用边界单元法求解弹性结构的动力响应

Solution of the Dynamic Response of Elastic Structures by Using Boundary Element Method

用与时间无关的Ｋｅｌｖｉｎ问题的基本解，作为加权函数的边界单元法求解弹性结构的动力响应．选用一组线性无关的坐标函数来近似域内点的位移，使惯性项的域积分转化为边界积分，把复杂的结构动力响应问题转化为边界上求解二阶线性常微分方程组的问题．利用Ｈｏｕｂｏｌｔ直接积分方法对时域进行离散，由初始条件逐步求出一系列离散时刻弹性结构的动力响应．

The fundamental solution of Kelvin's problem irrelative to time is used as the weighted residual function of boundary element method to solve the dynamic response of elastic structures in this paper. A set of linear irrelative coordinate functions are used to approximate displacement in domain,in order to transform domain integral of inertia term into boundary integral, so that the complicated problem of structural dynamic response can be transformed into simple mathematical problem. The examples in this paper demonstrate the applicability and efficiency of the method.