h-型自适应有限元法分析中的大坝应力取值标准

Study on determination of dam stress based on h-version adaptive FEM

本文提出了基于自适应有限元法计算的应力取值标准,即给定一个全局误差限作为自适应有限元网格剖分的准则,以此网格计算所得的应力即为有限元应力取值,它适用于工程计算的Z2后验误差估计方法以及h 型自适应策略。作为算例,文中给出了一个典型的重力坝剖面线弹性自适应有限元计算。结果表明,给定一个全局误差限,网格剖分调整若干次后即可满足误差要求,不会出现因角缘应力集中而导致的剖分不收敛情况;对于不同的初始网格,给定一个全局误差限,可以得到应力水平相当的有限元应力取值;存在一个全局误差限,超过该值后,继续降低误差限,坝踵和坝趾的角缘应力趋于稳定值。

The method for determining the dam stress based on h-version adaptive FEM is proposed. An appropriate global error limit is set in advance as the control criterion for the gridding of calculation mesh. The stress is then calculated as the result of FEM. In the process of calculation, the Zienkiewicz-Zhu posteriori error estimate and corresponding adaptive strategy methods are introduced. The linear elastic adaptive FEM calculation result of a typical gravity dam shows that satisfactory result is obtained after several times of adjustment for the gridding of mesh, and the stresses at dam heel and toe asymptotically converge to the stable values if the error limit is adopted as 5%.