基于边界元法的非均质薄板弯曲问题的解

BEM-based solution of heterogeneous thin plate bending problems

本文用边界元法研究非均质无限域弹性薄板弯曲问题。在数值实施过程中,对于夹杂和基体分别形成边界积分方程。通过离散边界积分方程,得到相应的方程组,然后结合界面条件,最终获得问题的求解方程组。在界面的相关量求得之后,可以根据需要来求解基体和夹杂中的有关位置的弯矩。数值结果与已有的解做了对比。

The boundary element method （BEM） is used to investigate heterogeneous infinite thin plate bending problems subjected to remote loading. In numerical implementation, the boundary integral equations for the inclusions and the matrix are respectively formed. Then the corresponding systems of linear algebraic equations are obtained using the well-known discretized technique. Based on the matrix-inclusion interface connecting conditions, the resulting system of linear algebraic equations which can be solved to obtain all the unknown interface quantities is presented. If needed, the bending moments at the given points within the inclusions and the matrix can easily be calculated. The obtained results are compared with the available solutions.