扩展的无网格流形方法

无网格流形方法采用了有限覆盖技术,克服了原有无网格类方法中在处理位移场中不连续时所采用绕射准则、透明准则和通视准则等经验方法的不足,给出了无网格类方法在处理不连续时的数学依据。在无网格流形方法中,当不连续没有贯穿该节点所形成的覆盖时,不连续将覆盖分割成不规则的子覆盖,给计算结果带来一定误差。为弥补该方法的不足,在无网格流形方法中引入强化分析方法。利用裂纹尖端位移场中的奇异项来扩展原有无网格流形方法的基函数,提出了扩展的无网格流形方法。最后给出数值算例,说明该方法的正确性和有效性。

ENRICHED MESHLESS MANIFOLD METHOD

In meshless manifold method,finite cover technology is employed. The mathematical finite cover approximation theory is used to model cracks that lead to displacement discontinuity. The discontinuity is treated mathematically instead of empirically by the existing methods such as:(1) the diffraction method;(2) the transparency method;and (3) the see-through method. One cover of a node is divided into two irregular sub-covers when the meshless manifold method is used to model the discontinuity. However the method sometimes causes numerical errors at the tip of a crack. To improve the precision of the meshless manifold method,the enriched methods are introduced. The enrichment of solution of the meshless manifold method near the tip of a linear- elastic crack is achieved by expanding the basis functions with special functions. The validity and accuracy of the enriched meshless manifold method are illustrated by numerical examples.