一维有限单元法位移模式研究  

ON DISPLACEMENT MODE OF ONE-DIMENSIONAL FINITE ELEMENT METHOD

作　　者：唐义军[1] 罗建辉[1] 

机构地区：[1]湖南大学土木工程学院,湖南长沙410082

出　　处：《工程力学》2013年第3期46-52,57,共8页Engineering Mechanics

摘　　要：通过基于完整位移模式与基于常规位移模式伽辽金方程的比较,导出了伽辽金方程精确成立的条件。论证了位移模式与泡函数的相关性。提出了一次元与泡函数结合的单元方案。利用精确成立的条件,通过量级分析,保留泡函数主要的影响项,避免了求解泡函数的解析表达式。该文的结果达到了h4阶的收敛精度,与收敛精度为h2阶的常规一次元相比,计算量并没有本质上的增加。理论分析和数值计算表明,该文单元是一个比高次元性能优的单元。Based on the comparison of the full displacement mode and conventional displacement mode of Galerkin equations, the exact conditions for the establishment of Galerkin equations is derived. The association of a displacement mode and the bubble function is demonstrated. The combination program of a liner element and a bubble function is proposed. Using the condition of precise establishment, by the analysis order of magnitude, retaining the main impact item of a bubble function, the analytical expression solving for bubble functions is avoided. The derivative accuracy has reached the order of h^4, compared with the liner element that the convergence precision is the order of h^2. The calculation does not be essentially increased. Theoretical analyses and numerical calculations show that this unit is a superior performance than a high-dimensional element.

关 键 词：有限元 位移模式 伽辽金方法 收敛精度 超收敛 

分 类 号：TU318[建筑科学—结构工程]