摘要
根据有限元解的超收敛特性提出了一种基于应力超收敛恢复技术的广义特征值问题后验误差估计。通过对单元内的应力超收敛点以及相邻单元的应力超收敛点进行插值或外推处理,得到单元内其它点处更高精度的应力解。通过高精度的应力值可以得到结构处理后改进的势能。将改进的势能代入瑞利商,最终得到比原始有限元解更高精度的特征解。将后处理特征解作为“准精确解”代替误差估计因子中未知的精确解,实现后验误差估计过程。数值计算结果表明,所提出的后验误差估计是渐进精确的,因此可作为结构广义特征值问题自适应有限元方法的误差估计因子。
A posteriori error estimation based on the stress super-convergence recovery technique is proposed. Utilizing the super-convergence characteristics of the finite element solutions at some special points (super-convergence points), the stress solutions at other points in the element can be obtained by interpolating or extrapolating the stress solutions at the super-convergence points in the element and its neighboring elements. The post-processed stress solutions are more precise than the original finite element solutions. The more accurate stress solutions can give an improved strain energy. In the end, the more accurate eigenfrequencies can be obtained through replacing the original strain energy in the Rayleigh quotient by the improved strain energy. The posteriori error estimator is finally achieved by substituting the higher quality eigenfreqencies for the unknown exact solution in the error expression. Numerical examples show that the posterior error estimation proposed in this paper is asymptotically exact. Thus, it can be used as an error estimator for the generalized eigenvalue problems in adaptive finite element analysis.
出处
《工程力学》
EI
CSCD
北大核心
2004年第3期111-117,共7页
Engineering Mechanics
基金
国家自然科学基金资助项目(19872029)
关键词
有限元
后验误差估计
应力超收敛性
广义特征值问题
finite element
error estimation
stress super-convergence
generalized eigenvalue problems
