三维接触边界元法的一种误差直接估计

Direct error estimate for the boundary element method for a 3-D contact problem

将作者所在研究组提出的二维弹性力学问题边界元解误差的直接估计推广到三维问题,给出了确定与域内解连续的边界位移的一种精确有效的方法。在此基础上提出将接触体接触单元间与域内解连续的边界位移之差的某种度量作为三维弹性接触问题边界元法的一种误差直接估计,并且提出了三维弹性接触问题的一种自适应边界元法计算方案。这种方案为确定没有解析解可作比较的复杂接触问题的边界元解精度提供了可能。文中对于三维弹性接触问题,给出了一个计算误差直接估计及自适应边界元法的算例。

A direct error estimate for the boundary element method (BEM) for 2-D elasticity problems was extended to the 3-D elastic contact problem. An accurate algorithm was developed to determine the boundary displacement consistent with the displacement field within the domain of an elastic body. The difference between the displacement limits for both sides of the contacted bodies was used to develop a local direct error estimate of the BEM solution for the 3-D elastic contact problem. An adaptive boundary element method was then developed to compensate for the error. The scheme can estimate the error for complicated contact problems without the corresponding analytical solution. A numerical example is presented to illustrate the efficiency of the direct error estimation method.