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自适应有限元在水利工程中的应用
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摘要：
本文将自适应有限元用于水利工程，提出了大坝有限元计算的应力取值标准：给定全局误差限作为自适应有限元网格剖分的准则，在此误差限控制下所得网格计算的应力为有限元应力取值。本文应用ZZ后验误差估计方法以及h-型自适应策略，对一个典型的重力坝剖面进行了线弹性自适应有限元计算。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出现剖分不收敛的情况；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，使得当继续降低误差限时，坝踵和坝趾的角缘应力趋于稳定值。
关键字：
后验误差估计 自适应有限元 容许误差限 重力坝
Abstract: The adoption of stress based on adaptive finite element is discussed, and it is received from a optimized mesh which is divided under control of a given global error limit. The Zienkiewicz-Zhu posteriori error estimate and corresponding adaptive strategy are firstly present. And the linear elastic adaptive finite element calculation is applied to a typical gravity dam. Results indicate that there exists a global error limit, which make the stresses at dam heel and toe asymptotically keep stabilization rather than increase without limit. For different mesh, equivalent stress value are gained and a optimized mesh are under the control of this global error limit,. 5% percent as a global error limit is suggested.
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