A posteriori error estimation of elasto-plastic analysis for ship structure

众所周知，有限元分析的精度在很大程度上取决于网格的划分。此外，对于一个工程问题，建立有限元模型需要花费许多天的时间。在这种背景下，一种能保证有限元分析精度的后验误差估计方法就显得尤为重要，本文在Ohtsubo和Kitamura关于一维弹性问题的理论基础上，推导了二维弹塑性问题有限元分析的后验误差估计公式。该公式首先应用于非线性弹性问题。所提出的误差估计方法适用于这两个问题。由于后验误差是逐个元素估计的，所以计算时间一点也不长。一种是为了更新应力解而加入误差。另一种方法是根据后验误差在计算域中的分布情况更新网格剖分。这两种方法在本研究中都是有用的，已经研究了当所有单元的误差能量范数都相同时，后验误差最小。利用这一理论和后验误差分析的结果，可以从误差最小的角度给出最佳的有限元模型。本研究开发了一个完整的有限元分析系统。利用这种集成的有限元系统可以给出合理的解。

It is well known that the accuracy of finite element analysis is deeply dependent on the mesh sub-division. Moreover, it takes many days to make the finite element model for an engineering problem. A posteriori error estimation method which can gives us the accuracy of the finite element analysis becomes very important because of this background.The formulation of a posteriori error estimation in finite element analysis for twodimensional elasto-plastic problems is derived based on the theory discussed by Ohtsubo and Kitamura for dimensional elastic problems. This formulation was applied into non-linear elastic problems first. The proposed error estimation method works well for both problems. Since a posteriori error is estimated element by element, the computational time is not large at all.The results of the a posteriori error estimation is used in two ways. One is that error is added in order to update stress solution. The other is that mesh sub-division is renewed based on the distribution of a posteriori error in the computational domain. Both techniques are useful in this research.It is already investigated that a posteriori error becomes minimum when all energy norm of error in all elements are the same. With this theory and the results of a posteriori error analysis can give the best finite element model from the view of least error. An integrated finite element system is developed in this research. The use of this integrated finite element system can give us the rational solution.