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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。
The pressure in the open structure of pressure vessels is highly concentrated. In order to accurately simulate the stress state of the structure, a three-dimensional high-order fast multipole BEM is proposed. Based on the three-dimensional elasto-mechanic boundary element method, the basic multi-polar unfolded scheme for the second order element is deduced. The algorithm expands the concept of multi-polar, greatly reducing the storage requirements, and without loss of accuracy. The high-order fast multipole boundary element method is used to analyze the overall structure of a pressure vessel with multiple openings. The obtained stress results are in good agreement with those of the large-scale high-order finite element method. The results show that the high-order fast multipole BEM is easy to analyze such large-scale problems and has high numerical accuracy to meet the requirements of engineering design.