...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Applied Mathematical Modelling >Clifford algebra valued boundary integral equations for three-dimensional elasticity
【24h】

Clifford algebra valued boundary integral equations for three-dimensional elasticity

机译：Clifford代数值的三维弹性边界积分方程

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Applications of Clifford analysis to three-dimensional elasticity are addressed in the present paper. The governing equation for the displacement field is formulated in terms of the Dirac operator and Clifford algebra valued functions so that a general solution is obtained analytically in terms of one monogenic function and one multiple-component spatial harmonic function together with its derivative. In order to solve numerically the three-dimensional problems of elasticity for an arbitrary domain with complicated boundary conditions, Clifford algebra valued boundary integral equations (BIEs) for multiple-component spatial harmonic functions at an observation point, either inside the domain, on the boundary, or outside the domain, are constructed. Both smooth and non-smooth boundaries are considered in the construction. Moreover, the singularities of the integrals are evaluated exactly so that in the end singularity-free BIEs for the observation point on the boundary taking values on Clifford numbers can be obtained. A Clifford algebra valued boundary element method (BEM) based on the singularity-free BIEs is then developed for solving three-dimensional problems of elasticity. The accuracy of the Clifford algebra valued BEM is demonstrated numerically.
机译：本文讨论了Clifford分析在三维弹性中的应用。根据Dirac算子和Clifford代数值函数来公式化位移场的控制方程，这样就可以解析地根据一个单基因函数和一个多分量空间谐波函数及其导数来获得一般解。为了用数值方法解决具有复杂边界条件的任意域的三维弹性问题，在域内或边界上的观测点上，多分量空间谐波函数的Clifford代数值边界积分方程（BIE） ，或在域外。构造中同时考虑了平滑边界和非平滑边界。此外，对积分的奇异性进行了精确评估，以便最终获得边界上观测点的无奇异BIE，并采用Clifford数的值。然后，开发了一种基于无奇异BIE的Clifford代数值边界元方法（BEM），以解决三维弹性问题。用数值方法证明了Clifford代数值BEM的准确性。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号