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

众所周知，有限元分析的精度很大程度上取决于网格细分。此外，为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，一种能够保证有限元分析精度的后验误差估计方法变得非常重要。基于Ohtsubo和Kitamura关于二维弹塑性问题的理论，推导了二维弹塑性问题有限元分析中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对这两个问题都能很好地解决。由于后验误差是逐单元估计的，因此计算时间并不大。后验误差估计的结果有两种用途。一种是为了更新应力解而增加误差。二是基于计算域中后验误差的分布更新网格细分。这两种技术在这项研究中都很有用。已经研究了当所有单元的能量误差范数相同时，后验误差最小。利用这一理论和后验误差分析的结果，可以从最小误差的角度给出最佳有限元模型。本研究开发了一套完整的有限元系统。利用该综合有限元系统可以得到合理的解。

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.