有限元差分法的构造及收敛性分析

A Formulation and Convergence Analysis for Finite Element-Difference Method

本文给出了有限元差分法的一般构造原理,用这种方法形成的总刚阵是带状对称的。收敛性分析指出,该方法的应力场收敛于最小势能解答。数值算例表明,该方法的应力及位移解答精度均显著高于经典有限元法。另外该方法具有规范的列式,能够形成通用的计算程序。

<abstract> A formulation theory with a convergence analysis forfinite element-difference method is represented in this paper. Themethod is able to directly provide continuous stress field and alsomake both the stress field and displacement field converge with sameorder to the structure minimum potential energy solution, itsignificantly increases the computational precision for stress anddisplacement, as well as keep some advantage of classical finiteelement method. Moreover, the method can be easily to work outstandard universal Programs and apply to engineering practice.