Based on the linear theories of thin cylindrical shells and viscoelastic materials, a governing equation describing vibration of a sandwich circular cylindrical shell with a viscoelastic core under harmonic excitation...Based on the linear theories of thin cylindrical shells and viscoelastic materials, a governing equation describing vibration of a sandwich circular cylindrical shell with a viscoelastic core under harmonic excitation is derived. The equation can be written as a matrix differential equation of the first order, and is obtained by considering the energy dissipation due to the shear deformation of the viscoelastic core layer and the interaction between all layers. A new matrix method for solving the governing equation is then presented With an extended homogeneous capacity precision integration approach. Having obtained these, vibration characteristics and damping effect of the sandwich cylindrical shell can be studied. The method differs from a recently published work as the state vector in the governing equation is composed of displacements and internal forces of the sandwich shell rather than displacements and their derivatives. So the present method can be applied to solve dynamic problems of the kind of sandwich shells with various boundary conditions and partially constrained layer damping. Numerical examples show that the proposed approach is effective and reliable compared with the existing methods.展开更多
Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite struc...Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite structures.The two smaller components of the mid-surface normal vector of shell at a node are defined as nodal rotational variables in the co-rotational local coordinate system.In the global coordinate system,two smaller components of one vector,together with the smallest or second smallest component of another vector,of an orthogonal triad at a node on a non-smooth intersection of plates and/or shells are defined as rotational variables,whereas the two smaller components of the mid-surface normal vector at a node on the smooth part of the plate or shell(away from non-smooth intersections)are defined as rotational variables.All these vectorial rotational variables can be updated in an additive manner during an incremental solution procedure,and thus improve the computational efficiency in the nonlinear solution of these composite shell structures.Due to the commutativity of all nodal variables in calculating of the second derivatives of the local nodal variables with respect to global nodal variables,and the second derivatives of the strain energy functional with respect to local nodal variables,symmetric tangent stiffness matrices in local and global coordinate systems are obtained.To overcome shear locking,the assumed transverse shear strains obtained from the line-integration approach are employed.The reliability and computational accuracy of the present 3-node triangular shell finite element are verified through modeling two patch tests,several smooth and non-smooth laminated composite shells undergoing large displacements and large rotations.展开更多
The α-cluster structures for 12^C and 16^O are investigated in the framework of the covariant density functional theory, where the pairing correlation is treated with a particle number conserving shell-model-like app...The α-cluster structures for 12^C and 16^O are investigated in the framework of the covariant density functional theory, where the pairing correlation is treated with a particle number conserving shell-model-like approach. The ground states of 12^C and 160 have been calculated and the density distributions demonstrate an equilateral triangle 3α clustering for 12^C and a regular tetrahedron 4α clustering for 16^O The existence of linear nα chain structure of both 12^C and 16^O is revealed at high quadrupole deformation.展开更多
The plate-shell structures with stiffeners are widely used in a broad range of engineering structures. This study presents the layout optimization of stiffeners. The minimum weight of stiffeners is taken as the object...The plate-shell structures with stiffeners are widely used in a broad range of engineering structures. This study presents the layout optimization of stiffeners. The minimum weight of stiffeners is taken as the objective function with the global stiffness constraint. In the layout optimization, the stiffeners should be placed at the locations with high strain energy/or stress. Conversely, elements of stiffeners with a small strain energy/or stress are considered to be used inefficiently and can be removed. Thus, to identify the element efficiency so that most inefficiently used elements of stiffeners can be removed, the element sensitivity of the strain energy of stiffeners is introduced, and a search criterion for locations of stiffeners is presented. The layout optimization approach is given for determining which elements of the stiffeners need to be kept or removed. In each iterative design, a high efficiency reanalysis approach is used to reduce the computational effort. The present approach is implemented for the layout optimization of stiffeners for a bunker loaded by the hydrostatic pressure. The numerical results show that the present approach is effective for dealing with layout optimization of stiffeners for plate-shell structures.展开更多
On the basis of the thin-shell theory and on the use of the transfer matrix approach, this paper presents the vibrational response and buckling analysis of three-lobed cross-section cylindrical shells, with circumfere...On the basis of the thin-shell theory and on the use of the transfer matrix approach, this paper presents the vibrational response and buckling analysis of three-lobed cross-section cylindrical shells, with circumferentially varying thickness, subjected to uniform axial membrane loads. A Fourier approach is used to separate the variables, and the governing equations of the shell are formulated in terms of eight first-order differential equations in the circumferential coordinate, and by using the transfer matrix of the shell, these equations are written in a matrix differential equation. The transfer matrix is derived from the non-linear differential equations of the cylindrical shells with variable thickness by introducing the trigonometric series in the longitudinal direction and applying a numerical integration in the circumferential direction. The natural frequencies and critical loads beside the mode shapes are calculated numerically in terms of the transfer matrix elements for the symmetrical and antisymmetrical vibration modes. The influences of the thickness variation of cross- section and radius展开更多
Ground state properties for Mg isotopes, including binding energies, one- and two-neutron separation energies, pairing energies, nuclear matter radii and quadrupole deformation parameters, are obtained from the self- ...Ground state properties for Mg isotopes, including binding energies, one- and two-neutron separation energies, pairing energies, nuclear matter radii and quadrupole deformation parameters, are obtained from the self- consistent relativistic mean field （RMF） model with the pairing correlations treated by a shell-mode-like approach （SLAP）, in which the particle-number is conserved and the blocking effects are treated exactly. The experimental data, including the binding energies and the one- and two-neutron separation energies, which are sensitive to the treatment of pairing correlations and block effects, are well reproduced by the RMF＋SLAP calculations.展开更多
基金supported by the National Natural Science Foundation of China (No. 10662003)the Doctoral Fund of Ministry of Education of China (No. 20040787013)
文摘Based on the linear theories of thin cylindrical shells and viscoelastic materials, a governing equation describing vibration of a sandwich circular cylindrical shell with a viscoelastic core under harmonic excitation is derived. The equation can be written as a matrix differential equation of the first order, and is obtained by considering the energy dissipation due to the shear deformation of the viscoelastic core layer and the interaction between all layers. A new matrix method for solving the governing equation is then presented With an extended homogeneous capacity precision integration approach. Having obtained these, vibration characteristics and damping effect of the sandwich cylindrical shell can be studied. The method differs from a recently published work as the state vector in the governing equation is composed of displacements and internal forces of the sandwich shell rather than displacements and their derivatives. So the present method can be applied to solve dynamic problems of the kind of sandwich shells with various boundary conditions and partially constrained layer damping. Numerical examples show that the proposed approach is effective and reliable compared with the existing methods.
基金This work was supported by National Natural Science Foundation of China under Grant 11672266.
文摘Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite structures.The two smaller components of the mid-surface normal vector of shell at a node are defined as nodal rotational variables in the co-rotational local coordinate system.In the global coordinate system,two smaller components of one vector,together with the smallest or second smallest component of another vector,of an orthogonal triad at a node on a non-smooth intersection of plates and/or shells are defined as rotational variables,whereas the two smaller components of the mid-surface normal vector at a node on the smooth part of the plate or shell(away from non-smooth intersections)are defined as rotational variables.All these vectorial rotational variables can be updated in an additive manner during an incremental solution procedure,and thus improve the computational efficiency in the nonlinear solution of these composite shell structures.Due to the commutativity of all nodal variables in calculating of the second derivatives of the local nodal variables with respect to global nodal variables,and the second derivatives of the strain energy functional with respect to local nodal variables,symmetric tangent stiffness matrices in local and global coordinate systems are obtained.To overcome shear locking,the assumed transverse shear strains obtained from the line-integration approach are employed.The reliability and computational accuracy of the present 3-node triangular shell finite element are verified through modeling two patch tests,several smooth and non-smooth laminated composite shells undergoing large displacements and large rotations.
基金Supported by Major State Basic Research Development (973) Program (2007CB815000)NSFC (11175002,11105005)Research Fund for the Doctoral Program of Higher Education (20110001110087)
文摘The α-cluster structures for 12^C and 16^O are investigated in the framework of the covariant density functional theory, where the pairing correlation is treated with a particle number conserving shell-model-like approach. The ground states of 12^C and 160 have been calculated and the density distributions demonstrate an equilateral triangle 3α clustering for 12^C and a regular tetrahedron 4α clustering for 16^O The existence of linear nα chain structure of both 12^C and 16^O is revealed at high quadrupole deformation.
基金Project supported by the Foundation of University's Doctorial Subjects of China (No.20010183013)985-Automotive Engineering of Jilin University.
文摘The plate-shell structures with stiffeners are widely used in a broad range of engineering structures. This study presents the layout optimization of stiffeners. The minimum weight of stiffeners is taken as the objective function with the global stiffness constraint. In the layout optimization, the stiffeners should be placed at the locations with high strain energy/or stress. Conversely, elements of stiffeners with a small strain energy/or stress are considered to be used inefficiently and can be removed. Thus, to identify the element efficiency so that most inefficiently used elements of stiffeners can be removed, the element sensitivity of the strain energy of stiffeners is introduced, and a search criterion for locations of stiffeners is presented. The layout optimization approach is given for determining which elements of the stiffeners need to be kept or removed. In each iterative design, a high efficiency reanalysis approach is used to reduce the computational effort. The present approach is implemented for the layout optimization of stiffeners for a bunker loaded by the hydrostatic pressure. The numerical results show that the present approach is effective for dealing with layout optimization of stiffeners for plate-shell structures.
文摘On the basis of the thin-shell theory and on the use of the transfer matrix approach, this paper presents the vibrational response and buckling analysis of three-lobed cross-section cylindrical shells, with circumferentially varying thickness, subjected to uniform axial membrane loads. A Fourier approach is used to separate the variables, and the governing equations of the shell are formulated in terms of eight first-order differential equations in the circumferential coordinate, and by using the transfer matrix of the shell, these equations are written in a matrix differential equation. The transfer matrix is derived from the non-linear differential equations of the cylindrical shells with variable thickness by introducing the trigonometric series in the longitudinal direction and applying a numerical integration in the circumferential direction. The natural frequencies and critical loads beside the mode shapes are calculated numerically in terms of the transfer matrix elements for the symmetrical and antisymmetrical vibration modes. The influences of the thickness variation of cross- section and radius
基金Supported by NSFC(11465001,11275098,11275248,11505058,11165001)Natural Science Foundation of Inner Mongolia of China(2016BS0102)
文摘Ground state properties for Mg isotopes, including binding energies, one- and two-neutron separation energies, pairing energies, nuclear matter radii and quadrupole deformation parameters, are obtained from the self- consistent relativistic mean field （RMF） model with the pairing correlations treated by a shell-mode-like approach （SLAP）, in which the particle-number is conserved and the blocking effects are treated exactly. The experimental data, including the binding energies and the one- and two-neutron separation energies, which are sensitive to the treatment of pairing correlations and block effects, are well reproduced by the RMF＋SLAP calculations.
