压力容器开孔结构分析的快速多极边界元研究

Fast multipole BEM for the analysis of pressure vessel opening structures

压力容器开孔结构的应力高度集中。为精确模拟该结构的应力状况,该文提出一种三维高阶快速多极边界元法。在三维弹性力学边界元法的基础上,推导出二阶单元的基本解快速多极展开格式。该算法通过多极展开概念,大大降低了对存储量的要求,并且不损失精度。使用高阶快速多极边界元法分析含多个开孔的压力容器整体结构,所得应力结果与大规模高阶有限元法的结果吻合得很好。研究结果表明,高阶快速多极边界元法易于分析此类大规模问题,并具有很高的数值计算精度,满足工程设计的要求。

High stress concentrations occur around the openings of pressure vessels. The stress fields of such structure around the opening were predicted using a three-dimensional, higher-order fast multipole boundary element method. The three-dimensional boundary element method for elastic materials was extended to develop a fast multipole expansion formulation of the fundamental solutions for quadratic elements. The multipole expansion algorithm greatly reduces the memory requirements without losing accuracy. The entire pressure vessel structure with multiple openings can be analyzed by the multipole boundary element method, with the result agreeing well with those of large higher-order finite element models. The results show that the higher-order, fast multipole boundary element method can be applied to large problems with high numerical accuracy for engineering designs.