弹性力学中的一种有限元高精度方法

A Finite Element Method with High Accruacy for Elasticity Mechanics

给出了一种有限元高精度方法，即有限元差分法的一般构造原理。用这种方法形成的总刚度阵是带状对称的。收敛性分析指出，该方法的应力场收敛于最小势能解答。数值算例表明，该方法的应力及位移解答精度均显著高于经典有限元法。另外该方法具有规范的列式。

A finite element method with high accuracy is presented in this paper,which is used to form the finite element difference method.The method can provide continuous stress field directly and also obtain a symmetric matrix of stress and displacement field.It converges to the results based on the structure minimum potential energy principle.It not only improves the computational precision for stress and displacement significantly,but also keeps some advantages of classical finite element method.In addition,the method can be easily used to work out a standard computer program and be applied to engineering practice.