拟协调元的弱连续条件及其变分解释

On the weak continuity condition of the quasi-conforming element method and its variational principle

简述有限元的发展过程 ,从广义平衡方程、广义协调方程和拟协调元弱连续条件等方面分析了拟协调元的理论基础 ,说明了拟协调元是有限元发展的必然趋势 ,其做法就是广义协调方程的直接解 ,自然满足平衡对弱连续条件的要求。拟协调元不需要应力满足平衡条件 ,简化了矩阵求逆计算 ,容易得出应变的离散精度 ,因此可以解决常规有限元难以适应的领域 。

The development process of the finite element method is introduced briefly,and the theoretic fundamentals of the quasi-conforming element method is analyzed from generalized equilibrium equations,generalized compatibility equations and its weak continuity condition. The calculation based on the quasi-conforming element method is the exact solution of generalized compatibility equations and satisfies the weak continuity requirement naturally,and in the calculation,which does not need satisfy stress equilibrium conditions,the calculating process of the matrix's inverse is simplified. The discrete precision can be predicted. The quasi-conforming element method can be used in the field in which the common finite element method is not feasible,so it is a landmark in computational mechanics.