能量法和加权残值法的联合应用——构造有限元的新途径

COMBINED APPLICATION OF THE ENERGY METHOD AND THE WEIGHTED RESIDUALS METHOD-A NEW WAY TO CONSTRUCT THE FINITE ELEMENTS

本文将能量法和加权残值法结合起来(记为EWR方法),构造非协调位移元,特点是(1)做法简便——用加权残值法来放松单元间位移连续条件。可使能量泛函中不再包含不协调位移引起的能量贡献项,于是单元只有位移一类变量。(2)使用可靠——由于将加权残值法与能量泛函统一考虑.权残方程可赋予明确的物理意义。一方面。适当选择权函数,权残方程的满足就意味着非协调元收敛准则的满足。另一方面,变换权函数,可将现有各种位移型单元纳入EWR方法的统一形式中。

In this paper, a new way of combined application of the energy method and the weighted residuals method(called EWR method) to construct finite elements is proposed, Firstlly, the condition of displacement continuity is relaxed using the method of weighted residuals. As a result, only one variable (displacement) remains in the variational principle as the energy item caused by the incompatible displacement no longer exists. Secondly, since the method of weighted residuals used here is considered relating to the element energy functional, it is easy to give a physical explanation to the weighted residual equation. Thus, if the weighted function is chosen properly, the satisfi-cation of the weighted residual equation will be equivalent to the element converglnce criterion. Moreover, changing the weighttd function, various existing displacement-based elements can be derived from the proposed b. VVR method.