拟协调有限元弱形式的辛算法  

The symplectic algorithm for the weak formulation equations of quasi-conforming element

作　　者：丁克伟[1] Ding Kewei(School of Civil Engineering, Anhui Jianzhu Universit)

机构地区：[1]安徽建筑大学土木工程学院,合肥230601

出　　处：《应用力学学报》2017年第1期174-179,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11472005);安徽省科技计划项目(1501041133;1408085QE96)

摘　　要：基于弱形式的力学方程,阐述了弱形式广义方程是拟协调有限元的内在本质,用弱形式给出的微分方程和边界条件根本上是降低了函数光滑性,不过对工程问题而言,给出的有限元解比原始方程更接近真实解,其数值解就是广义协调方程的直接解,同时满足平衡和几何方程弱连续条件。进而就导出的对偶体系弱形式哈密尔顿方程,采用辛相似变换,利用平方约化法求解哈密尔顿矩阵特征值问题,使其哈密尔顿结构得到了保证。辛算法具有较强的有效性,可以解决常规有限元难以适应的领域,对计算力学发展有着重要的作用。The paper explains that the generalized weak formulation is of the inherent nature for the quasi-conforming element based on weak formulation elasticity equations. It points out that the existing equilibrium differential equations with boundary conditions also can be seen as a starting point for variational formulation, the weak formulation is of more fundamental and original. Formally, through the weak form, the continuity of the function is reduced, as generalized direct solutions, more accurate solutions to the differential equations are obtained. The equilibrium equations and geometric equations, then their weak forms, are also satisfied. Weak formulation of the dual system of Hamilton equations can be solved by means of symplectic similarity transformation which reflects the structure of the Hamiltonian matrices. This algorithm has preferable validity, and therefore the quasi-conforming element can be used in the field in which the common finite element is not feasible, so it is a landmark in computational mechanics.

关 键 词：拟协调元 弱形式 哈密尔顿元 辛算法 广义方程 

分 类 号：O151.21[理学—数学]