Timoshenko梁单元超收敛结点应力的EEP法计算  

Computation of Super-Convergent Nodal Stresses of Timoshenko Beam Elements by EEP Method

作　　者：王枚[1] 袁驷[1] 

机构地区：[1]清华大学土木工程系,北京100084

出　　处：《应用数学和力学》2004年第11期1124-1134,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(50278046);教育部博士点基金资助项目(97000315)

摘　　要：　将新近提出的单元能量投影(ElementEnergyProjection,简称EEP)法应用于Timoshenko梁单元的超收敛结点应力计算·　根据单元投影定理具体推导了一般单元的计算公式,并对两个有代表性的单元给出了数值算例·　分析和算例表明,EEP法对于解答是向量函数(即常微分方程组)的问题具有同样优良的表现,不仅能给出与结点位移精度同阶、同量级的超收敛结点应力。The newly proposed element energy projection(EEP) method has been applied to the computation of super-convergent nodal stresses of Timoshenko beam elements.General formulas based on element projection theorem were derived and illustrative numerical examples using two typical elements were given.Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions.The EEP method gives super-convergent nodal stresses,which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude.And in addition,it can overcome the 'shear locking' difficulty for stresses even when the displacements are badly affected.This research paves the way for application of the EEP method to general one-dimensional systems of ordinary differential equations.

关 键 词：Timoshenko梁单元 超收敛应力 单元能量投影法 剪切闭锁 

分 类 号：O242.21[理学—计算数学]