory and U.S.DOE,Office of Fossil Energy as part of the National Risk Assessment Partnershipfunded by the U.S.DOE Office of Vehicle Technologies
文摘This work develops a three-dimensional(3D) multiscale model to analyze a complex carbon dioxide(CO_2) faulted reservoir that includes some key geologic features of the San Andreas and nearby faults southwest of the Kimberlina site.The model uses the STOMP-CO2 code for flow modeling that is coupled to the ABAQUS~ finite element package for geomechanical analysis.A 3D ABAQUS~ finite element model is developed that contains a large number of 3D solid elements with two nearly parallel faults whose damage zones and cores are discretized using the same continuum elements.Five zones with different mineral compositions are considered:shale,sandstone,fault damaged sandstone,fault damaged shale,and fault core.Rocks' elastic properties that govern their poroelastic behavior are modeled by an Eshelby-Mori-Tanaka approach(EMTA).which can account for up to 15 mineral phases.The permeability of fault damage zones affected by crack density and orientations is also predicted by an EMTA formulation.A STOMP-CO2 grid that exactly maps the ABAQUS~ finite element model is built for coupled hydromechanical analyses.Simulations of the reservoir assuming three different crack pattern situations(including crack volume fraction and orientation) for the fault damage zones are performed to predict the potential leakage of CO_2 due to cracks that enhance the permeability of the fault damage zones.The results illustrate the important effect of the crack orientation on fault permeability that can lead to substantial leakage along the fault attained by the expansion of the CO_2 plume.Potential hydraulic fracture and tendency for the faults to slip are also examined and discussed in terms of stress distributions and geomechanical properties.
基金supported by the National Science Fund for Distinguished Young Scholars(42225107)the National Natural Science Foundation of China(42001326,42371414,42171409,and 42271419)+1 种基金the Natural Science Foundation of Guangdong Province of China(2022A1515012207)the Basic and Applied Basic Research Project of Guangzhou Science and Technology Planning(202201011539)。
文摘Three-dimensional(3D)urban structures play a critical role in informing climate mitigation strategies aimed at the built environment and facilitating sustainable urban development.Regrettably,there exists a significant gap in detailed and consistent data on 3D building space structures with global coverage due to the challenges inherent in the data collection and model calibration processes.In this study,we constructed a global urban structure(GUS-3D)dataset,including building volume,height,and footprint information,at a 500 m spatial resolution using extensive satellite observation products and numerous reference building samples.Our analysis indicated that the total volume of buildings worldwide in2015 exceeded 1×10^(12)m^(3).Over the 1985 to 2015 period,we observed a slight increase in the magnitude of 3D building volume growth(i.e.,it increased from 166.02 km3 during the 1985–2000 period to 175.08km3 during the 2000–2015 period),while the expansion magnitudes of the two-dimensional(2D)building footprint(22.51×10^(3) vs 13.29×10^(3)km^(2))and urban extent(157×10^(3) vs 133.8×10^(3)km^(2))notably decreased.This trend highlights the significant increase in intensive vertical utilization of urban land.Furthermore,we identified significant heterogeneity in building space provision and inequality across cities worldwide.This inequality is particularly pronounced in many populous Asian cities,which has been overlooked in previous studies on economic inequality.The GUS-3D dataset shows great potential to deepen our understanding of the urban environment and creates new horizons for numerous 3D urban studies.
