The aim of the present study is to develop an efficient weak form quadrature element for free vibration analysis of arbitrarily shaped membranes.The arbitrarily shaped membrane is firstly mapped into a regular domain ...The aim of the present study is to develop an efficient weak form quadrature element for free vibration analysis of arbitrarily shaped membranes.The arbitrarily shaped membrane is firstly mapped into a regular domain using blending functions,and the displacement in the element is assumed as the trigonometric functions.Explicit formulations are worked out for nodes of any type and a varying number of nodes.For verifications,results are compared with exact solutions and data obtained by other numerical methods.It is demonstrated that highly accurate frequencies can be obtained with a small number of nodes by present method.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
基金supported by the National Natural Science Foundation of China(Nos.52005256,12072154)the Natural Science Foundation of Jiangsu Province(No.BK20190394)+1 种基金the Jiangsu Post-Doctoral Research Funding Program(No.2020Z437)the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘The aim of the present study is to develop an efficient weak form quadrature element for free vibration analysis of arbitrarily shaped membranes.The arbitrarily shaped membrane is firstly mapped into a regular domain using blending functions,and the displacement in the element is assumed as the trigonometric functions.Explicit formulations are worked out for nodes of any type and a varying number of nodes.For verifications,results are compared with exact solutions and data obtained by other numerical methods.It is demonstrated that highly accurate frequencies can be obtained with a small number of nodes by present method.
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.
