Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The ...Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors, so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some ill-conditioned problems in usual finite elements. The cause why the new method could transform the ill-conditioned problems into well-conditioned problem, is analyzed finally.展开更多
In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split i...In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation.After the linearization of the nonlinear part by Newton’s method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.展开更多
The finite element method is used to simulate the orbital structure,and the finite element model of"rail-sleepers-ballast"can be established.The model of the elastic modulus of different ballast and sleeper ...The finite element method is used to simulate the orbital structure,and the finite element model of"rail-sleepers-ballast"can be established.The model of the elastic modulus of different ballast and sleeper is calculated,and the rail displacement,the sleeper stress and the fastening force are deduced.The results show that the elastic modulus of the ballast can be increased to reduce the displacement of the rail and the supporting force of the fastener,but the stress of the sleeper will be increased.When the modu-lus of elasticity increases,the rail displacement,small.展开更多
The distribution and magnitude of surface substrates were investigated by finite element method and subsurface stresses of the （FEM）. The models of coating single-layer sprayed-coatings on monolithic configurations ...The distribution and magnitude of surface substrates were investigated by finite element method and subsurface stresses of the （FEM）. The models of coating single-layer sprayed-coatings on monolithic configurations with different thicknesses and elastic modulus ratios of coating to substrate were introduced, and the effects of thickness and elastic modulus ratio on the stresses were addressed. The calculation results show that the coating/substrate interface shear stress obviously decreases with increasing coating thickness, due to the location of the maximum shear stress moving away from the coating/substrate interface. At the same time, the magnitude of von Mises stress also declines in the case of thicker coatings. However, the high elastic modulus ratio results in extremely high maximum shear stress and the severe discontinuity of the von Mises stress curves, which leads to the intensive stress concentration on the coating/substrate interface. So the coating configurations with the larger coating thickness and lower difference of elastic modulus between coating and substrate exhibit excellent resistant performance of rolling contact fatigue （RCF）.展开更多
To solve the problems of divergence,low accuracy and project application of membrane wrinkling analysis,an analysis method of zero shear modulus and equivalent stiffness was proposed.This method is an improvement to t...To solve the problems of divergence,low accuracy and project application of membrane wrinkling analysis,an analysis method of zero shear modulus and equivalent stiffness was proposed.This method is an improvement to the previous method (Method I) of local coordinate transposition and stiffness equivalence.The new method is derived and the feasibility is theoretically proved.A small-scale membrane structure is analyzed by the two methods,and the results show that the computational efficiency of the new method (Method II) is approximately 23 times that of Method I.When Method II is applied to a large-scale membrane stadium structure,it is found that this new method can quickly make the second principal stress of one way wrinkled elements zero,and make the two principal stresses of two-way wrinkled elements zero as well.It could attain the correct load responses right after the appearance of wrinkled elements,which indicates that Method II can be applied to wrinkling analysis of large-scale membrane structures.展开更多
Micro/nano-thin films are widely used in the fields of micro/nano-electromechanical system(MEMS/NEMS)and flexible electronics,and their mechanical properties have an important impact on the stability and reliability o...Micro/nano-thin films are widely used in the fields of micro/nano-electromechanical system(MEMS/NEMS)and flexible electronics,and their mechanical properties have an important impact on the stability and reliability of components.However,accurate characterization of the mechanical properties of thin films still faces challenges due to the complexity of film-substrate structure,and the characterization efficiency of traditional techniques is insufficient.In this paper,a high-throughput determination method of the elastic modulus of thin films is proposed based on the strain variance method,the feasibility of which is analyzed by the finite element method(FEM),and the specific tensile configuration with array-distributed thin films is designed and optimized.Based on the strain difference between the film-substrate region and the uncoated region,the elastic modulus of multiple films is obtained simultaneously,and the influences of film width,spacing,thickness,and distribution on the measurement of elastic modulus are elucidated.The results show that the change in film width has a more obvious effect on the elastic modulus determination than film spacing and thickness,i.e.,the larger the film width is,the closer the calculation results are to the theoretical value,and the change in calculation results tends to be stabilized when the film width increases to a certain length.Specifically,the simultaneous measurement of the elastic modulus of eight metal films on a polyimide(PI)substrate with a length of 110 mm and a width of 30 mm can be realized,and the testing throughput can be further increased with the extension of the substrate length.This study provides an efficient and low-cost method for measuring the elastic modulus of thin films,which is expected to accelerate the development of new thin film materials.展开更多
To get the quantitive value of abnormal biological tissues, an inverse algorithm about the Young＇s modulus based on the boundary extraction and the image registration technologies is proposed. With the known displace...To get the quantitive value of abnormal biological tissues, an inverse algorithm about the Young＇s modulus based on the boundary extraction and the image registration technologies is proposed. With the known displacements of boundary tissues and the force distribution, the Young＇s modulus is calculated by constructing the unit system and the inverse finite element method （IFEM）. Then a tough range of the modulus for the whole tissue is estimated referring the value obtained before. The improved particle swarm optimizer （PSO） method is adopted to calculate the whole Yong＇s modulus distribution. The presented algorithm overcomes some limitations in other Young＇s modulus reconstruction methods and relaxes the displacements and force boundary condition requirements. The repetitious numerical simulation shows that errors in boundary displacement are not very sensitive to the estimation of next process; a final feasible solution is obtained by the improved PSO method which is close to the theoretical values obtained during searching in an extensive range.展开更多
In this paper,mechanical properties of Nickel film under residual stress have been systematically examined by finite element method in nanoindentation.It was found that load-displacement curves shifted under elastic r...In this paper,mechanical properties of Nickel film under residual stress have been systematically examined by finite element method in nanoindentation.It was found that load-displacement curves shifted under elastic residual stress and residual stress exceeded the yield stress for fixed indentation depth.Indentation profiles changed monotonously with compressive and tensile stresses at peak force which determinates contact area observed directly by finite element modeling （FEM）.The elastic residual stress has an effect slightly on the hardness but residual stress exceeded the yield stress shows a remarkable effect in nickel film.The hardness increased when residual stress exceeded the yield stress increased under tensile and compressive stress applied to specimen.The relationship between residual stress and hardness was linear.It was found that residual stresses didn＇t affect elastic modulus whether elastic residual stress or plastic stress was applied to specimen.展开更多
The finite element method is used to simulate the rectification process of shield machine, to study the relationship between rectification moment and angle and to explore the influence laws of different soil parameter...The finite element method is used to simulate the rectification process of shield machine, to study the relationship between rectification moment and angle and to explore the influence laws of different soil parameters and buried depth on rectification moment. It is hoped that the reference value of rectification moment can be offered to operator, and theoretical foundation can be laid for future automatic rectification technology. The results show that the rectification moment and angle generally exhibit good linear behavior in clay layers with different soil parameters or buried depths, and then the concept of rectification coefficient, that is, the ratio of rectification angle to rectification moment, is proposed; different soil parameters and buried depths have different influences on rectification coefficient, in which elastic modulus has great influence but others have little influences; the simulations of rectification process are preformed in clay layers with different elastic modulus, and fitting results show that elastic modulus and rectification coefficient present the quadratic function relation.展开更多
In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bil...In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in ｜｜·｜｜div,h norm for p and optimal error estimates in L2 norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes.展开更多
The bimodulus material is a classical model to describe the elastic behavior of materials with tension-compression asymmetry.Due to the inherently nonlinear properties of bimodular materials,traditional iteration meth...The bimodulus material is a classical model to describe the elastic behavior of materials with tension-compression asymmetry.Due to the inherently nonlinear properties of bimodular materials,traditional iteration methods suffer from low convergence efficiency and poor adaptability for large-scale structures in engineering.In this paper,a novel 3D algorithm is established by complementing the three shear moduli of the constitutive equation in principal stress coordinates.In contrast to the existing 3D shear modulus constructed based on experience,in this paper the shear modulus is derived theoretically through a limit process.Then,a theoretically self-consistent complemented algorithm is established and implemented in ABAQUS via UMAT;its good stability and convergence efficiency are verified by using benchmark examples.Numerical analysis shows that the calculation error for bimodulus structures using the traditional linear elastic theory is large,which is not in line with reality.展开更多
Based on the finite element numerical algorithm, the coseismic displacements of the Wenchuan Ms8.0 earthquake are calculated with the rupture slip vectors derived by Ji and Hayes as well as Nishimura and Yaji. Except ...Based on the finite element numerical algorithm, the coseismic displacements of the Wenchuan Ms8.0 earthquake are calculated with the rupture slip vectors derived by Ji and Hayes as well as Nishimura and Yaji. Except in a narrow strip around the rupture zone, the coseismic displacements are consistent with those from GPS observation and InSAR interpretation. Numerical results show that rupture slip vectors and elastic properties have profound influences on the surface coseismic deformation, Results from models with different elastic parameters indicate that： （1） in homogeneous elastic medium, the surface displacements are weakly dependent on Poisson＇s ratio and independent of the elastic modulus; （2） in horizontally homogeneous medium with a weak zone at its middle, the thickness of the weak zone plays a significant role on calculating the surface displacements; （3） in horizontally and vertically heterogeneous medium, the surface displacements depend on both Poisson＇s ratio and elastic modulus. Calculations of eoseismic deformation should take account of the spatial variation of the elastic properties. The misfit of the numerical results with that from the GPS observations in the narrow strip around the rupture zone suggests that a much more complicated rupture model of the Wenchuan earthquake needs to be established in future study.展开更多
In the present study, the indentation testing with a flat cylindrical indenter on typical multi-layer material systems was simulated successfully by finite element method. The emphasis was put on the methods of extrac...In the present study, the indentation testing with a flat cylindrical indenter on typical multi-layer material systems was simulated successfully by finite element method. The emphasis was put on the methods of extracting the yield stresses and strain-hardening modulus of upper and middle-layers of three-layer material systems from the indentation testing. The slope of the indentation depth to the applied indentation stress curve was found to have a turning point, which can be used to determine the yield stress of the upper-layer. Then, a different method was also presented to determine the yield stress of the middle-layer. This method was based on a set of assumed applied indentation stresses which were to be intersected by the experimental results in order to meet the requirement of having the experimental indentation depth. At last, a reverse numerical algorithm was explored to determine the yield stresses of upper and middle-layers simultaneously by using the indentation testing with two different size indenters. This method assumed two ranges of yield stresses to simulate the indentation behavior. The experimental depth behavior was used to intersect the simulated indentation behavior. And the intersection corresponded to the values of yield stresses of upper and middle-layers. This method was also used further to determine the strain-hardening modulus of upper and middle-layers simultaneously.展开更多
An experimental method for a single layer is extended to determine the elastic properties of nanostructured W/C u multilayers on a flexible substrate.The strain difference between the W/Cu-polyimide-W/Cu composite and...An experimental method for a single layer is extended to determine the elastic properties of nanostructured W/C u multilayers on a flexible substrate.The strain difference between the W/Cu-polyimide-W/Cu composite and the uncoated substrate,measured by dual digital image correlation,allows us to extract the effective Young's modulus of W/Cu multilayers(20 periods)equaling 216±13 GPa.Finite element method is then performed,which agrees well with the experiment and classical rule of mixture(ROM)theory demonstrating that the extension to multilayers is effective and reliable.The numerical analysis also interestingly shows that the strain difference is linearly related to the thickness ratio(W/Cu),periods and sublayer thickness,respectively.In contrast to ROM theory,this approach could potentially be used for the evaluation of properties and design of emerging/unknown functional multilayers,whether or not they are crystalline or amorphous.展开更多
This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-d...This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares （IMLS） approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.展开更多
Split Hopkinson pressure bar（SHPB） apparatus, usually used for testing behavior of material in median and high strain-rate, is now widely used in the study of rock dynamic constitutive relation, damage evolvement me...Split Hopkinson pressure bar（SHPB） apparatus, usually used for testing behavior of material in median and high strain-rate, is now widely used in the study of rock dynamic constitutive relation, damage evolvement mechanism and energy consumption. However, the possible reasons of sampling disturbance, machining error and so on often lead to the scattering of test results, and bring ultimate difficulty for forming general test conclusion. Based on the stochastic finite element method, the uncertain parameters of specimen density ps, specimen radius Rs, specimen elastic modulus Es and specimen length Ls in the data processing of SHPB test were considered, and the correlation between the parameters and the test results was analyzed. The results show that the specimen radius Rs has direct correlation with the test result, improving the accuracy in preparing and measuring of specimen is an effective way to improve the accuracy of test and minish the scattering of results for SHPB test.展开更多
Based on the thermal kinetic and mass conservation, a series of controlling equations for the finite element are derived and related programs are developed to simulate the damage microcrack healing process controlled ...Based on the thermal kinetic and mass conservation, a series of controlling equations for the finite element are derived and related programs are developed to simulate the damage microcrack healing process controlled by surface diffusion. Two kinds of typical models for microcrack splitting are proposed, i.e., the grain boundary energy existing on the crack surface and residual stresses applying on the crack surface. And the conditions of microcrack splitting in the two models are given as a function of the microcrack aspect ratio. The microcrack with traction-free surfaces will directly evolve into a spheroid.展开更多
In micro-electro-mechanical systems,interface expansion issues are commonly encountered,and due to their small size,they often exist at the micro-or nano-scale.The influence of the micro-structural effect on interface...In micro-electro-mechanical systems,interface expansion issues are commonly encountered,and due to their small size,they often exist at the micro-or nano-scale.The influence of the micro-structural effect on interface mechanics cannot be ignored.This paper focuses on studying the impact of micro-structural effect on interface crack propagation.Modified couple stress theory(MCST)is used to study the buckling delamination of ultra-thin film-substrate systems.The equivalent elastic modulus(EEM)and equivalent flexural rigidity(EFR)are derived based on MCST.Substituting EEM and EFR into the classical Kirchhoff plate theory,the governing equations of ultra-thin film-substrate system with micro-structural effect can be obtained.The finite element method(FEM)was used to calculate the critical strain energy release rate for crack extension.Differences between the three theoretical approaches of MCST,classical theory(CT),and FEM were compared.The effects of stress ratioσ/σ_(c),initial crack length,film thickness,and micro-structural effect parameters on crack extension were analyzed.The results show that the FEM calculations coincide with the CT calculations.The stress ratioσ/σ_(c),initial crack length,film thickness,and micro-structural effect parameters have significantly influence crack extension.展开更多
文摘Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors, so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some ill-conditioned problems in usual finite elements. The cause why the new method could transform the ill-conditioned problems into well-conditioned problem, is analyzed finally.
基金financially supported by the National Natural Science Foundation of China(Grant No.51349011)the Foundation of Si’chuan Educational Committee(Grant No.17ZB0452)+1 种基金the Innovation Team Project of Si’chuan Educational Committee(Grant No.18TD0019)the Longshan Academic Talent Research Support Program of the Southwest of Science and Technology(Grant Nos.18LZX715 and 18LZX410)
文摘In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation.After the linearization of the nonlinear part by Newton’s method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.
文摘The finite element method is used to simulate the orbital structure,and the finite element model of"rail-sleepers-ballast"can be established.The model of the elastic modulus of different ballast and sleeper is calculated,and the rail displacement,the sleeper stress and the fastening force are deduced.The results show that the elastic modulus of the ballast can be increased to reduce the displacement of the rail and the supporting force of the fastener,but the stress of the sleeper will be increased.When the modu-lus of elasticity increases,the rail displacement,small.
基金Project(2007AA04Z408) supported by the National High-Tech Research and Development Program of ChinaProject(50735006) supported by the National Natural Science Foundation of China
文摘The distribution and magnitude of surface substrates were investigated by finite element method and subsurface stresses of the （FEM）. The models of coating single-layer sprayed-coatings on monolithic configurations with different thicknesses and elastic modulus ratios of coating to substrate were introduced, and the effects of thickness and elastic modulus ratio on the stresses were addressed. The calculation results show that the coating/substrate interface shear stress obviously decreases with increasing coating thickness, due to the location of the maximum shear stress moving away from the coating/substrate interface. At the same time, the magnitude of von Mises stress also declines in the case of thicker coatings. However, the high elastic modulus ratio results in extremely high maximum shear stress and the severe discontinuity of the von Mises stress curves, which leads to the intensive stress concentration on the coating/substrate interface. So the coating configurations with the larger coating thickness and lower difference of elastic modulus between coating and substrate exhibit excellent resistant performance of rolling contact fatigue （RCF）.
基金Project(020940) supported by the Natural Science Foundation of Guangdong Province,China
文摘To solve the problems of divergence,low accuracy and project application of membrane wrinkling analysis,an analysis method of zero shear modulus and equivalent stiffness was proposed.This method is an improvement to the previous method (Method I) of local coordinate transposition and stiffness equivalence.The new method is derived and the feasibility is theoretically proved.A small-scale membrane structure is analyzed by the two methods,and the results show that the computational efficiency of the new method (Method II) is approximately 23 times that of Method I.When Method II is applied to a large-scale membrane stadium structure,it is found that this new method can quickly make the second principal stress of one way wrinkled elements zero,and make the two principal stresses of two-way wrinkled elements zero as well.It could attain the correct load responses right after the appearance of wrinkled elements,which indicates that Method II can be applied to wrinkling analysis of large-scale membrane structures.
文摘Micro/nano-thin films are widely used in the fields of micro/nano-electromechanical system(MEMS/NEMS)and flexible electronics,and their mechanical properties have an important impact on the stability and reliability of components.However,accurate characterization of the mechanical properties of thin films still faces challenges due to the complexity of film-substrate structure,and the characterization efficiency of traditional techniques is insufficient.In this paper,a high-throughput determination method of the elastic modulus of thin films is proposed based on the strain variance method,the feasibility of which is analyzed by the finite element method(FEM),and the specific tensile configuration with array-distributed thin films is designed and optimized.Based on the strain difference between the film-substrate region and the uncoated region,the elastic modulus of multiple films is obtained simultaneously,and the influences of film width,spacing,thickness,and distribution on the measurement of elastic modulus are elucidated.The results show that the change in film width has a more obvious effect on the elastic modulus determination than film spacing and thickness,i.e.,the larger the film width is,the closer the calculation results are to the theoretical value,and the change in calculation results tends to be stabilized when the film width increases to a certain length.Specifically,the simultaneous measurement of the elastic modulus of eight metal films on a polyimide(PI)substrate with a length of 110 mm and a width of 30 mm can be realized,and the testing throughput can be further increased with the extension of the substrate length.This study provides an efficient and low-cost method for measuring the elastic modulus of thin films,which is expected to accelerate the development of new thin film materials.
文摘To get the quantitive value of abnormal biological tissues, an inverse algorithm about the Young＇s modulus based on the boundary extraction and the image registration technologies is proposed. With the known displacements of boundary tissues and the force distribution, the Young＇s modulus is calculated by constructing the unit system and the inverse finite element method （IFEM）. Then a tough range of the modulus for the whole tissue is estimated referring the value obtained before. The improved particle swarm optimizer （PSO） method is adopted to calculate the whole Yong＇s modulus distribution. The presented algorithm overcomes some limitations in other Young＇s modulus reconstruction methods and relaxes the displacements and force boundary condition requirements. The repetitious numerical simulation shows that errors in boundary displacement are not very sensitive to the estimation of next process; a final feasible solution is obtained by the improved PSO method which is close to the theoretical values obtained during searching in an extensive range.
基金supported by the National Natural Science Foundation of China (NSFC,No. 10702057)Hunan Provincial Natural Science Foundation of China (No.09JJ3003)Hunan Provincial Innovation Foundation for Postgraduate (No. CX2009B130)
文摘In this paper,mechanical properties of Nickel film under residual stress have been systematically examined by finite element method in nanoindentation.It was found that load-displacement curves shifted under elastic residual stress and residual stress exceeded the yield stress for fixed indentation depth.Indentation profiles changed monotonously with compressive and tensile stresses at peak force which determinates contact area observed directly by finite element modeling （FEM）.The elastic residual stress has an effect slightly on the hardness but residual stress exceeded the yield stress shows a remarkable effect in nickel film.The hardness increased when residual stress exceeded the yield stress increased under tensile and compressive stress applied to specimen.The relationship between residual stress and hardness was linear.It was found that residual stresses didn＇t affect elastic modulus whether elastic residual stress or plastic stress was applied to specimen.
基金Project(2007CB714006)supported by the National Basic Research Program of China
文摘The finite element method is used to simulate the rectification process of shield machine, to study the relationship between rectification moment and angle and to explore the influence laws of different soil parameters and buried depth on rectification moment. It is hoped that the reference value of rectification moment can be offered to operator, and theoretical foundation can be laid for future automatic rectification technology. The results show that the rectification moment and angle generally exhibit good linear behavior in clay layers with different soil parameters or buried depths, and then the concept of rectification coefficient, that is, the ratio of rectification angle to rectification moment, is proposed; different soil parameters and buried depths have different influences on rectification coefficient, in which elastic modulus has great influence but others have little influences; the simulations of rectification process are preformed in clay layers with different elastic modulus, and fitting results show that elastic modulus and rectification coefficient present the quadratic function relation.
基金Supported by the National Natural Science Foundation of China(No.10971203,11271340,11101384)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20094101110006)
文摘In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in ｜｜·｜｜div,h norm for p and optimal error estimates in L2 norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes.
基金the National Natural Science Foundation of China(Grant 51908071)Scientific Research Project of Education Department of Hunan Province(Grant 18C0194)Open Fund of Key Laboratory of Road Structure and Material of Ministry of Transport,Changsha University of Science&Technology(Grant kfi 170303).
文摘The bimodulus material is a classical model to describe the elastic behavior of materials with tension-compression asymmetry.Due to the inherently nonlinear properties of bimodular materials,traditional iteration methods suffer from low convergence efficiency and poor adaptability for large-scale structures in engineering.In this paper,a novel 3D algorithm is established by complementing the three shear moduli of the constitutive equation in principal stress coordinates.In contrast to the existing 3D shear modulus constructed based on experience,in this paper the shear modulus is derived theoretically through a limit process.Then,a theoretically self-consistent complemented algorithm is established and implemented in ABAQUS via UMAT;its good stability and convergence efficiency are verified by using benchmark examples.Numerical analysis shows that the calculation error for bimodulus structures using the traditional linear elastic theory is large,which is not in line with reality.
基金supported by the National Natural Science Foundation of China under grant No.40774045supported by the program from Chinese Academy of Sciences under grant No. KZCX2-YW-QN507
文摘Based on the finite element numerical algorithm, the coseismic displacements of the Wenchuan Ms8.0 earthquake are calculated with the rupture slip vectors derived by Ji and Hayes as well as Nishimura and Yaji. Except in a narrow strip around the rupture zone, the coseismic displacements are consistent with those from GPS observation and InSAR interpretation. Numerical results show that rupture slip vectors and elastic properties have profound influences on the surface coseismic deformation, Results from models with different elastic parameters indicate that： （1） in homogeneous elastic medium, the surface displacements are weakly dependent on Poisson＇s ratio and independent of the elastic modulus; （2） in horizontally homogeneous medium with a weak zone at its middle, the thickness of the weak zone plays a significant role on calculating the surface displacements; （3） in horizontally and vertically heterogeneous medium, the surface displacements depend on both Poisson＇s ratio and elastic modulus. Calculations of eoseismic deformation should take account of the spatial variation of the elastic properties. The misfit of the numerical results with that from the GPS observations in the narrow strip around the rupture zone suggests that a much more complicated rupture model of the Wenchuan earthquake needs to be established in future study.
基金the National Natural Science Foundation of China （No. 10472094） the Research Fund for the Doctoral Program of Higher Education （N6CJ0001） Doctorate Fund of Northwestern Polytechnical University.
文摘In the present study, the indentation testing with a flat cylindrical indenter on typical multi-layer material systems was simulated successfully by finite element method. The emphasis was put on the methods of extracting the yield stresses and strain-hardening modulus of upper and middle-layers of three-layer material systems from the indentation testing. The slope of the indentation depth to the applied indentation stress curve was found to have a turning point, which can be used to determine the yield stress of the upper-layer. Then, a different method was also presented to determine the yield stress of the middle-layer. This method was based on a set of assumed applied indentation stresses which were to be intersected by the experimental results in order to meet the requirement of having the experimental indentation depth. At last, a reverse numerical algorithm was explored to determine the yield stresses of upper and middle-layers simultaneously by using the indentation testing with two different size indenters. This method assumed two ranges of yield stresses to simulate the indentation behavior. The experimental depth behavior was used to intersect the simulated indentation behavior. And the intersection corresponded to the values of yield stresses of upper and middle-layers. This method was also used further to determine the strain-hardening modulus of upper and middle-layers simultaneously.
基金This research is financially supported by the National Natural Science Foundation of China(Grant 11802156)China Postdoctoral Science Foundation(Grant 2018M641331)French Government Program“Investissements d’Avenir”(Labex Interactifs,Grant ANR-11-LABX-0017-01).
文摘An experimental method for a single layer is extended to determine the elastic properties of nanostructured W/C u multilayers on a flexible substrate.The strain difference between the W/Cu-polyimide-W/Cu composite and the uncoated substrate,measured by dual digital image correlation,allows us to extract the effective Young's modulus of W/Cu multilayers(20 periods)equaling 216±13 GPa.Finite element method is then performed,which agrees well with the experiment and classical rule of mixture(ROM)theory demonstrating that the extension to multilayers is effective and reliable.The numerical analysis also interestingly shows that the strain difference is linearly related to the thickness ratio(W/Cu),periods and sublayer thickness,respectively.In contrast to ROM theory,this approach could potentially be used for the evaluation of properties and design of emerging/unknown functional multilayers,whether or not they are crystalline or amorphous.
基金supported by the National Natural Science Foundation of China (Grants 11571223, 51404160)Shanxi Province Science Foundation for Youths (Grant 2014021025-1)
文摘This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares （IMLS） approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.
基金Projects(50490274, 50534030) supported by the National Natural Science Foundation of ChinaProject supported by the Natural Science Foundatin of Hunan Province, China
文摘Split Hopkinson pressure bar（SHPB） apparatus, usually used for testing behavior of material in median and high strain-rate, is now widely used in the study of rock dynamic constitutive relation, damage evolvement mechanism and energy consumption. However, the possible reasons of sampling disturbance, machining error and so on often lead to the scattering of test results, and bring ultimate difficulty for forming general test conclusion. Based on the stochastic finite element method, the uncertain parameters of specimen density ps, specimen radius Rs, specimen elastic modulus Es and specimen length Ls in the data processing of SHPB test were considered, and the correlation between the parameters and the test results was analyzed. The results show that the specimen radius Rs has direct correlation with the test result, improving the accuracy in preparing and measuring of specimen is an effective way to improve the accuracy of test and minish the scattering of results for SHPB test.
基金The project supported by the National Natural Science Foundation of China(19972053 and 59889101)the National Outstanding Young Scientist Fund of China(59925104)
文摘Based on the thermal kinetic and mass conservation, a series of controlling equations for the finite element are derived and related programs are developed to simulate the damage microcrack healing process controlled by surface diffusion. Two kinds of typical models for microcrack splitting are proposed, i.e., the grain boundary energy existing on the crack surface and residual stresses applying on the crack surface. And the conditions of microcrack splitting in the two models are given as a function of the microcrack aspect ratio. The microcrack with traction-free surfaces will directly evolve into a spheroid.
基金supported by the National Key R&D Program of China(No.2022YFB3207100)the Hubei Provincial Strategic Scientist Training Plan(No.2022EJD009)the Fundamental Research Funds for the Central Universities(No.2042023kf1041).
文摘In micro-electro-mechanical systems,interface expansion issues are commonly encountered,and due to their small size,they often exist at the micro-or nano-scale.The influence of the micro-structural effect on interface mechanics cannot be ignored.This paper focuses on studying the impact of micro-structural effect on interface crack propagation.Modified couple stress theory(MCST)is used to study the buckling delamination of ultra-thin film-substrate systems.The equivalent elastic modulus(EEM)and equivalent flexural rigidity(EFR)are derived based on MCST.Substituting EEM and EFR into the classical Kirchhoff plate theory,the governing equations of ultra-thin film-substrate system with micro-structural effect can be obtained.The finite element method(FEM)was used to calculate the critical strain energy release rate for crack extension.Differences between the three theoretical approaches of MCST,classical theory(CT),and FEM were compared.The effects of stress ratioσ/σ_(c),initial crack length,film thickness,and micro-structural effect parameters on crack extension were analyzed.The results show that the FEM calculations coincide with the CT calculations.The stress ratioσ/σ_(c),initial crack length,film thickness,and micro-structural effect parameters have significantly influence crack extension.
