Taylor级数多极边界元法及其在轧制工程中的应用

The Taylor series multipole boundary element method(TSM-BEM) and its applications in rolling engineering

通过基本解的多极展开与边界元线性方程组的隐式求解方法(GMRES)相结合,开发出了快速多极边界元法。Taylor级数多极边界元法更新了传统边界元法的求解模式,大大提高了计算效率,扩大了边界元法的求解规模。介绍了Taylor级数多极边界元法的发展历史和现状,给出了Taylor级数多极边界元法的基本思想、基本原理和分类,给出了基本解的Taylor展开方法和边界积分的基本实现步骤。将该方法应用于轧制工程中,通过轧辊弹性变形和HC轧机辊系接触和变形的数值解析,说明了Taylor级数多极边界元法适合于大规模轧制工程问题的解析。

The fast multipole boundary element methods （FM-BEMs） are developed by means of the multipole expansions in conjunction with the implicit solution GMRES （generalized minimum residual method） of linear system arising from BEM. The Taylor series multipole boundary element method （TSM- BEM） updates the solution mode of conventional BEM, enhances the computational efficiency rapidly, and enlarges the scale of solution. The development and research status of TSM-BEM are introduced, the basic ideas and principles are described, and the classify methods are presented. The Taylor series expansions for fundamental solutions and basic procedures of boundary elements integrals are presented for multipole BEM. The numerical method is applied to rolling engineering. The elastic deformation of rollers and the contact and deformation analysis of HC mill roll system are provided. The numerical example demonstrates that the TSM-BEM is suitable for the solution of large scale rolling engineering problems.