拟协调元广义协调方程的研究

GENERALIZED COMPATIBILITY EQUATIONS OF QUASI-CONFORMING ELEMENT METHODS

从弱形式广义协调方程和拟协调元的弱连续条件等方面分析了拟协调元的理论基础 ,从形式上看弱形式对函数的连续性降低了 ,但对实际的物理问题常常较原始的微分方程更逼近真正解 ,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 。

Brief development process of the finite element method,foundation of quasi conforming element has been analyzed from weak formulation generalized compatibility equations and its weak continuity condition.The quasi conforming element methods are the exact solution of generalized compatibility equations and satisfy the weak continuity requirement naturally.The quasi conforming element methods do not satisfy the stress equilibrium conditions and they can simplify the calculating process of matrix's athwart.The discrete precision can be predicted in prior. It also extends space of original finite element method and is a landmark in computational mechanics.