摘要
基于文［８］发展的混合结构问题稳定方法的框架，针对自由边界条件轴对称薄圆柱壳体问题，给出了其新型混合有限元计算模型。应用线性元，已证明该模型是强制的，其对称正定代数方程组的条件数为Ｏ（ｈ－２）。该方法具有Ｈ１－模Ｏ（ｈ）和Ｌ２－模Ｏ（ｈ２）误差阶。数值结果验证了本文的理论分析，同时表明：按Ｌ２－模本文方法在较粗网格时比经典Ｂａｂｕｓｋａ－Ｂｒｅｚｚｉ方法收敛快，而按Ｈ１－模两者并无差别。
Based on the framework of stabilized methods developed by H. YDUAN for mixed variational problems, a new mixed formulation based on Riesz representing operotors is presented for the thin axisymmetric cylindrical shell with free egde boundary conditions. With the linear interpolation element, we show that this new for mulation is coercive, and that the resulted algebraic linear system is symmetric positive definite with spectral condition number O(h -2 ). Moreover, O(h) and O(h 2) are obtained by employing H 1 norm and L 2 norm respectively. Finally, numerical experiments verify the above theoretical results, and in addition indicate that the methodology devised here converges faster than the classical Babuka Brezzi method in the norm of L 2 when the triangulation is coaser but just the same in the case of H 1 norm.
出处
《计算力学学报》
CAS
CSCD
1999年第1期63-72,共10页
Chinese Journal of Computational Mechanics
关键词
自由边界
薄圆柱壳体
混合有限元
轴对称
free edge
thin axisymmetric cylindrical shell
least squares mixed finite element approximating method
