部分重叠覆盖流形法的覆盖加密方法

摘要

部分重叠覆盖的流形法是一种新型的数值流形方法,它以独立覆盖的分析为主,便于在各区域采用合适的覆盖函数以适应物理场的局部特征.以往的研究表明,在实际物理场分布较复杂的区域采用较小的覆盖可以更好地逼近真实解,这就涉及到与周边较大覆盖的连接问题.针对部分重叠的矩形覆盖提出覆盖加密方法,可以很容易地将大覆盖加密成为较小的覆盖,并使其与周边的大覆盖保持协调过渡,相对于以往采用有限元网格的流形法而言在大小网格过渡上要方便得多.应用重力坝应力分析和圆孔应力集中2个算例验证了该方法的有效性.%Numerical Manifold Method (NMM) with partially overlapping covers is a new type of NMM which uses independent covers to approach true physical field.Previous researches indicate that using small covers is a better approximation way than using big covers in the area with complex field distributions.Then we encounter the problem of connecting these small covers to their ambient big covers.In this paper we present a method of cover refinement for NMM with partially overlapping rectangular covers.It is easy to divide a big cover into some small covers and to connect these small covers to their ambient big covers in a compatible way,which is more convenient than NMM using FEM meshes in terms of transition between big meshes and small meshes.Two given examples,stress analysis of a gravity dam and computation of stress concentration factor of a circular hole,illustrate the validity of the method.