A multi-resolution rectangular shell element with membrane-bending based on the Kirchhoff-Love theory is proposed. The multi-resolution analysis （MRA） framework is formulated out of a mutually nesting displacement s...A multi-resolution rectangular shell element with membrane-bending based on the Kirchhoff-Love theory is proposed. The multi-resolution analysis （MRA） framework is formulated out of a mutually nesting displacement subspace sequence, whose basis functions are constructed of scaling and shifting on the element domain of basic node shape functions. The basic node shape functions are constructed from shifting to other three quadrants around a specific node of a basic element in one quadrant and joining the corresponding node shape functions of four elements at the specific node. The MRA endows the proposed element with the resolution level （RL） to adjust the element node number, thus modulating structural analysis accuracy accordingly. The node shape functions of Kronecker delta property make the treatment of element boundary condition quite convenient and enable the stiffness matrix and the loading column vectors of the proposed element to be automatically acquired through quadraturing around nodes in RL adjusting. As a result, the traditional 4-node rectangular shell element is a mono-resolution one and also a special case of the proposed element. The accuracy of a structural analysis is actually determined by the RL, not by the mesh. The simplicity and clarity of node shape function formulation with the Kronecker delta property, and the rational MRA enable the proposed element method to be implemented more rationally, easily and efficiently than the conventional mono-resolution rectangular shell element method or other corresponding MRA methods.展开更多
The simulation of three-dimensional （3D） non-isothermal, non-Newtonian fluid filling process is an extremely difficult task and remains a challenging problem, which includes polymer melt flow with free surface coupl...The simulation of three-dimensional （3D） non-isothermal, non-Newtonian fluid filling process is an extremely difficult task and remains a challenging problem, which includes polymer melt flow with free surface coupled with transient heat transfer. This paper presents a full 3D non-isothermal two-phase flow model to predict the complex flow in melt filling process, where the Cross-WLF model is applied to characterize the rheological behav- ior of polymer melt. The governing equations are solved using finite volume method with SIMPLEC algorithm on collocated grids and the melt front is accurately captured by a high resolution level set method. A domain exten- sion technique is adopted to deal with the complex cavities, which greatly reduces the computational burden. To verify the validity of the developed 3D approach, the melts filling processes in two thin rectangular cavities （one of them with a cylindrical insert） are simulated. The predicted melt front interfaces are in good agreement with the experiment and commercial software prediction. For a case with a rather complex cavity, the dynamic filling process in a hemispherical shell is successfully simulated. All of the numerical results show that the developed numerical procedure can provide a reasonable orediction for injection molding process.展开更多
A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a new finite element method is hence presented. The MRA framework is formulated out of a mutually nesting dis...A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a new finite element method is hence presented. The MRA framework is formulated out of a mutually nesting displacement subspace sequence whose basis functions are constructed of scaling and shifting on the element domain of basic full node shape function. The basic full node shape function is constructed by extending the split node shape function of a traditional Mindlin plate element to other three quadrants around the coordinate zero point. As a result, a new rational MRA concept together with the resolution level (RL) is constituted for the element. The traditional 4-node rectangular Mindlin plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The analysis clarity of a plate structure is actually determined by the RL, not by the mesh. Thus, the accuracy of a plate structural analysis is replaced by the clarity, the irrational MRA by the rational and the mesh model by the RL that is the discretized model by the integrated.展开更多
Through densified surface sampling of foraminifera and accurate elevation measurement a-long three transect lines in open-coast tidal salt-marsh of Jianchuan, particular salt-marsh foraminifera assemblages were found....Through densified surface sampling of foraminifera and accurate elevation measurement a-long three transect lines in open-coast tidal salt-marsh of Jianchuan, particular salt-marsh foraminifera assemblages were found. The salt-marsh foraminifera assemblages are distributed in well-defined vertical zonations with respect to elevation and closely parallel marsh floral zonations. At the top of the vertical zonation all foraminifera disappear abruptly which are accurately located at the highest high water datum. This distribution pattern can be used to relocate former sea levels accurately (to an accuracy of within ±5 cm). A modern regional criterion of foraminifera for relocating the former sea levels in high resolution in our country is provided, and deficiencies of studying the vertical zonation only in sheltered coast salt-marsh abroad are filled up.展开更多
A multiresolution hexahedron element is presented with a new multiresolution analysis(MRA)framework.The MRA framework is formulated out of a mutually nesting displacement subspace sequence,whose basis functions are co...A multiresolution hexahedron element is presented with a new multiresolution analysis(MRA)framework.The MRA framework is formulated out of a mutually nesting displacement subspace sequence,whose basis functions are constructed of scaling and shifting on element domain of a basic node shape function.The basic node shape function is constructed from shifting to other seven quadrants around a specific node of a basic isoparametric element in one quadrant and joining the corresponding node shape functions of eight elements at the specific node.The MRA endows the proposed element with the resolution level(RL)to adjust structural analysis accuracy.As a result,the traditional 8-node hexahedron element is a monoresolution one and also a special case of the proposed element.The meshing for the monoresolution finite element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the solid mathematical basis.The simplicity and clarity of shape function construction with the Kronecker delta property and the rational MRA enable the proposed element method to be more rational,easier and efficient in its implementation than the conventional mono-resolution solid element method or other MRA methods.The multiresolution hexahedron element method is more adapted to dealing with the accurate computation of structural problems.展开更多
We study complete cohomology of complexes with finite Gorenstein AC-projective dimension. We show first that the class of complexes admitting a complete level resolution is exactly the class of complexes with finite G...We study complete cohomology of complexes with finite Gorenstein AC-projective dimension. We show first that the class of complexes admitting a complete level resolution is exactly the class of complexes with finite Gorenstein AC-projective dimension. This lets us give some general techniques for computing complete cohomology of complexes with finite Gorenstein AC- projective dimension. As a consequence, the classical relative cohomology for modules of finite Gorenstein AC-projective dimension is extended. Finally, the relationships between projective dimension and Gorenstein AC-projective dimension for complexes are given.展开更多
基金financial support by the Open Foundation of Chongqing Key Laboratory of Geomechanics and Geoenvironment Protection(Logistical Engineering University)(No.GKLGGP 2013-02)
文摘A multi-resolution rectangular shell element with membrane-bending based on the Kirchhoff-Love theory is proposed. The multi-resolution analysis （MRA） framework is formulated out of a mutually nesting displacement subspace sequence, whose basis functions are constructed of scaling and shifting on the element domain of basic node shape functions. The basic node shape functions are constructed from shifting to other three quadrants around a specific node of a basic element in one quadrant and joining the corresponding node shape functions of four elements at the specific node. The MRA endows the proposed element with the resolution level （RL） to adjust the element node number, thus modulating structural analysis accuracy accordingly. The node shape functions of Kronecker delta property make the treatment of element boundary condition quite convenient and enable the stiffness matrix and the loading column vectors of the proposed element to be automatically acquired through quadraturing around nodes in RL adjusting. As a result, the traditional 4-node rectangular shell element is a mono-resolution one and also a special case of the proposed element. The accuracy of a structural analysis is actually determined by the RL, not by the mesh. The simplicity and clarity of node shape function formulation with the Kronecker delta property, and the rational MRA enable the proposed element method to be implemented more rationally, easily and efficiently than the conventional mono-resolution rectangular shell element method or other corresponding MRA methods.
基金Supported by the National Basic Research Program of China(2012CB025903)the National Natural Science Foundation of China(91434201,11402210)
文摘The simulation of three-dimensional （3D） non-isothermal, non-Newtonian fluid filling process is an extremely difficult task and remains a challenging problem, which includes polymer melt flow with free surface coupled with transient heat transfer. This paper presents a full 3D non-isothermal two-phase flow model to predict the complex flow in melt filling process, where the Cross-WLF model is applied to characterize the rheological behav- ior of polymer melt. The governing equations are solved using finite volume method with SIMPLEC algorithm on collocated grids and the melt front is accurately captured by a high resolution level set method. A domain exten- sion technique is adopted to deal with the complex cavities, which greatly reduces the computational burden. To verify the validity of the developed 3D approach, the melts filling processes in two thin rectangular cavities （one of them with a cylindrical insert） are simulated. The predicted melt front interfaces are in good agreement with the experiment and commercial software prediction. For a case with a rather complex cavity, the dynamic filling process in a hemispherical shell is successfully simulated. All of the numerical results show that the developed numerical procedure can provide a reasonable orediction for injection molding process.
文摘A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a new finite element method is hence presented. The MRA framework is formulated out of a mutually nesting displacement subspace sequence whose basis functions are constructed of scaling and shifting on the element domain of basic full node shape function. The basic full node shape function is constructed by extending the split node shape function of a traditional Mindlin plate element to other three quadrants around the coordinate zero point. As a result, a new rational MRA concept together with the resolution level (RL) is constituted for the element. The traditional 4-node rectangular Mindlin plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The analysis clarity of a plate structure is actually determined by the RL, not by the mesh. Thus, the accuracy of a plate structural analysis is replaced by the clarity, the irrational MRA by the rational and the mesh model by the RL that is the discretized model by the integrated.
基金This study was supported by the National Natural Science Foundation of China under contract No. 49671071.
文摘Through densified surface sampling of foraminifera and accurate elevation measurement a-long three transect lines in open-coast tidal salt-marsh of Jianchuan, particular salt-marsh foraminifera assemblages were found. The salt-marsh foraminifera assemblages are distributed in well-defined vertical zonations with respect to elevation and closely parallel marsh floral zonations. At the top of the vertical zonation all foraminifera disappear abruptly which are accurately located at the highest high water datum. This distribution pattern can be used to relocate former sea levels accurately (to an accuracy of within ±5 cm). A modern regional criterion of foraminifera for relocating the former sea levels in high resolution in our country is provided, and deficiencies of studying the vertical zonation only in sheltered coast salt-marsh abroad are filled up.
基金supported by the Foundation of Municipal Key Laboratory of Geomechanics and Geological Environment Protection at Chongqing Institute of Logistics Engineering of PLA(Grant No.GKLGGP 2013-02)the National Natural Science Foundation of China(Grant No.51178222)
文摘A multiresolution hexahedron element is presented with a new multiresolution analysis(MRA)framework.The MRA framework is formulated out of a mutually nesting displacement subspace sequence,whose basis functions are constructed of scaling and shifting on element domain of a basic node shape function.The basic node shape function is constructed from shifting to other seven quadrants around a specific node of a basic isoparametric element in one quadrant and joining the corresponding node shape functions of eight elements at the specific node.The MRA endows the proposed element with the resolution level(RL)to adjust structural analysis accuracy.As a result,the traditional 8-node hexahedron element is a monoresolution one and also a special case of the proposed element.The meshing for the monoresolution finite element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the solid mathematical basis.The simplicity and clarity of shape function construction with the Kronecker delta property and the rational MRA enable the proposed element method to be more rational,easier and efficient in its implementation than the conventional mono-resolution solid element method or other MRA methods.The multiresolution hexahedron element method is more adapted to dealing with the accurate computation of structural problems.
基金This work was partially supported by the National Natural Science Foundation of China （Grant Nos. 11371187, 11501257） and Jiangsu University of Technology of China （KYY14015, KYY14016）.
文摘We study complete cohomology of complexes with finite Gorenstein AC-projective dimension. We show first that the class of complexes admitting a complete level resolution is exactly the class of complexes with finite Gorenstein AC-projective dimension. This lets us give some general techniques for computing complete cohomology of complexes with finite Gorenstein AC- projective dimension. As a consequence, the classical relative cohomology for modules of finite Gorenstein AC-projective dimension is extended. Finally, the relationships between projective dimension and Gorenstein AC-projective dimension for complexes are given.
