模拟不连续介质的非连续有限元法  

Discontinuous finite element method for simulation of discontinuities

作　　者：夏晓舟[1] 章青[1] 李国华[1] 徐道远[1] 刘光焰[2] 

机构地区：[1]河海大学土木工程学院,江苏南京210098 [2]桂林工学院土木工程系,广西桂林541004

出　　处：《河海大学学报（自然科学版）》2005年第6期682-687,共6页Journal of Hohai University(Natural Sciences)

基　　金：国家自然科学基金资助项目(50379004)

摘　　要：在传统有限元的框架上提出一个能模拟诸如裂纹、节理等非连续性结构的新技术———非连续有限元法,该方法通过反映非连续场和尖端渐进场的附加函数来丰富传统有限元的近似模式,以达到场内非协调的目的;该技术允许整个非连续性结构独立于网格,使得在模拟非连续性结构(裂纹、节理等)的演化发展时无需重剖网格.详细讨论了非连续附加函数的构造,并用弱解形式推导了非连续有限元格式,并给出算例.A new technique for modeling discontinuities, such as cracks and joints in the finite element framework, was presented. A standard displacement-based approximation was enriched near a discontinuity by incorporating the enrichment functions for both discontinuous fields and near tip asymptotic fields. The technique allows the entire discontinuities to be independent of the mesh, therefore remeshing is unnecessary to model the evolvement of discontinuities. Moreover, the construction of the discontinuous enrichment function was discussed in detail, and the discontinuous finite element discrete equation was deduced from the weak form. Numerical experiments were provided to demonstrate the utilitv and robustness of the proposed technique.

关 键 词：非连续有限元 附加自由度 非连续附加函数 

分 类 号：TB124[理学—工程力学]