Multiresolution Finite Element Method Based on a New Locking-Free Rectangular Mindlin Plate Element

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.

Discovery and features of vertical zonations of tidal salt-marsh foraminifera in Jianchuan, North Jiangsu Province, China

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.

A RECTANGULAR SHELL ELEMENT FORMULATION WITH A NEW MULTI-RESOLUTION ANALYSIS

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.