数值流形方法的网格自动剖分技术及其数值方法

AUTOMATIC MESH GENERATION AND NUMERICAL ALGORITHM OF NUMERICAL MANIFOLD METHOD

数值流形方法包含数学覆盖与物理覆盖双重网格,数学网格用以构造流形单元的插值函数,物理覆盖确定了流形单元的积分区域。数值流形方法的前处理一直是一个难题。讨论了数值流形方法的网格自动生成技术,解决了数值流形方法的前处理问题。无论是连续性材料还是非连续性材料,数学覆盖都保持不变,因此,借助现有的有限元技术生成数值流形方法的数学网格,利用面向对象的编程方法生成了数值流形方法的物理网格。实例应用表明,这种方法是可行的和有效的。

In the numerical manifold method developed by Genhua Shi,two types of mesh systems,mathematical covers and physical covers,are involved. Mathematical covers constitute the whole interpolation domain while physical covers are used to define the integral domain. Pre-process of computational model used for numerical manifold method is usually difficult in practical applications. Although some efforts have been made in past,there is lack of efficient solving algorithms. Therefore,a computer-based technique of automatic mesh generation especially adapted for numerical manifold method is developed in this paper. In the proposed method,mathematical covers are kept to be invariants independent of the constitutive media which may continuous or discontinuous. Mathematical meshes of numerical manifold method can be automatically generated by using the same mesh-generation technique as employed in finite element methods while physical meshes are generated by virtue of objective-oriented programming. An effective algorithm is presented for implementation of the proposed technique. It is shown through an example analysis that both the proposed technique and numerical algorithm are practically feasible and effective for the numerical manifold method.