The challenge of solving nonlinear problems in multi-connected domains with high accuracy has garnered significant interest.In this paper,we propose a unified wavelet solution method for accurately solving nonlinear b...The challenge of solving nonlinear problems in multi-connected domains with high accuracy has garnered significant interest.In this paper,we propose a unified wavelet solution method for accurately solving nonlinear boundary value problems on a two-dimensional(2D)arbitrary multi-connected domain.We apply this method to solve large deflection bending problems of complex plates with holes.Our solution method simplifies the treatment of the 2D multi-connected domain by utilizing a natural discretization approach that divides it into a series of one-dimensional(1D)intervals.This approach establishes a fundamental relationship between the highest-order derivative in the governing equation of the problem and the remaining lower-order derivatives.By combining a wavelet high accuracy integral approximation format on 1D intervals,where the convergence order remains constant regardless of the number of integration folds,with the collocation method,we obtain a system of algebraic equations that only includes discrete point values of the highest order derivative.In this process,the boundary conditions are automatically replaced using integration constants,eliminating the need for additional processing.Error estimation and numerical results demonstrate that the accuracy of this method is unaffected by the degree of nonlinearity of the equations.When solving the bending problem of multi-perforated complex-shaped plates under consideration,it is evident that directly using higher-order derivatives as unknown functions significantly improves the accuracy of stress calculation,even when the stress exhibits large gradient variations.Moreover,compared to the finite element method,the wavelet method requires significantly fewer nodes to achieve the same level of accuracy.Ultimately,the method achieves a sixth-order accuracy and resembles the treatment of one-dimensional problems during the solution process,effectively avoiding the need for the complex 2D meshing process typically required by conventional methods when solving problems with multi-connected domains.展开更多
The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition a...The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate. The latter can be solved by using the superposition principle. Making use of the recommended method, the bending of the plate with all kinds of...展开更多
In order to study the calculation methods of bending behavior of Chinese reinforced concrete beams from 1912 to 1949, tests on the mechanical performance of 66 rebars from different modem Chinese concrete buildings, t...In order to study the calculation methods of bending behavior of Chinese reinforced concrete beams from 1912 to 1949, tests on the mechanical performance of 66 rebars from different modem Chinese concrete buildings, the concrete compressive strength of 12 modem Chinese concrete buildings, and the concrete cover thickness of 9 modem Chinese concrete buildings are carried out; and the actual material properties and structural conformations of modem Chinese concrete buildings are obtained. Then, the comparison on calculation methods of bending behavior including the original Chinese calculation method, the present Chinese calculation method, the present American calculation method and the present European calculation method is studied. The results show that the original Chinese calculation method of bending behavior is based on the allowable stress calculation method, and the design safety factors are 3.55 to 4. 0. In term of the calculation area of longitudinal rebars of reinforced concrete beams, without considering earthquake action, the original Chinese structural calculation method is safer than the present Chinese structural calculation method, the present European structural calculation method, and the present American structural calculation method. The results can provide support for the structural safety assessments of modem Chinese reinforced concrete buildings.展开更多
Using the single crack solution and the regular solution of plane harmonic function, the problem of Saint_Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equation...Using the single crack solution and the regular solution of plane harmonic function, the problem of Saint_Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equations and its general solution was then obtained. Based on the obtained solution, a method to calculate the bending center and the stress intensity factors of the cracked cylinger whose cross_section is not thin_walled, but of small torsion rigidity is proposed. Some numerical examples are given.展开更多
A new numerical manifold （NMM） method is derived on the basis of quartic uniform B-spline interpolation. The analysis shows that the new interpolation function possesses higher-order continuity and polynomial consis...A new numerical manifold （NMM） method is derived on the basis of quartic uniform B-spline interpolation. The analysis shows that the new interpolation function possesses higher-order continuity and polynomial consistency compared with the conven- tional NMM. The stiffness matrix of the new element is well-conditioned. The proposed method is applied for the numerical example of thin plate bending. Based on the prin- ciple of minimum potential energy, the manifold matrices and equilibrium equation are deduced. Numerical results reveal that the NMM has high interpolation accuracy and rapid convergence for the global cover function and its higher-order partial derivatives.展开更多
A wavelet method for solving strongly nonlinear boundary value problems is described, which has been demonstrated early to have a convergence rate of order 4, almost independent of the nonlinear intensity of the equat...A wavelet method for solving strongly nonlinear boundary value problems is described, which has been demonstrated early to have a convergence rate of order 4, almost independent of the nonlinear intensity of the equations. By using such a method, we study the bending problem of a circular plate with arbitrary large deflection. As the deflection increases, the bending behavior usually exhibits a so-called plate-to-membrane transition. Capturing such a transition has ever frustrated researchers for decades. However, without introducing any addi- tional treatment, we show in this study that the proposed wavelet solutions can naturally cover the plate-membrane transition region as the plate deflection increases. In addition, the high accuracy and efficiency of the wavelet method in solving strongly nonlinear problems is numerically confirmed, and applicable scopes for the linear, the membrane and the yon Karman plate theories are identified with respect to the large deformation bending of circular plates.展开更多
Springback is one of important factors influencing the forming quality of numerical control （NC） bending of thin-walled tube. In this paper, a numerical-analytic method for springback angle prediction of the process...Springback is one of important factors influencing the forming quality of numerical control （NC） bending of thin-walled tube. In this paper, a numerical-analytic method for springback angle prediction of the process was put forward. The method is based on springback angle model derived using analytic method and simulation results from three-dimensional （3D） rigid-plastic finite element method （FEM）. The method is validated through comparison with experimental results. The features of the method are as follows： （1） The method is high in efficiency because it combines advantages of rigid-plastic FEM and analytic method. （2） The method is satisfactory in accuracy, since the field variables used in the model is resulting from 3D rigid-plastic FEM solution, and the effects both of axial force and strain neutral axis shift have been included. （3） Research on multi-factor effects can be carried out using the method due to its advantage inheriting from rigid-plastic FEM. The method described here is also of general significance to other bending processes.展开更多
The semi? analytic perturbation weighted residuals method was used to solve the nonlinear bending problem of shallow shells, and the fifth order B spline was taken as trial function to seek an efficient method for n...The semi? analytic perturbation weighted residuals method was used to solve the nonlinear bending problem of shallow shells, and the fifth order B spline was taken as trial function to seek an efficient method for nonlinear bending problem of shallow shells. The results from the present method are in good agreement with those derived from other methods. The present method is of higher accuracy, lower computing time and wider adaptability. In addition, the design of computer program is simple and it is easy to be programmed.展开更多
Lead zirconate titanium solid-solution (PZT) thin films with variousthickness are synthesized on titanium substrates by repeated hydrothermal treatments. Young modulus,electric-field-induced displacement and the densi...Lead zirconate titanium solid-solution (PZT) thin films with variousthickness are synthesized on titanium substrates by repeated hydrothermal treatments. Young modulus,electric-field-induced displacement and the density of the PZT film are measured respectively.Bimorph- type bending actuators are fabricated using these films. The model, which is used toanalyze the driving ability of bimorph-type bending actuators by hydrothermal method, is set up. Itcan be seen that the driving ability of bimorph-type bending actuators can be greatly improved byoptimizing the thickness of PZT thin film and substrate from the theoretical analysis results. Themeasured values are expected to agree with the theoretical values calculated by the above model.展开更多
The typical quadrangular and triangular elements for thin plate bending based on Kirchhoff assumptions are the non- conforming elements with low computational accuracy and limitative application range in fmite element...The typical quadrangular and triangular elements for thin plate bending based on Kirchhoff assumptions are the non- conforming elements with low computational accuracy and limitative application range in fmite element method（FEM）. Some compatible elements can be developed by the means of supplementing correction functions, increasing nodes in element or on the boundaries, expanding nodal degrees of freedom（DOF）, etc, but these elements are inconvenient to apply in practice for the high calculation complexity. In this paper, in order to overcome the defects of thin plate bending finite element, numerical manifold method（NMM） was introduced to solve thin plate bending deformation problem. Rectangular mesh was adopted as mathematical mesh to form f＇mite element cover system, and then 16-cover manifold element was proposed. Numerical manifold formulas were constructed on the basis of minimum potential energy principle, displacement boundary conditions are implemented by penalty function method, and all the element matrixes were derived in details. The 16-cover element has a simple calculation process for employing only the transverse displacement cover DOFs as the basic unknown variables, and has been proved to meet the requirements of completeness and full compatibility. As an application, the presented 16-cover element has been used to analyze bending deformation of square thin plate under different loads and boundary conditions, and the results show that numerical manifold method with compatible element, compared with finite element method, can improve computational accuracy and convergence greatly.展开更多
A finite difference method at arbitrary meshes for the bending of plates with variable thickness is presented in this paper. The method is completely general with respect to various boundary conditions, load cases and...A finite difference method at arbitrary meshes for the bending of plates with variable thickness is presented in this paper. The method is completely general with respect to various boundary conditions, load cases and shapes of plates. This difference scheme is simple and the numerical results agree well with those obtained by other methods.展开更多
This paper presents a new method to estimate the height of the atmospheric boundary layer(ABL) by using COSMIC radio occultation bending angle(BA) data. Using the numerical differentiation method combined with the reg...This paper presents a new method to estimate the height of the atmospheric boundary layer(ABL) by using COSMIC radio occultation bending angle(BA) data. Using the numerical differentiation method combined with the regularization technique, the first derivative of BA profiles is retrieved, and the height at which the first derivative of BA has the global minimum is defined to be the ABL height. To reflect the reliability of estimated ABL heights, the sharpness parameter is introduced, according to the relative minimum of the BA derivative. Then, it is applied to four months of COSMIC BA data(January, April, July, and October in 2008), and the ABL heights estimated are compared with two kinds of ABL heights from COSMIC products and with the heights determined by the finite difference method upon the refractivity data. For sharp ABL tops(large sharpness parameters), there is little difference between the ABL heights determined by different methods, i.e.,the uncertainties are small; whereas, for non-sharp ABL tops(small sharpness parameters), big differences exist in the ABL heights obtained by different methods, which means large uncertainties for different methods. In addition, the new method can detect thin ABLs and provide a reference ABL height in the cases eliminated by other methods. Thus, the application of the numerical differentiation method combined with the regularization technique to COSMIC BA data is an appropriate choice and has further application value.展开更多
In nature,there are widely distributed bi-modulus materials with different deformation characteristics under compressive and tensile stress states,such as concrete,rock and ceramics.Due to the lack of constitutive mod...In nature,there are widely distributed bi-modulus materials with different deformation characteristics under compressive and tensile stress states,such as concrete,rock and ceramics.Due to the lack of constitutive model that could reasonably consider the bi-modulus property of materials,and the lack of simple and reliable measurement methods for the tensile elastic parameters of materials,scientists and engineers always neglect the effect of the bi-modulus property of materials in engineering design and numerical simulation.To solve this problem,this study utilizes the uncoupled strain-driven constitutive model proposed by Latorre and Montáns(2020)to systematically study the distributions and magnitudes of stresses and strains of bi-modulus materials in the three-point bending test through the numerical method.Furthermore,a new method to synchronously measure the tensile and compressive elastic moduli of materials through the four-point bending test is proposed.The numerical results show that the bi-modulus property of materials has a significant effect on the stress,strain and displacement in the specimen utilized in the three-point and four-point bending tests.Meanwhile,the results from the numerical tests,in which the elastic constitutive model proposed by Latorre and Montáns(2020)is utilized,also indicate that the newly proposed measurement method has a good reliability.Although the new measurement method proposed in this study can synchronously and effectively measure the tensile and compressive elastic moduli,it cannot measure the tensile and compressive Poisson’s ratios.展开更多
A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth...A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex domains.In the solution of differential equations,various derivatives of the unknown function are denoted as new functions.Then,the integral relations between these functions are applied in terms of wavelet approximation of multiple integrals.Therefore,the original equation with derivatives of various orders can be converted to a system of algebraic equations with discrete nodal values of the highest-order derivative.During the application of the proposed method,boundary conditions can be automatically included in the integration operations,and relevant matrices can be assured to exhibit perfect sparse patterns.As examples,we consider several second-order mathematics problems defined on regular and irregular domains and the fourth-order bending problems of plates with various shapes.By comparing the solutions obtained by the proposed method with the exact solutions,the new multiresolution method is found to have a convergence rate of fifth order.The solution accuracy of this method with only a few hundreds of nodes can be much higher than that of the finite element method(FEM)with tens of thousands of elements.In addition,because the accuracy order for direct approximation of a function using the proposed basis function is also fifth order,we may conclude that the accuracy of the proposed method is almost independent of the equation order and domain complexity.展开更多
Recently, pH-sensitive hydrogels have been utilized in the diverse applications including sensors, switches, and actuators. In order to have continuous stress and deformation ?elds, a new semi-analytical approach is d...Recently, pH-sensitive hydrogels have been utilized in the diverse applications including sensors, switches, and actuators. In order to have continuous stress and deformation ?elds, a new semi-analytical approach is developed to predict the swelling induced?nite bending for a functionally graded(FG) layer composed of a pH-sensitive hydrogel,in which the cross-link density is continuously distributed along the thickness direction under the plane strain condition. Without considering the intermediary virtual reference,the initial state is mapped into the deformed con?guration in a circular shape by utilizing a total deformation gradient tensor stemming from the inhomogeneous swelling of an FG layer in response to the variation of the pH value of the solvent. To enlighten the capability of the presented analytical method, the ?nite element method(FEM) is used to verify the accuracy of the analytical results in some case studies. The perfect agreement con-?rms the accuracy of the presented method. Due to the applicability of FG pH-sensitive hydrogels, some design factors such as the semi-angle, the bending curvature, the aspect ratio, and the distributions of deformation and stress ?elds are studied. Furthermore, the tangential free-stress axes are illustrated in deformed con?guration.展开更多
Aiming at high cost and low efficiency of conventional branch bending method in the modern intensive planting and labor-saving cultivation mode of young pear trees,this paper provides a new branch bending method with ...Aiming at high cost and low efficiency of conventional branch bending method in the modern intensive planting and labor-saving cultivation mode of young pear trees,this paper provides a new branch bending method with wide source of raw materials,cheap price and simple operation,which is also suitable for the management of low-age branches in the process of high grafting and upgrading of traditional big trees.展开更多
Using the single crack solution and the regular solution elf plane harmonic function, the problem of Saint-Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equatio...Using the single crack solution and the regular solution elf plane harmonic function, the problem of Saint-Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equations and its general solution was then obtained. Based on the obtained solution, a method to calculate the bending center and the stress intensity factors of the cracked cylinger whose cross-section is not thin-walled, but of small torsion rigidity is proposed. Some numerical examples are given.展开更多
In this paper, based on the step reduction method, a new method, the exact element method for constructing finite element, is presented. Since the new method doesn 't need the variational principle, it can be appl...In this paper, based on the step reduction method, a new method, the exact element method for constructing finite element, is presented. Since the new method doesn 't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a triangle noncompatible element with 6 degrees of freedom is derived to solve the bending of nonhomogeneous plate. The convergence of displacements and stress resultants which have satisfactory numerical precision is proved. Numerical examples are given at the end of this paper, which indicate satisfactory results of stress resultants and displacements can be obtained by the present method.展开更多
A theorem of solving a system of linear non-homogeneous differential equations through integrating and adding its basic solutions is put forward and proved, the mathematical role and physical nature of the theorem is ...A theorem of solving a system of linear non-homogeneous differential equations through integrating and adding its basic solutions is put forward and proved, the mathematical role and physical nature of the theorem is interpreted briefly. As an example, the theorem is applied to solve the problem of thermo-force bending of a thick plate.展开更多
Owing to the existence of distributed holes, it is difficult tosolve the bending problem of perforated plates by the conventionalfinite element method. A homogenization-based method for this problemis presented in thi...Owing to the existence of distributed holes, it is difficult tosolve the bending problem of perforated plates by the conventionalfinite element method. A homogenization-based method for this problemis presented in this paper. As an example, the bending analysis of acircular perforated plate with distributed step-wise cylindricalholes is made. The deflection and the fundamental frequen- cyobtained by present method are in good agreement with experimentaldata, this implies that the method is effective.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11925204).
文摘The challenge of solving nonlinear problems in multi-connected domains with high accuracy has garnered significant interest.In this paper,we propose a unified wavelet solution method for accurately solving nonlinear boundary value problems on a two-dimensional(2D)arbitrary multi-connected domain.We apply this method to solve large deflection bending problems of complex plates with holes.Our solution method simplifies the treatment of the 2D multi-connected domain by utilizing a natural discretization approach that divides it into a series of one-dimensional(1D)intervals.This approach establishes a fundamental relationship between the highest-order derivative in the governing equation of the problem and the remaining lower-order derivatives.By combining a wavelet high accuracy integral approximation format on 1D intervals,where the convergence order remains constant regardless of the number of integration folds,with the collocation method,we obtain a system of algebraic equations that only includes discrete point values of the highest order derivative.In this process,the boundary conditions are automatically replaced using integration constants,eliminating the need for additional processing.Error estimation and numerical results demonstrate that the accuracy of this method is unaffected by the degree of nonlinearity of the equations.When solving the bending problem of multi-perforated complex-shaped plates under consideration,it is evident that directly using higher-order derivatives as unknown functions significantly improves the accuracy of stress calculation,even when the stress exhibits large gradient variations.Moreover,compared to the finite element method,the wavelet method requires significantly fewer nodes to achieve the same level of accuracy.Ultimately,the method achieves a sixth-order accuracy and resembles the treatment of one-dimensional problems during the solution process,effectively avoiding the need for the complex 2D meshing process typically required by conventional methods when solving problems with multi-connected domains.
文摘The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate. The latter can be solved by using the superposition principle. Making use of the recommended method, the bending of the plate with all kinds of...
基金The National Natural Science Foundation of China(No.51138002)the Foundation for the Author of National Excellent Doctoral Dissertation of PR China(No.201452)the Open Fund of Shanghai Key Laboratory of Engineering Structure Safety(No.2015-KF06)
文摘In order to study the calculation methods of bending behavior of Chinese reinforced concrete beams from 1912 to 1949, tests on the mechanical performance of 66 rebars from different modem Chinese concrete buildings, the concrete compressive strength of 12 modem Chinese concrete buildings, and the concrete cover thickness of 9 modem Chinese concrete buildings are carried out; and the actual material properties and structural conformations of modem Chinese concrete buildings are obtained. Then, the comparison on calculation methods of bending behavior including the original Chinese calculation method, the present Chinese calculation method, the present American calculation method and the present European calculation method is studied. The results show that the original Chinese calculation method of bending behavior is based on the allowable stress calculation method, and the design safety factors are 3.55 to 4. 0. In term of the calculation area of longitudinal rebars of reinforced concrete beams, without considering earthquake action, the original Chinese structural calculation method is safer than the present Chinese structural calculation method, the present European structural calculation method, and the present American structural calculation method. The results can provide support for the structural safety assessments of modem Chinese reinforced concrete buildings.
文摘Using the single crack solution and the regular solution of plane harmonic function, the problem of Saint_Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equations and its general solution was then obtained. Based on the obtained solution, a method to calculate the bending center and the stress intensity factors of the cracked cylinger whose cross_section is not thin_walled, but of small torsion rigidity is proposed. Some numerical examples are given.
基金supported by the Fund of National Engineering and Research Center for Highways in Mountain Area(No.gsgzj-2012-05)the Fundamental Research Funds for the Central Universities of China(No.CDJXS12240003)the Scientific Research Foundation of State Key Laboratory of Coal Mine Disaster Dynamics and Control(No.2011DA105287-MS201213)
文摘A new numerical manifold （NMM） method is derived on the basis of quartic uniform B-spline interpolation. The analysis shows that the new interpolation function possesses higher-order continuity and polynomial consistency compared with the conven- tional NMM. The stiffness matrix of the new element is well-conditioned. The proposed method is applied for the numerical example of thin plate bending. Based on the prin- ciple of minimum potential energy, the manifold matrices and equilibrium equation are deduced. Numerical results reveal that the NMM has high interpolation accuracy and rapid convergence for the global cover function and its higher-order partial derivatives.
基金Project supported by the National Natural Science Foundation of China(Nos.11472119,11032006 and 11121202)the National Key Project of Magneto-Constrained Fusion Energy Development Program(No.2013GB110002)the Scientific and Technological Self-innovation Foundation of Huazhong Agricultural University(No.52902-0900206074)
文摘A wavelet method for solving strongly nonlinear boundary value problems is described, which has been demonstrated early to have a convergence rate of order 4, almost independent of the nonlinear intensity of the equations. By using such a method, we study the bending problem of a circular plate with arbitrary large deflection. As the deflection increases, the bending behavior usually exhibits a so-called plate-to-membrane transition. Capturing such a transition has ever frustrated researchers for decades. However, without introducing any addi- tional treatment, we show in this study that the proposed wavelet solutions can naturally cover the plate-membrane transition region as the plate deflection increases. In addition, the high accuracy and efficiency of the wavelet method in solving strongly nonlinear problems is numerically confirmed, and applicable scopes for the linear, the membrane and the yon Karman plate theories are identified with respect to the large deformation bending of circular plates.
基金This work was supported by the National Natural Science Foundation of China for Distinguished Young Scholars （Grant No. 50225518）the Teaching and Research Award Program for 0utstanding Young Teachers in Higher Education Institution of M0E, PRCthe Aeronautical Science Foundation of China （Grant No. 04H53057）.
文摘Springback is one of important factors influencing the forming quality of numerical control （NC） bending of thin-walled tube. In this paper, a numerical-analytic method for springback angle prediction of the process was put forward. The method is based on springback angle model derived using analytic method and simulation results from three-dimensional （3D） rigid-plastic finite element method （FEM）. The method is validated through comparison with experimental results. The features of the method are as follows： （1） The method is high in efficiency because it combines advantages of rigid-plastic FEM and analytic method. （2） The method is satisfactory in accuracy, since the field variables used in the model is resulting from 3D rigid-plastic FEM solution, and the effects both of axial force and strain neutral axis shift have been included. （3） Research on multi-factor effects can be carried out using the method due to its advantage inheriting from rigid-plastic FEM. The method described here is also of general significance to other bending processes.
文摘The semi? analytic perturbation weighted residuals method was used to solve the nonlinear bending problem of shallow shells, and the fifth order B spline was taken as trial function to seek an efficient method for nonlinear bending problem of shallow shells. The results from the present method are in good agreement with those derived from other methods. The present method is of higher accuracy, lower computing time and wider adaptability. In addition, the design of computer program is simple and it is easy to be programmed.
基金This project is supported by National Natural Science Foundation of China(No.90207003) and Returnee Foundation of Dalian.
文摘Lead zirconate titanium solid-solution (PZT) thin films with variousthickness are synthesized on titanium substrates by repeated hydrothermal treatments. Young modulus,electric-field-induced displacement and the density of the PZT film are measured respectively.Bimorph- type bending actuators are fabricated using these films. The model, which is used toanalyze the driving ability of bimorph-type bending actuators by hydrothermal method, is set up. Itcan be seen that the driving ability of bimorph-type bending actuators can be greatly improved byoptimizing the thickness of PZT thin film and substrate from the theoretical analysis results. Themeasured values are expected to agree with the theoretical values calculated by the above model.
基金supported by National Natural Science Foundation of China (Grant No. 50775044, Grant No. 50975050)Guangdong Provincial and Ministry of Education Industry-University-Research Integration Project of China (Grant No. 2009B090300044)
文摘The typical quadrangular and triangular elements for thin plate bending based on Kirchhoff assumptions are the non- conforming elements with low computational accuracy and limitative application range in fmite element method（FEM）. Some compatible elements can be developed by the means of supplementing correction functions, increasing nodes in element or on the boundaries, expanding nodal degrees of freedom（DOF）, etc, but these elements are inconvenient to apply in practice for the high calculation complexity. In this paper, in order to overcome the defects of thin plate bending finite element, numerical manifold method（NMM） was introduced to solve thin plate bending deformation problem. Rectangular mesh was adopted as mathematical mesh to form f＇mite element cover system, and then 16-cover manifold element was proposed. Numerical manifold formulas were constructed on the basis of minimum potential energy principle, displacement boundary conditions are implemented by penalty function method, and all the element matrixes were derived in details. The 16-cover element has a simple calculation process for employing only the transverse displacement cover DOFs as the basic unknown variables, and has been proved to meet the requirements of completeness and full compatibility. As an application, the presented 16-cover element has been used to analyze bending deformation of square thin plate under different loads and boundary conditions, and the results show that numerical manifold method with compatible element, compared with finite element method, can improve computational accuracy and convergence greatly.
文摘A finite difference method at arbitrary meshes for the bending of plates with variable thickness is presented in this paper. The method is completely general with respect to various boundary conditions, load cases and shapes of plates. This difference scheme is simple and the numerical results agree well with those obtained by other methods.
基金supported by the National Natural Science Foundation of China (Grant No. 41475021)
文摘This paper presents a new method to estimate the height of the atmospheric boundary layer(ABL) by using COSMIC radio occultation bending angle(BA) data. Using the numerical differentiation method combined with the regularization technique, the first derivative of BA profiles is retrieved, and the height at which the first derivative of BA has the global minimum is defined to be the ABL height. To reflect the reliability of estimated ABL heights, the sharpness parameter is introduced, according to the relative minimum of the BA derivative. Then, it is applied to four months of COSMIC BA data(January, April, July, and October in 2008), and the ABL heights estimated are compared with two kinds of ABL heights from COSMIC products and with the heights determined by the finite difference method upon the refractivity data. For sharp ABL tops(large sharpness parameters), there is little difference between the ABL heights determined by different methods, i.e.,the uncertainties are small; whereas, for non-sharp ABL tops(small sharpness parameters), big differences exist in the ABL heights obtained by different methods, which means large uncertainties for different methods. In addition, the new method can detect thin ABLs and provide a reference ABL height in the cases eliminated by other methods. Thus, the application of the numerical differentiation method combined with the regularization technique to COSMIC BA data is an appropriate choice and has further application value.
基金funding support from the National Key Research and Development Program of China(Grant No.2022YFC3102402)as well as from the National Natural Science Foundation of China(Grant No.51879257).
文摘In nature,there are widely distributed bi-modulus materials with different deformation characteristics under compressive and tensile stress states,such as concrete,rock and ceramics.Due to the lack of constitutive model that could reasonably consider the bi-modulus property of materials,and the lack of simple and reliable measurement methods for the tensile elastic parameters of materials,scientists and engineers always neglect the effect of the bi-modulus property of materials in engineering design and numerical simulation.To solve this problem,this study utilizes the uncoupled strain-driven constitutive model proposed by Latorre and Montáns(2020)to systematically study the distributions and magnitudes of stresses and strains of bi-modulus materials in the three-point bending test through the numerical method.Furthermore,a new method to synchronously measure the tensile and compressive elastic moduli of materials through the four-point bending test is proposed.The numerical results show that the bi-modulus property of materials has a significant effect on the stress,strain and displacement in the specimen utilized in the three-point and four-point bending tests.Meanwhile,the results from the numerical tests,in which the elastic constitutive model proposed by Latorre and Montáns(2020)is utilized,also indicate that the newly proposed measurement method has a good reliability.Although the new measurement method proposed in this study can synchronously and effectively measure the tensile and compressive elastic moduli,it cannot measure the tensile and compressive Poisson’s ratios.
基金Project supported by the National Natural Science Foundation of China(No.11925204)the 111 Project(No.B14044)。
文摘A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex domains.In the solution of differential equations,various derivatives of the unknown function are denoted as new functions.Then,the integral relations between these functions are applied in terms of wavelet approximation of multiple integrals.Therefore,the original equation with derivatives of various orders can be converted to a system of algebraic equations with discrete nodal values of the highest-order derivative.During the application of the proposed method,boundary conditions can be automatically included in the integration operations,and relevant matrices can be assured to exhibit perfect sparse patterns.As examples,we consider several second-order mathematics problems defined on regular and irregular domains and the fourth-order bending problems of plates with various shapes.By comparing the solutions obtained by the proposed method with the exact solutions,the new multiresolution method is found to have a convergence rate of fifth order.The solution accuracy of this method with only a few hundreds of nodes can be much higher than that of the finite element method(FEM)with tens of thousands of elements.In addition,because the accuracy order for direct approximation of a function using the proposed basis function is also fifth order,we may conclude that the accuracy of the proposed method is almost independent of the equation order and domain complexity.
文摘Recently, pH-sensitive hydrogels have been utilized in the diverse applications including sensors, switches, and actuators. In order to have continuous stress and deformation ?elds, a new semi-analytical approach is developed to predict the swelling induced?nite bending for a functionally graded(FG) layer composed of a pH-sensitive hydrogel,in which the cross-link density is continuously distributed along the thickness direction under the plane strain condition. Without considering the intermediary virtual reference,the initial state is mapped into the deformed con?guration in a circular shape by utilizing a total deformation gradient tensor stemming from the inhomogeneous swelling of an FG layer in response to the variation of the pH value of the solvent. To enlighten the capability of the presented analytical method, the ?nite element method(FEM) is used to verify the accuracy of the analytical results in some case studies. The perfect agreement con-?rms the accuracy of the presented method. Due to the applicability of FG pH-sensitive hydrogels, some design factors such as the semi-angle, the bending curvature, the aspect ratio, and the distributions of deformation and stress ?elds are studied. Furthermore, the tangential free-stress axes are illustrated in deformed con?guration.
基金Technology Innovation Special Project of Hebei Academy of Agriculture and Forestry Sciences(2022KJCXZX-CGS-7,2023KJCXZX-CGS-11)Key Research and Development Program of Hebei Province(21326308D-1-2)+1 种基金Hebei Agriculture Research System(HBCT2024170406)China Agricultural(Pear)Research System(CARS-28-27).
文摘Aiming at high cost and low efficiency of conventional branch bending method in the modern intensive planting and labor-saving cultivation mode of young pear trees,this paper provides a new branch bending method with wide source of raw materials,cheap price and simple operation,which is also suitable for the management of low-age branches in the process of high grafting and upgrading of traditional big trees.
文摘Using the single crack solution and the regular solution elf plane harmonic function, the problem of Saint-Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equations and its general solution was then obtained. Based on the obtained solution, a method to calculate the bending center and the stress intensity factors of the cracked cylinger whose cross-section is not thin-walled, but of small torsion rigidity is proposed. Some numerical examples are given.
文摘In this paper, based on the step reduction method, a new method, the exact element method for constructing finite element, is presented. Since the new method doesn 't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a triangle noncompatible element with 6 degrees of freedom is derived to solve the bending of nonhomogeneous plate. The convergence of displacements and stress resultants which have satisfactory numerical precision is proved. Numerical examples are given at the end of this paper, which indicate satisfactory results of stress resultants and displacements can be obtained by the present method.
文摘A theorem of solving a system of linear non-homogeneous differential equations through integrating and adding its basic solutions is put forward and proved, the mathematical role and physical nature of the theorem is interpreted briefly. As an example, the theorem is applied to solve the problem of thermo-force bending of a thick plate.
基金the National Natural Science Foundation (19602007)National Outstanding Youth Foundation (19525206)
文摘Owing to the existence of distributed holes, it is difficult tosolve the bending problem of perforated plates by the conventionalfinite element method. A homogenization-based method for this problemis presented in this paper. As an example, the bending analysis of acircular perforated plate with distributed step-wise cylindricalholes is made. The deflection and the fundamental frequen- cyobtained by present method are in good agreement with experimentaldata, this implies that the method is effective.
