一维有限单元法位移模式研究

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。

"ON DISPLACEMENT MODE OF ONE-DIMENSIONAL FINITE ELEMENT METHOD "

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 h4, compared with the liner element that the convergence precision is the order of h2. 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.