多分辨率Timoshenko梁单元  

A MUTI-RESOLUTION TIMOSHENKO BEAM ELEMENT FORMULATION

作　　者：夏逸鸣[1,2] 唐敢[2] 江世永[1] 

机构地区：[1]后勤工程学院军事建筑工程系,重庆401331 [2]南京航空航天大学土木工程系,南京210016

出　　处：《固体力学学报》2014年第1期57-62,共6页Chinese Journal of Solid Mechanics

基　　金：岩土力学与地质环境保护重庆市重点实验室(后勤工程学院)开放基金(GKLGGP2013-02);国家自然科学基金项目(51008067;50978135);航空科学基金项目(2010ZA52009)资助

摘　　要：基于Timoshenko梁的假定,通过基本节点形函数的扩展,并在梁区域上进行伸缩和平移,论文构建了基函数系,由此生成相互嵌套、逐级包含的位移空间序列,最后,采用最小势能原理,得到梁的平衡方程,从而构造了多分辨率Timoshenko梁单元.该单元具有如下特性:(1)可通过自由调节单元分辨率的大小来增减单元内的节点数量,从而调整单元的计算精度,其精度与相同节点分布条件下任意多个传统梁单元计算的相一致;(2)经重新排布节点后的单元整体刚度、质量矩阵及等效节点荷载向量可按节点直接获得,不像传统梁单元那样需要重新生成;(3)与传统梁单元一样可以很方便地处理各种边界条件.因此,传统Timoshenko梁单元本质上是一种单分辨率单元,为论文单元的特例.论文首次将多分辨率概念引入到传统的Timoshenko梁单元中,并构建了梁结构节点排布的数学依据—位移空间序列,同时,揭示了共同节点可以采用人工叠加方法形成整体刚阵的缘由—连续的节点扩展形函数.A multi-resolution beam element based on the Timoshenko theory is proposed.The multiresolution analysis(MRA)performance is formulated out of a nesting displacement subspace sequence, whose basis functions are constructed of scaling and shifting on the interval[0,1]of node shape functions extended from the traditional interval[0,1]to the[-1,1].The proposed method have some merits such as:(1)The node extended shape functions make all the sub-elements connect together at the nodes as a whole as the initial proposed element in the resolution level adjusting process,that is,the stiffness,the mass matrices and the equivalent node loading vectors can be obtained automatically around the nodes without being reassembled artificially around the sub-elements.(2)In addition,the proposed beam element can deal with the boundary conditions conveniently just as a conventional Timoshenko beam element does.(3) Since the displacement subspace for the proposed element at the lowest resolution level is equivalent to the displacement field for a traditional Timoshenko beam element,the traditional Timoshenko beam element is a mono-resolution one and a special case of the proposed.In this paper,the MRA concept is fulfilled for the first time for a Timoshenko beam element and the mathematic essence,a nesting displacement subspace sequence,is found for node redistributing of beam structure.

关 键 词：TIMOSHENKO梁 多分辨分析 节点扩展形函数 伸缩和平移 位移空间序列 

分 类 号：O302[理学—力学]