Researches on the Generation of Three-Dimensional Manifold Element under FEM Mesh Cover

Zhang Guoxing,Li HaiFeng

doi:10.1155/2014/140180

Abstract

Three-dimensional manifold element generation and contact detection algorithm between blocks are the bottleneck for the development of three-dimensional numerical manifold method (NMM). For building mathematics cover, the technology of three-dimensional finite element mesh generation is utilized in the paper. Aiming at the characteristics of complex formation and difficult identification of three-dimensional manifold block, three-dimensional manifold cutting technology is developed. It is important to achieve the coding of mathematical cover (MC) and physical cover (PC) for NMM, which directly determines the correctness of three-dimensional manifold element generation. Based on the character that the coding of three-dimensional manifold is the same as two-dimensional field essentially, coding algorithm of PC system proposed by Dr. Shi is extended to be three-dimensional. A three-dimensional manifold cutting program 3D MC.f90 is developed in this paper, which can generate an arbitrary three-dimensional manifold element under tetrahedral and hexahedral mesh cover. Several examples are made, and results show that three-dimensional manifold block shape and the coding of manifold node and element generated by three-dimensional manifold cutting program all agree well with the definition of three-dimensional manifold element.

Highlights

IntroductionNumerical manifold method (NMM) is proposed by Shi [1,2,3] as an extension of discontinuous deformation analysis (DDA)
Numerical manifold method (NMM) is proposed by Shi [1,2,3] as an extension of discontinuous deformation analysis (DDA). It is a very flexible numerical method which contains and combines finite element method (FEM) and blocky systems considered in DDA in a unified form
Mathematical cover (MC) system is built by 3D finite element mesh generation technology, and 3D block-cut technology is developed into manifold cutting technology for the formation of 3D manifold element, by the improvement of block data structure and block recognition algorithm, encode algorithm of physical cover (PC) system proposed by Shi is extended from 2D to 3D, which achieves the generation of 3D manifold element

Summary

Introduction

Numerical manifold method (NMM) is proposed by Shi [1,2,3] as an extension of discontinuous deformation analysis (DDA). It is a very flexible numerical method which contains and combines finite element method (FEM) and blocky systems considered in DDA in a unified form. This method combines the advantages of DDA and FEM together and is applicable to a much wider range of problems. Cheng and Zhang [14] proposed a 3D NMM based on tetrahedron and hexahedron elements and derived the matrices of corresponding equilibrium equations from the minimum potential energy principle. Mathematical cover (MC) system is built by 3D finite element mesh generation technology, and 3D block-cut technology is developed into manifold cutting technology for the formation of 3D manifold element, by the improvement of block data structure and block recognition algorithm, encode algorithm of physical cover (PC) system proposed by Shi is extended from 2D to 3D, which achieves the generation of 3D manifold element

Fundamentals of the NMM

Manifold Cutting and the Generation of Three-Dimensional Manifold Element

The Formation of Manifold Block

Illustration Examples

Conclusions