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在前期研究部分重叠的矩形覆盖基础上,首次提出基于任意形状覆盖的数值流形方法,其特点是:独特的数学覆盖形式,即任意形状的覆盖+条形的覆盖重叠区域;以独立覆盖为主的分析方式;单位分解函数表述的独特性及严格的插值性。对此方法展开初步研究,给出任意形状覆盖的基本形式,以及基于完全重叠覆盖和自由度之间约束关系的实现方法,算例分析初步验证了该方法的有效性。
Based on the overlapped rectangular covering in previous studies, a numerical manifold method based on arbitrary shape covering is proposed for the first time. It is characterized by a unique mathematical covering form, that is, an overlapping overlapping area covered by any shape and a bar; Lord’s analysis; unit decomposition function expression of the uniqueness and strict interpolation. A preliminary study on this method is given. The basic form of arbitrary shape coverage and the realization method based on complete overlapping coverage and degree of freedom are given. The example analysis proves the validity of this method.