区间五次Hermite样条多小波Euler-Bernoulli梁单元  

EULER-BERNOULLI BEAM ELEMENT FORMULATION USING MULTIWAVELETS BASED ON THE QUINTIC HERMITE SPLINE FUNCTION ON THE INTERVAL

作　　者：夏逸鸣[1,2] 唐敢[2,3] 江世永[1] 

机构地区：[1]解放军后勤工程学院军事建筑工程系,重庆400042 [2]南京航空航天大学土木工程系,南京210016 [3]东南大学土木工程学院,南京210096

出　　处：《固体力学学报》2013年第3期305-310,共6页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(51008067;50978135);航空科学基金(2010ZA52009);南京航空航天大学基本科研业务费项目(NS2010018和2010ZA52009);江苏省六大人才高峰项目;住房和城乡建设部科学技术计划项目(2011-K1-68)资助

摘　　要：首先采用区间五次Hermite样条函数,分别构造了三节点梁的边界和内部节点的多小波尺度函数,然后,基于节点尺度函数在区间内伸缩、平移的思想,构建了梁单元相互嵌套、逐级包含的多尺度位移近似空间序列;最后,采用最小势能原理,得到弯曲梁的平衡方程,从而构造了区间五次Hermite样条多小波Euler-Bernoulli梁单元.算例结果表明,该小波单元可通过改变尺度来重新划分网格,从而可自由调节单个小波单元的计算精度,其计算精度与在相同网格划分下采用任意多个传统三节点Hermite梁单元计算梁构件的完全一致.与其它小波单元相比较,该小波单元具有计算简单明了,物理意义明确,易于理解的特点.The quintic Hermite spline function on the interval was adopted to formulate multiwavelet scaling functions for the boundary and the inner nodes of a three-node beam. Based on the concept of shifting and dilating on the interval of the scaling functions, the nested approximate displacement space sequence was constituted for this element. The principle of minimum potential energy was used to establish the beam equilibrium equations as a result,the Euler-Bernoulli beam element was formulated with the mul- tiwavelets based on the quintic Hermite spline function on the interval. Numerical examples show that the multi-resolution property enables the proposed element to be re-meshed by changing its scale, and thus can adjust its calculation accuracy freely. Compared with other wavelet beam elements,this wavelet element is more simple, more solid physically and more easy to understand.

关 键 词：EULER-BERNOULLI梁 五次Hermite样条函数 边界节点 内部节点 尺度函数 

分 类 号：O174.2[理学—数学]