拟协调有限元

THE QUASI-CONFORMING ELEMENT METHODS

拟协调元出现 2 0多年了 ,已被承认和采用。本文从广义方程出发 ,主要陈述弱形式弹性力学基本方程是拟协调元的内在本质 ,揭示最小势能原理可由弱形式派生出来 ,指出用弱形式表达的平衡条件既有微分方程也有边界条件 ,可看成是变分的出发点 ,是更根本和原始的条件。因此变分解也是一种弱形式解 。

The quasi-conforming element method was accepted and adopted when it appeared twenty years ago. This paper explains that the weak formulation of basic equation is the very nature of the quasi-conforming element method on the basis of generalized equation.It also proves that the minimum potential energy theorem can be derived by weak formulation. The weak equilibrium equation contains both differential equation and boundary condition. Those equations are the ultimate and original precondition on elasticity. It emphasizes that the solution of variational principle is that of weak formulation at the same time. It points out that the quasi-conforming element method is an inexorable tendency in developing the classical finite element method.