Rotation-free shell formulation is a simple and effective method to model a shell with large deformation. Moreover, it can be compatible with the existing theories of finite element method. However, a rotation-free sh...Rotation-free shell formulation is a simple and effective method to model a shell with large deformation. Moreover, it can be compatible with the existing theories of finite element method. However, a rotation-free shell is seldom employed in multibody systems. Using a derivative of rigid body motion, an efficient nonlinear shell model is proposed based on the rotation-free shell element and corotational frame. The bending and membrane strains of the shell have been simplified by isolating deformational displacements from the detailed description of rigid body motion. The consistent stiffness matrix can be obtained easily in this form of shell model. To model the multibody system consisting of the presented shells, joint kinematic constraints including translational and rotational constraints are deduced in the context of geometric nonlinear rotation-free element. A simple node-to-surface contact discretization and penalty method are adopted for contacts between shells. A series of analyses for multibody system dynamics are presented to validate the proposed formulation. Furthermore,the deployment of a large scaled solar array is presented to verify the comprehensive performance of the nonlinear shell model.展开更多
A new 4-node quadrilateral flat shell element is developed for geometrically nonlinear analyses of thin and moderately thick laminated shell structures. The fiat shell element is constructed by combining a quadrilater...A new 4-node quadrilateral flat shell element is developed for geometrically nonlinear analyses of thin and moderately thick laminated shell structures. The fiat shell element is constructed by combining a quadrilateral area co- ordinate method （QAC） based membrane element AGQ6- II, and a Timoshenko beam function （TBF） method based shear deformable plate bending element ARS-Q12. In order to model folded plates and connect with beam elements, the drilling stiffness is added to the element stiffness matrix based on the mixed variational principle. The transverse shear rigidity matrix, based on the first-order shear deformation theory （FSDT）, for the laminated composite plate is evaluated using the transverse equilibrium conditions, while the shear correction factors are not needed. The conventional TBF methods are also modified to efficiently calculate the element stiffness for laminate. The new shell element is extended to large deflection and post-buckling analyses of isotropic and laminated composite shells based on the element independent corotational formulation. Numerical re- sults show that the present shell element has an excellent numerical performance for the test examples, and is applicable to stiffened plates.展开更多
A forward recursive formulation based on corotational frame is proposed for flexible planar beams with large displacement.The traditional recursive formulation has been successfully used for flexible mutibody dynamics...A forward recursive formulation based on corotational frame is proposed for flexible planar beams with large displacement.The traditional recursive formulation has been successfully used for flexible mutibody dynamics to improve the computational efficiency based on floating frame,in which the assumption of small strain and deflection is adopted.The proposed recursive formulation could be used for large displacement problems based on the corotational frame.It means that the recursive scheme is used not only for adjacent bodies but also for adjacent beam elements.The nodal relative rotation coordinates of the planar beam are used to obtain equations with minimal generalized coordinates in present formulation.The proposed formulation is different from absolute nodal coordinate formulation and the geometrically exact beam formulation in which the absolute coordinates are used.The recursive scheme and minimal set of dynamic equations lead to a high computational efficiency in numerical integration.Numerical examples are carried out to demonstrate the accuracy and validity of this formulation.For all of the examples,the results of the present formulation are in good agreement with results obtained using commercial software and the published results.Moreover,it is shown that the present formulation is more efficient than the formulation in ANSYS based on GEBF.展开更多
This paper presents an efficient mesh updating scheme(MUS)for the arbitrary Lagrangian-Eulerian(ALE)formulation of an arbitrarily curved beam based on the corotational method.By discretizing the beam using both Lagran...This paper presents an efficient mesh updating scheme(MUS)for the arbitrary Lagrangian-Eulerian(ALE)formulation of an arbitrarily curved beam based on the corotational method.By discretizing the beam using both Lagrangian elements and ALE elements,the proposed MUS can take full advantage of the simple expression form of the Lagrangian formulation and the accurate moving-load description of the ALE node.The deleting-node and adding-node procedures of the MUS can avoid the negative influence of the variation of the ALE element length on the element accuracy and stiffness matrix singularity.In contrast to the adding-node procedure for Lagrangian elements,interpolation cannot be used directly.Inserting a Lagrangian node in an ALE element is investigated,and the displacement,velocity,and acceleration of the newly added node are evaluated accurately based on the corotational method.Three examples are investigated to verify the validity,computational accuracy and computational efficiency of the proposed MUS by comparing the results of the MUS with those from literature that utilized traditional ALE formulation.These examples show that the proposed MUS has significant advantages in terms of computational time and computer memory.展开更多
The effect of a tilted-dipole three-dimensional corotating interaction region(CIR)on the transport and acceleration of solar energetic particles(SEPs)is studied.In this work,we discussed how the particle intensity lon...The effect of a tilted-dipole three-dimensional corotating interaction region(CIR)on the transport and acceleration of solar energetic particles(SEPs)is studied.In this work,we discussed how the particle intensity longitudinal and radial dependence might be influenced by the background structures.Moreover,we investigate how the spectral index distribution is modulated by the CIR structure We use the focused transport equation(FTE)to describe the propagation and acceleration of SEPs in a tilt-dipole 3D CIR,generated by the high-resolution 3D magnetohydrodynamic(MHD)model.The forward stochastic differential method is used to solve the FTE.The protons with theE~(-4.4)spectrum from 0.5 to 15 MeV are injected uniformly at the heliographic equator of 0.15 AU.Physical quantities are extracted along each interplanetary magnetic field(IMF)line to show the results.In the tilted-dipole CIR background,if injected from the solar equator at the inner boundary,particles in the slow flow are transported to higher latitudes due to the extension of the IMF lines to higher latitudes.The longitudinal patterns of the particles are dominated by the density of IMF lines.The focusing effect modulates the longitudinal variation of the particle intensity and gives rise to new longitudinal intensity peaks.The adiabatic effect largely increases the intensity fluctuation along the longitude.The structure of the solar wind can also lead to the difference of the indexαin the empirical functionI_(max)=kR~(-α),describing the radial variation of peak intensity according to our simulation.Under the influence of the CIR structure,the indexαvaries from 1.9 to 3.4 at 0.3-1.0 AU.The variation of the solar wind speed should be considered when estimating the radial dependence of the SEP peak intensity.The spectra indices rise near the CIR boundaries and drop near the stream interface(SI).The adiabatic effect makes the spatial variability of the spectral index larger.The spectral index could be similar at different radial distances in the CIR structure.展开更多
In this paper, the generalized Prandtl-Reuss (P-R) constitutive equations of elastic-plastic material in the presence of finite deformations through a new approach are studied. It analyzes the generalized P-R equation...In this paper, the generalized Prandtl-Reuss (P-R) constitutive equations of elastic-plastic material in the presence of finite deformations through a new approach are studied. It analyzes the generalized P-R equation based on the material corotational rate and clarifies the puzzling problem of the simple shear stress oscillation mentioned in some literature. The paper proposes a modified relative rotational rate with which to constitute the objective rates of stress in the generalized P-R equation and concludes that the decomposition of total deformation rate into elastic and plastic parts is not necessary in developing the generalized P-R equations. Finally, the stresses of simple shear deformation are worked out.展开更多
Possible bulk compositions of the super-Earth exoplanets CoRoT-7b, Kepler-9d, and Kepler-10b are investigated by applying a commonly used silicate model and a non-standard carbon model. Their internal structures are d...Possible bulk compositions of the super-Earth exoplanets CoRoT-7b, Kepler-9d, and Kepler-10b are investigated by applying a commonly used silicate model and a non-standard carbon model. Their internal structures are deduced using a suitable equation of state for the materials. The degeneracy problems of their compo- sitions can be partly overcome, based on the fact that all three planets are extremely close to their host stars. By analyzing the numerical results, we conclude： 1） the iron core of CoRoT-7b is not more than 27% of its total mass within lc~ mass-radius error bars, so an Earth-like composition is less likely, but its carbon rich model can be com- patible with an Earth-like core/mantle mass fraction; 2） Kepler-10b is more likely to have a Mercury-like composition, with its old age implying that its high iron content may be a result of strong solar wind or giant impact; 3） the transiting-only super-Earth Kepler-9d is also discussed. Combining its possible composition with the formation theory, we can place some constraints on its mass and bulk composition.展开更多
Based on the consistent symrnetrizable equilibrated （CSE） corotational formulation, a linear triangular flat thin shell element with 3 nodes and 18~ of freedom, constructed by combination of the optimal membrane ele...Based on the consistent symrnetrizable equilibrated （CSE） corotational formulation, a linear triangular flat thin shell element with 3 nodes and 18~ of freedom, constructed by combination of the optimal membrane element and discrete Kirchhoff trian- gle （DKT） bending plate element, was extended to the geometric nonlinear analysis of thin shells with large rotation and small strain. Through derivation of the consistent tangent stiffness matrix and internal force vector, the corotational nonlinear finite element equations were established. The nonlinear equations were solved by using the Newton-Raphson iteration algorithm combined with an automatic load controlled technology. Three typical case studies, i.e., the slit annular thin plate, top opened hemispherical shell and cylindrical shell, validated the accuracy of the formulation established in this paper.展开更多
On the basis of the finite element corotational formulation for geometric nonlinear static analysis of thin shells with large rota- tion and small strain established before and from the generalized-a time integration ...On the basis of the finite element corotational formulation for geometric nonlinear static analysis of thin shells with large rota- tion and small strain established before and from the generalized-a time integration algorithm, the energy conserving and de- caying algorithms for corotational formulation nonlinear dynamic response analysis of thin shells are established in this paper. Responses are solved by means of a predictor-corrector procedure. In the case of ignoring the structural damping, the conserv- ing or decaying total energy of structure and the controllable numerical damping for high frequency responses can ensure the numerical stability of the algorithm. The inertial parts are linearly interpolated directly in the fixed global coordinate system by using the element nodal displacement in the global coordinate system for obtaining the constant mass matrix, while the elastic parts adopt the corotational formulation. Hence, the whole formulation obtained in this paper is element independent. Through three typical numerical examples, the performances of the algorithm in this paper were compared with those of the classical Newmak and HHT-a algorithms to indicate that the algorithm in this paper could accurately solve nonlinear dynamic respons- es of thin shells with large displacements and large rotations.展开更多
In this study, we examined variability of sun-related energies, auroral electrojet current, ring current, and magnetopause current during solar cycles 23 and 24. The study revealed a dependence of sun-related energies...In this study, we examined variability of sun-related energies, auroral electrojet current, ring current, and magnetopause current during solar cycles 23 and 24. The study revealed a dependence of sun-related energies to the Sun and Earth currents systems with solar activity from 1996 to 2019. A decrease in the correlation between sun-related energies and sunspot number was observed over solar cycles 23 and 24 (0.88 for the solar cycle 23 and 0.66 for the solar cycle 24), with a drop in the speed of magnetic disturbances in the solar wind. These results could be attributed to the decrease in Sun’s magnetic field toroidal component magnitude induced by a weak in sunspots number and solar flares during the solar cycle 24. A weak in the Earth currents systems (auroral electrojet current, ring current, and magnetopause current) is also observed. During the decrease in the Earth currents, several peaks are observed, indicating a nonlinear dependence in the Earth currents variation (ring current, auroral electrojet current, and magnetopause current) from solar cycle 23 to solar cycle 24. This could be attributed to the Corotating Interaction Regions (CIRs) observed during the declining phase of solar cycle 23 and the deep minimum preceding solar cycle 24.展开更多
基金supported by the National Natural Science Foundation of China (Grants 11772188, 11132007)
文摘Rotation-free shell formulation is a simple and effective method to model a shell with large deformation. Moreover, it can be compatible with the existing theories of finite element method. However, a rotation-free shell is seldom employed in multibody systems. Using a derivative of rigid body motion, an efficient nonlinear shell model is proposed based on the rotation-free shell element and corotational frame. The bending and membrane strains of the shell have been simplified by isolating deformational displacements from the detailed description of rigid body motion. The consistent stiffness matrix can be obtained easily in this form of shell model. To model the multibody system consisting of the presented shells, joint kinematic constraints including translational and rotational constraints are deduced in the context of geometric nonlinear rotation-free element. A simple node-to-surface contact discretization and penalty method are adopted for contacts between shells. A series of analyses for multibody system dynamics are presented to validate the proposed formulation. Furthermore,the deployment of a large scaled solar array is presented to verify the comprehensive performance of the nonlinear shell model.
文摘A new 4-node quadrilateral flat shell element is developed for geometrically nonlinear analyses of thin and moderately thick laminated shell structures. The fiat shell element is constructed by combining a quadrilateral area co- ordinate method （QAC） based membrane element AGQ6- II, and a Timoshenko beam function （TBF） method based shear deformable plate bending element ARS-Q12. In order to model folded plates and connect with beam elements, the drilling stiffness is added to the element stiffness matrix based on the mixed variational principle. The transverse shear rigidity matrix, based on the first-order shear deformation theory （FSDT）, for the laminated composite plate is evaluated using the transverse equilibrium conditions, while the shear correction factors are not needed. The conventional TBF methods are also modified to efficiently calculate the element stiffness for laminate. The new shell element is extended to large deflection and post-buckling analyses of isotropic and laminated composite shells based on the element independent corotational formulation. Numerical re- sults show that the present shell element has an excellent numerical performance for the test examples, and is applicable to stiffened plates.
基金Projects(11772188,11132007,11202126)supported by the National Natural Science Foundation of ChinaProject(11ZR1417000)supported by the Natural Science Foundation of Shanghai,China
文摘A forward recursive formulation based on corotational frame is proposed for flexible planar beams with large displacement.The traditional recursive formulation has been successfully used for flexible mutibody dynamics to improve the computational efficiency based on floating frame,in which the assumption of small strain and deflection is adopted.The proposed recursive formulation could be used for large displacement problems based on the corotational frame.It means that the recursive scheme is used not only for adjacent bodies but also for adjacent beam elements.The nodal relative rotation coordinates of the planar beam are used to obtain equations with minimal generalized coordinates in present formulation.The proposed formulation is different from absolute nodal coordinate formulation and the geometrically exact beam formulation in which the absolute coordinates are used.The recursive scheme and minimal set of dynamic equations lead to a high computational efficiency in numerical integration.Numerical examples are carried out to demonstrate the accuracy and validity of this formulation.For all of the examples,the results of the present formulation are in good agreement with results obtained using commercial software and the published results.Moreover,it is shown that the present formulation is more efficient than the formulation in ANSYS based on GEBF.
基金supported by the Guangdong Basic and Applied Basic Research Foundation(2022A1515110856)the National Natural Science Foundation of China(Project Nos.62188101 and 12132002)。
文摘This paper presents an efficient mesh updating scheme(MUS)for the arbitrary Lagrangian-Eulerian(ALE)formulation of an arbitrarily curved beam based on the corotational method.By discretizing the beam using both Lagrangian elements and ALE elements,the proposed MUS can take full advantage of the simple expression form of the Lagrangian formulation and the accurate moving-load description of the ALE node.The deleting-node and adding-node procedures of the MUS can avoid the negative influence of the variation of the ALE element length on the element accuracy and stiffness matrix singularity.In contrast to the adding-node procedure for Lagrangian elements,interpolation cannot be used directly.Inserting a Lagrangian node in an ALE element is investigated,and the displacement,velocity,and acceleration of the newly added node are evaluated accurately based on the corotational method.Three examples are investigated to verify the validity,computational accuracy and computational efficiency of the proposed MUS by comparing the results of the MUS with those from literature that utilized traditional ALE formulation.These examples show that the proposed MUS has significant advantages in terms of computational time and computer memory.
基金jointly supported by the National Natural Science Foundation of China(42330210 and 41974202)the National Key R&D Program of China(grant Nos.2022YFF0503800 and2021YFA0718600)+1 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences(grant No.XDB 41000000)the Specialized Research Fund for State Key Laboratories。
文摘The effect of a tilted-dipole three-dimensional corotating interaction region(CIR)on the transport and acceleration of solar energetic particles(SEPs)is studied.In this work,we discussed how the particle intensity longitudinal and radial dependence might be influenced by the background structures.Moreover,we investigate how the spectral index distribution is modulated by the CIR structure We use the focused transport equation(FTE)to describe the propagation and acceleration of SEPs in a tilt-dipole 3D CIR,generated by the high-resolution 3D magnetohydrodynamic(MHD)model.The forward stochastic differential method is used to solve the FTE.The protons with theE~(-4.4)spectrum from 0.5 to 15 MeV are injected uniformly at the heliographic equator of 0.15 AU.Physical quantities are extracted along each interplanetary magnetic field(IMF)line to show the results.In the tilted-dipole CIR background,if injected from the solar equator at the inner boundary,particles in the slow flow are transported to higher latitudes due to the extension of the IMF lines to higher latitudes.The longitudinal patterns of the particles are dominated by the density of IMF lines.The focusing effect modulates the longitudinal variation of the particle intensity and gives rise to new longitudinal intensity peaks.The adiabatic effect largely increases the intensity fluctuation along the longitude.The structure of the solar wind can also lead to the difference of the indexαin the empirical functionI_(max)=kR~(-α),describing the radial variation of peak intensity according to our simulation.Under the influence of the CIR structure,the indexαvaries from 1.9 to 3.4 at 0.3-1.0 AU.The variation of the solar wind speed should be considered when estimating the radial dependence of the SEP peak intensity.The spectra indices rise near the CIR boundaries and drop near the stream interface(SI).The adiabatic effect makes the spatial variability of the spectral index larger.The spectral index could be similar at different radial distances in the CIR structure.
文摘In this paper, the generalized Prandtl-Reuss (P-R) constitutive equations of elastic-plastic material in the presence of finite deformations through a new approach are studied. It analyzes the generalized P-R equation based on the material corotational rate and clarifies the puzzling problem of the simple shear stress oscillation mentioned in some literature. The paper proposes a modified relative rotational rate with which to constitute the objective rates of stress in the generalized P-R equation and concludes that the decomposition of total deformation rate into elastic and plastic parts is not necessary in developing the generalized P-R equations. Finally, the stresses of simple shear deformation are worked out.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10833001 and 10925313)Ph.D traininggrant of China (20090091110002)+1 种基金Fundamental Research Funds for the Central Universities(No. 1112020102)support from the Shandong Provincial Natural Science Foundation,China (ZR2010AQ023)
文摘Possible bulk compositions of the super-Earth exoplanets CoRoT-7b, Kepler-9d, and Kepler-10b are investigated by applying a commonly used silicate model and a non-standard carbon model. Their internal structures are deduced using a suitable equation of state for the materials. The degeneracy problems of their compo- sitions can be partly overcome, based on the fact that all three planets are extremely close to their host stars. By analyzing the numerical results, we conclude： 1） the iron core of CoRoT-7b is not more than 27% of its total mass within lc~ mass-radius error bars, so an Earth-like composition is less likely, but its carbon rich model can be com- patible with an Earth-like core/mantle mass fraction; 2） Kepler-10b is more likely to have a Mercury-like composition, with its old age implying that its high iron content may be a result of strong solar wind or giant impact; 3） the transiting-only super-Earth Kepler-9d is also discussed. Combining its possible composition with the formation theory, we can place some constraints on its mass and bulk composition.
基金supported by the National Natural Science Foundation of China (Grant No. 51075208)the Innovation Project for Graduate Students of Jiangsu Province (Grant No. CX07B-162z)the Fund for Innovative and Excellent Doctoral Dissertation of NUAA (Grant No.BCXJ07-01)
文摘Based on the consistent symrnetrizable equilibrated （CSE） corotational formulation, a linear triangular flat thin shell element with 3 nodes and 18~ of freedom, constructed by combination of the optimal membrane element and discrete Kirchhoff trian- gle （DKT） bending plate element, was extended to the geometric nonlinear analysis of thin shells with large rotation and small strain. Through derivation of the consistent tangent stiffness matrix and internal force vector, the corotational nonlinear finite element equations were established. The nonlinear equations were solved by using the Newton-Raphson iteration algorithm combined with an automatic load controlled technology. Three typical case studies, i.e., the slit annular thin plate, top opened hemispherical shell and cylindrical shell, validated the accuracy of the formulation established in this paper.
基金supported by the National Natural Science Foundation of China (Grant No. 51075208)the Innovation Project for Graduate Students of Jiangsu Province (Grant No. CX07B-162z)the Fund for Innovative and Excellent Doctoral Dissertation of NUAA (Grant No. BCXJ07-01)
文摘On the basis of the finite element corotational formulation for geometric nonlinear static analysis of thin shells with large rota- tion and small strain established before and from the generalized-a time integration algorithm, the energy conserving and de- caying algorithms for corotational formulation nonlinear dynamic response analysis of thin shells are established in this paper. Responses are solved by means of a predictor-corrector procedure. In the case of ignoring the structural damping, the conserv- ing or decaying total energy of structure and the controllable numerical damping for high frequency responses can ensure the numerical stability of the algorithm. The inertial parts are linearly interpolated directly in the fixed global coordinate system by using the element nodal displacement in the global coordinate system for obtaining the constant mass matrix, while the elastic parts adopt the corotational formulation. Hence, the whole formulation obtained in this paper is element independent. Through three typical numerical examples, the performances of the algorithm in this paper were compared with those of the classical Newmak and HHT-a algorithms to indicate that the algorithm in this paper could accurately solve nonlinear dynamic respons- es of thin shells with large displacements and large rotations.
文摘In this study, we examined variability of sun-related energies, auroral electrojet current, ring current, and magnetopause current during solar cycles 23 and 24. The study revealed a dependence of sun-related energies to the Sun and Earth currents systems with solar activity from 1996 to 2019. A decrease in the correlation between sun-related energies and sunspot number was observed over solar cycles 23 and 24 (0.88 for the solar cycle 23 and 0.66 for the solar cycle 24), with a drop in the speed of magnetic disturbances in the solar wind. These results could be attributed to the decrease in Sun’s magnetic field toroidal component magnitude induced by a weak in sunspots number and solar flares during the solar cycle 24. A weak in the Earth currents systems (auroral electrojet current, ring current, and magnetopause current) is also observed. During the decrease in the Earth currents, several peaks are observed, indicating a nonlinear dependence in the Earth currents variation (ring current, auroral electrojet current, and magnetopause current) from solar cycle 23 to solar cycle 24. This could be attributed to the Corotating Interaction Regions (CIRs) observed during the declining phase of solar cycle 23 and the deep minimum preceding solar cycle 24.
