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 rise of artificial microstructures has made it possible to modulate propagation of various kinds of waves,such as light,sound and heat.Among them,the focusing effect is a modulation function of particular interest...The rise of artificial microstructures has made it possible to modulate propagation of various kinds of waves,such as light,sound and heat.Among them,the focusing effect is a modulation function of particular interest.We propose an atomic level triangular structure to realize the phonon focusing effect in single-layer graphene.In the positive incident direction,our phonon wave packet simulation results confirm that multiple features related to the phonon focusing effect can be controlled by adjusting the height of the triangular structure.More interestingly,a completed different focusing pattern and an enhanced energy transmission coefficient are found in the reverse incident direction.The detailed mode conversion physics is discussed based on the Fourier transform analysis on the spatial distribution of the phonon wave packet.Our study provides physical insights to achieving phonon focusing effect by designing atomic level microstructures.展开更多
In this paper, a neural-network-based variable structure control scheme is presented for a class of nonlinear systems with a general low triangular structure. The proposed variable structure controller is proved to be...In this paper, a neural-network-based variable structure control scheme is presented for a class of nonlinear systems with a general low triangular structure. The proposed variable structure controller is proved to be Cl, thus can be applied for backstepping design, which has extended the scope of previous nonlinear systems in the form of strict-feedback and pure-feedback. With the help of neural network approximator, H-∞ performance analysis of stability is given. The effectiveness of proposed control law is verified via simulation.展开更多
Triangular systems play a fundamental role in matrix computations. It has become commonplace that triangular systems are solved to be more accurate even if they are ill-conditioned. In this paper, we define structured...Triangular systems play a fundamental role in matrix computations. It has become commonplace that triangular systems are solved to be more accurate even if they are ill-conditioned. In this paper, we define structured condition number and give structured (forward) perturbation bound. In addition, we derive the representation of optimal structured backward perturbation bound.展开更多
The reaction of molybdenum hexacarbonyl with C6H5CH2OC6H4ONa and Et4NBr in CH3CN at 60 ℃ afforded the di-nuclear Mo（0） compound [Et4N]3[Mo2（CO）6（μ-OC6H4OCH2C6H5）3] 1. 1 crystallizes in monoclinic, space group ...The reaction of molybdenum hexacarbonyl with C6H5CH2OC6H4ONa and Et4NBr in CH3CN at 60 ℃ afforded the di-nuclear Mo（0） compound [Et4N]3[Mo2（CO）6（μ-OC6H4OCH2C6H5）3] 1. 1 crystallizes in monoclinic, space group P21/c with a = 15.359（2）, b = 18.378（3）, c = 24.952（2） A, β = 102.268（4）°, V = 6882.3（1 6） A^3, Mr = 1348.34, Z = 4, Dc = 1.301 g/cm^3, F（000） = 2832 and μ= 0.424 mm^-1 The final R = 0.0606 and wR = 0.1552 for 9396 observed reflections （I 〉 2σ（I））. I contains a [Mo2O3]^3 core in triangular bi-pyralnidal configuration and each Mo atom adopts a distorted octahedral geometry with three carbon atoms from carbonyls and three ,μ-O atoms from C6H5CH2OC6H4O^- bridging ligands. The Mo…Mo distance is 3.30（8） A, indicating no metalmetal bonding. A formation pathway via forming a di-molybdenum（0） di-bridging OR compound [Mo2（μ-OR）2（CO）8]2 has been figured out and the reaction of Mo（CO）6 with alkoxide has also been discussed.展开更多
Practical techniques for smooth geodesic patterning of membrane structures were investigated.For the geodesic search,adjustment of the subplane of the extracted elements series was proposed,and various spline approxim...Practical techniques for smooth geodesic patterning of membrane structures were investigated.For the geodesic search,adjustment of the subplane of the extracted elements series was proposed,and various spline approximation methods were used to flatten the strip for the generation of a smooth pattern.This search approach is very simple,and the geodesic line could be easily attained by the proposed method without the need for a difficult computation method.Smooth cutting patterning can also be generated by spline approximation without the noise in discrete nodal information.Additionally,the geodesic cutting pattern saved about 21%of the required area for the catenary model due to the reduction of the curvature of the planar pattern seam line.展开更多
Notions of quasi-Jacobi bialgebroid and its Dirac-Jacobi structure are introduced.The necessary and sufficient conditions for a maximal isotropic subbundle L to be a DiracJacobi structure are proved.Meanwhile several ...Notions of quasi-Jacobi bialgebroid and its Dirac-Jacobi structure are introduced.The necessary and sufficient conditions for a maximal isotropic subbundle L to be a DiracJacobi structure are proved.Meanwhile several special examples are presented.展开更多
Compared with other migration methods, reverse-time migration is based on a precise wave equation, not an approximation, and performs extrapolation in the depth domain rather than the time domain. It is highly accurat...Compared with other migration methods, reverse-time migration is based on a precise wave equation, not an approximation, and performs extrapolation in the depth domain rather than the time domain. It is highly accurate and not affected by strong subsurface structure complexity and horizontal velocity variations. The difference method based on triangular grids maintains the simplicity of the difference method and the precision of the finite element method. It can be used directly for forward modeling on models with complex top surfaces and migration without statics preprocessing. We apply a finite difference method based on triangular grids for post-stack reverse-time migration for the first time. Tests on model data verify that the combination of the two methods can achieve near-perfect results in application.展开更多
We present a study on the Jahn–Teller(JT)distortions of the TiO_(6),NiO_(6)and MnO_(6)complexes in NaTiO_(2),NaNiO_(2)and NaMnO_(2)triangular compounds with a C_(2)/m structure.The JT vibronic normal modes are found ...We present a study on the Jahn–Teller(JT)distortions of the TiO_(6),NiO_(6)and MnO_(6)complexes in NaTiO_(2),NaNiO_(2)and NaMnO_(2)triangular compounds with a C_(2)/m structure.The JT vibronic normal modes are found to be Q3,Q'4 and Q6 by the group symmetry on the C2/m structure.The magnitude of the normal coordinates(Q3,Q'4,Q6)and the structural parameters of distorted octahedra MO_(6)(M=Ti,Ni,Mn)are obtained and in good agreement with experimental data.The energy level splitting of 3d orbitals and the highest occupied molecular orbital(HOMO)character in the MO_(6)complex are also calculated in accordance with the JT distortions.These results provide a first insight into the groundstate and magnetic properties of distorted triangular compounds AMO_(2).展开更多
By applying the first principles calculations combined with density functional theory (DFT), this study explored the optical properties, electronic structure, and structure stability of triangular borophene decorated ...By applying the first principles calculations combined with density functional theory (DFT), this study explored the optical properties, electronic structure, and structure stability of triangular borophene decorated chemically, B3X (X=F, Cl) in a systematical manner. As revealed from the results of formation energy, phonon dispersion, and molecular dynamics simulation study, all the borophene decorated chemically were superior and able to be fabricated. In the present study, triangular borophene was reported to be converted into Dirac-like materials when functionalized by F and Cl exhibiting narrow direct band gaps as 0.19 eV and 0.17 eV, separately. Significant light absorption was assessed in the visible light and ultraviolet region. According the mentioned findings, these two-dimensional (2D) materials show large and wide promising applications for future nanoelectronics and optoelectronics.展开更多
The intersection is a widely used traffic line structure from the shallow tunnel to the deep roadway,and determining the subsidence hidden danger area of the roof is the key to its stability control.However,applying t...The intersection is a widely used traffic line structure from the shallow tunnel to the deep roadway,and determining the subsidence hidden danger area of the roof is the key to its stability control.However,applying traditional maximum equivalent span beam(MESB)theory to determine deformation range,peak point,and angle influence poses a challenge.Considering the overall structure of the intersection roof,the maximum equivalent triangular plate(METP)theory is proposed,and its geometric parameter calculation formula and deflection calculation formula are obtained.The application of the two theories in 18 models with different intersection angles,roadway types,and surrounding rock lithology is verified by numerical analysis.The results show that:1)The METP structure of the intersection roof established by the simulation results of each model successfully determined the location of the roof’s high displacement zone;2)The area comparison method of the METP theory can be reasonably explained:①The roof subsidence of the intersection decreases with the increase of the intersection angle;②The roof subsidence at the intersection of different roadway types has a rectangular type>arch type>circular type;③The roof subsidence of the intersection with weak surrounding rock is significantly larger than that of the intersection with hard surrounding rock.According to the application results of the two theories,the four advantages of the METP theory are compared and clarified in the basic assumptions,mechanical models,main viewpoints,and mechanism analysis.The large deformation inducement of the intersection roof is then explored.The J 2 peak area of the roof drives the large deformation of the area,the peak point of which is consistent with the center of gravity position of the METP.Furthermore,the change in the range of this peak is consistent with the change law of the METP’s area.Hence,this theory clarifies the large deformation area of the intersection roof,which provides a clear guiding basis for its initial support design,mid-term monitoring,and late local reinforcement.展开更多
A new 3 d transition-metal molybdate-tellurite(NH4)2 Co(TeMo2O9)2 was obtained through a conventional hydrothermal method.This compound was confirmed to crystallize in the monoclinic system of space group P2_(1)/c wit...A new 3 d transition-metal molybdate-tellurite(NH4)2 Co(TeMo2O9)2 was obtained through a conventional hydrothermal method.This compound was confirmed to crystallize in the monoclinic system of space group P2_(1)/c with a=10.5133(5),b=10.6456(5),c=7.6078(5)Å,β=108.879(6)o,V=805.66(8)Å^(3),Z=2,M_(r)=1021.97,Dc=4.213 g/cm^(3),μ=7.685 mm^(–1),F(000)=930,the final R=0.0399 and w R=0.1025 for 1580 observed reflections with I>2σ(I),showing a tunnel structure with spin triangle-lattice composed by CoO_(6) octahedra.Magnetic and heat capacity measurements confirmed a paramagnetic behavior down to 2 K with a negative Weiss temperature of–20 K,suggesting remarkable spin frustration in the system.展开更多
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 the National Natural Science Foundation of China(Grant Nos.12075168 and 11890703)the Science and Technology Commission of Shanghai Municipality(Grant No.21JC1405600)the Fundamental Research Funds for the Central Universities(Grant No.22120230212)。
文摘The rise of artificial microstructures has made it possible to modulate propagation of various kinds of waves,such as light,sound and heat.Among them,the focusing effect is a modulation function of particular interest.We propose an atomic level triangular structure to realize the phonon focusing effect in single-layer graphene.In the positive incident direction,our phonon wave packet simulation results confirm that multiple features related to the phonon focusing effect can be controlled by adjusting the height of the triangular structure.More interestingly,a completed different focusing pattern and an enhanced energy transmission coefficient are found in the reverse incident direction.The detailed mode conversion physics is discussed based on the Fourier transform analysis on the spatial distribution of the phonon wave packet.Our study provides physical insights to achieving phonon focusing effect by designing atomic level microstructures.
基金Shanghai Leading Academic Discipline Project(B504)
文摘In this paper, a neural-network-based variable structure control scheme is presented for a class of nonlinear systems with a general low triangular structure. The proposed variable structure controller is proved to be Cl, thus can be applied for backstepping design, which has extended the scope of previous nonlinear systems in the form of strict-feedback and pure-feedback. With the help of neural network approximator, H-∞ performance analysis of stability is given. The effectiveness of proposed control law is verified via simulation.
文摘Triangular systems play a fundamental role in matrix computations. It has become commonplace that triangular systems are solved to be more accurate even if they are ill-conditioned. In this paper, we define structured condition number and give structured (forward) perturbation bound. In addition, we derive the representation of optimal structured backward perturbation bound.
基金This research was supported by NNSFC (No. 90203017 29733090), NBRP (2004CB7201005) and SKLSC
文摘The reaction of molybdenum hexacarbonyl with C6H5CH2OC6H4ONa and Et4NBr in CH3CN at 60 ℃ afforded the di-nuclear Mo（0） compound [Et4N]3[Mo2（CO）6（μ-OC6H4OCH2C6H5）3] 1. 1 crystallizes in monoclinic, space group P21/c with a = 15.359（2）, b = 18.378（3）, c = 24.952（2） A, β = 102.268（4）°, V = 6882.3（1 6） A^3, Mr = 1348.34, Z = 4, Dc = 1.301 g/cm^3, F（000） = 2832 and μ= 0.424 mm^-1 The final R = 0.0606 and wR = 0.1552 for 9396 observed reflections （I 〉 2σ（I））. I contains a [Mo2O3]^3 core in triangular bi-pyralnidal configuration and each Mo atom adopts a distorted octahedral geometry with three carbon atoms from carbonyls and three ,μ-O atoms from C6H5CH2OC6H4O^- bridging ligands. The Mo…Mo distance is 3.30（8） A, indicating no metalmetal bonding. A formation pathway via forming a di-molybdenum（0） di-bridging OR compound [Mo2（μ-OR）2（CO）8]2 has been figured out and the reaction of Mo（CO）6 with alkoxide has also been discussed.
基金Project(12 High-tech Urban C22)supported by High-tech Urban Development Program,Ministry of Land,Transport and Moritime Affairs of Korea
文摘Practical techniques for smooth geodesic patterning of membrane structures were investigated.For the geodesic search,adjustment of the subplane of the extracted elements series was proposed,and various spline approximation methods were used to flatten the strip for the generation of a smooth pattern.This search approach is very simple,and the geodesic line could be easily attained by the proposed method without the need for a difficult computation method.Smooth cutting patterning can also be generated by spline approximation without the noise in discrete nodal information.Additionally,the geodesic cutting pattern saved about 21%of the required area for the catenary model due to the reduction of the curvature of the planar pattern seam line.
基金Supported by the Scientific Reseaxch Common Program of Beijing Municipal Commission of Education(SQKM201211232017)Supported by the Beijing Excellent Training Grant(2012D005007000005)Supported by the Funding Program for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality(11530500015)
文摘Notions of quasi-Jacobi bialgebroid and its Dirac-Jacobi structure are introduced.The necessary and sufficient conditions for a maximal isotropic subbundle L to be a DiracJacobi structure are proved.Meanwhile several special examples are presented.
基金sponsored by National Natural Science Foundation(40474041)National Symposium of 863(2006AA06Z206)+1 种基金National Symposium of 973(2007CB209605)CNPC Geophysical Key Laboratory of the China University of Petroleum (East China) Research Department
文摘Compared with other migration methods, reverse-time migration is based on a precise wave equation, not an approximation, and performs extrapolation in the depth domain rather than the time domain. It is highly accurate and not affected by strong subsurface structure complexity and horizontal velocity variations. The difference method based on triangular grids maintains the simplicity of the difference method and the precision of the finite element method. It can be used directly for forward modeling on models with complex top surfaces and migration without statics preprocessing. We apply a finite difference method based on triangular grids for post-stack reverse-time migration for the first time. Tests on model data verify that the combination of the two methods can achieve near-perfect results in application.
基金by the National Natural Science Foundation of China under Grant No 10874186the Knowledge Innovation Project of the Chinese Academy of Sciences.
文摘We present a study on the Jahn–Teller(JT)distortions of the TiO_(6),NiO_(6)and MnO_(6)complexes in NaTiO_(2),NaNiO_(2)and NaMnO_(2)triangular compounds with a C_(2)/m structure.The JT vibronic normal modes are found to be Q3,Q'4 and Q6 by the group symmetry on the C2/m structure.The magnitude of the normal coordinates(Q3,Q'4,Q6)and the structural parameters of distorted octahedra MO_(6)(M=Ti,Ni,Mn)are obtained and in good agreement with experimental data.The energy level splitting of 3d orbitals and the highest occupied molecular orbital(HOMO)character in the MO_(6)complex are also calculated in accordance with the JT distortions.These results provide a first insight into the groundstate and magnetic properties of distorted triangular compounds AMO_(2).
基金Project supported by the National Natural Science Foundation of China(Grant No.11947006)the Cultivating Project for Young Scholar at Hubei University of Medicine,China(Grant No.2018QDJZR22).
文摘By applying the first principles calculations combined with density functional theory (DFT), this study explored the optical properties, electronic structure, and structure stability of triangular borophene decorated chemically, B3X (X=F, Cl) in a systematical manner. As revealed from the results of formation energy, phonon dispersion, and molecular dynamics simulation study, all the borophene decorated chemically were superior and able to be fabricated. In the present study, triangular borophene was reported to be converted into Dirac-like materials when functionalized by F and Cl exhibiting narrow direct band gaps as 0.19 eV and 0.17 eV, separately. Significant light absorption was assessed in the visible light and ultraviolet region. According the mentioned findings, these two-dimensional (2D) materials show large and wide promising applications for future nanoelectronics and optoelectronics.
基金Project(52204164)supported by the National Natural Science Foundation of ChinaProject(2021QNRC001)supported by the Young Elite Scientists Sponsorship Program by CAST,China。
文摘The intersection is a widely used traffic line structure from the shallow tunnel to the deep roadway,and determining the subsidence hidden danger area of the roof is the key to its stability control.However,applying traditional maximum equivalent span beam(MESB)theory to determine deformation range,peak point,and angle influence poses a challenge.Considering the overall structure of the intersection roof,the maximum equivalent triangular plate(METP)theory is proposed,and its geometric parameter calculation formula and deflection calculation formula are obtained.The application of the two theories in 18 models with different intersection angles,roadway types,and surrounding rock lithology is verified by numerical analysis.The results show that:1)The METP structure of the intersection roof established by the simulation results of each model successfully determined the location of the roof’s high displacement zone;2)The area comparison method of the METP theory can be reasonably explained:①The roof subsidence of the intersection decreases with the increase of the intersection angle;②The roof subsidence at the intersection of different roadway types has a rectangular type>arch type>circular type;③The roof subsidence of the intersection with weak surrounding rock is significantly larger than that of the intersection with hard surrounding rock.According to the application results of the two theories,the four advantages of the METP theory are compared and clarified in the basic assumptions,mechanical models,main viewpoints,and mechanism analysis.The large deformation inducement of the intersection roof is then explored.The J 2 peak area of the roof drives the large deformation of the area,the peak point of which is consistent with the center of gravity position of the METP.Furthermore,the change in the range of this peak is consistent with the change law of the METP’s area.Hence,this theory clarifies the large deformation area of the intersection roof,which provides a clear guiding basis for its initial support design,mid-term monitoring,and late local reinforcement.
基金financially supported by the National Natural Science Foundation of China(NSFC,Nos.21573235,U1632159 and 21875249)。
文摘A new 3 d transition-metal molybdate-tellurite(NH4)2 Co(TeMo2O9)2 was obtained through a conventional hydrothermal method.This compound was confirmed to crystallize in the monoclinic system of space group P2_(1)/c with a=10.5133(5),b=10.6456(5),c=7.6078(5)Å,β=108.879(6)o,V=805.66(8)Å^(3),Z=2,M_(r)=1021.97,Dc=4.213 g/cm^(3),μ=7.685 mm^(–1),F(000)=930,the final R=0.0399 and w R=0.1025 for 1580 observed reflections with I>2σ(I),showing a tunnel structure with spin triangle-lattice composed by CoO_(6) octahedra.Magnetic and heat capacity measurements confirmed a paramagnetic behavior down to 2 K with a negative Weiss temperature of–20 K,suggesting remarkable spin frustration in the system.
