比例边界有限元分析侧边界上施加不连续荷载的问题

摘要

比例边界有限元方法是一种半解析的数值计算方法.与边界元一样,比例边界有限元可以将求解问题的维度降低一维.由于比例边界有限元对通过相似中心的侧面边界不进行离散,在实际计算时,作用在侧面边界上的荷载分布需用径向坐标的幂函数进行逼近.然而当指定的侧面边界荷载不连续时,就不可以按照这种形式近似表达.这时就需要在不连续点处划分为较多的多边形单元,从而导致前处理中的网格划分十分复杂.本文对比例边界有限元侧面边界上作用不连续荷载的情况提出了一种简便、有效的处理方法.当侧边界荷载分布改变时无需调整网格划分,使计算简化.本方法拓宽了比例边界有限元的应用范围,算例显示了所提方法的有效性.%The scaled boundary finite element method (SBFEM) is a semi-analytical numerical technique.It's dimensionality number can be reduced by one similar to the boundary element method of the problem.Since the side-faces passing through the scaling center are not discretized in SBFEM,the load acting on the side-faces is approximated as varying as a power function of the radical coordinate in practical application.However,when the assigned distribution of the load is not continuous,some complex treatment,such as introducing superfluous polygon elements near the point of discontinuity,is needed.A simple and effective approach is presented to deal with such situation.Thus,when the load distributed on the side-faces changes,it's unnecessary to adjust meshes,which simplifies the computation and extends the application range of the SBFEM.Numerical examples validate the effectiveness of the proposed approach.