Adaptive remeshing of tetrahedral elements by partial redistribution of nodes in sub-domains and its application to the preform design of 3D forming processes

Abstract

In the finite element analysis of forming process, objects are described with a finite number of elements and nodes and the approximated solutions can be obtained by the variational principle. One of the shortcomings of a finite element analysis is that the structure of mesh has become inefficient and unusable because discretization error increases as deformation proceeds due to severe distortion of elements. If the state of current mesh satisfies a certain remeshing criterion, analysis is stopped instantly and resumed with a reconstructed mesh. In order to reduce the discretization error, desired mesh sizes in each region of the workpiece are calculated using the Zinkiewicz and Zhu’s a-posteriori error estimation scheme and the density map is constructed. Piecewise density functions are then constructed with the radial basis function in order to interpolate the discrete data of the density map accurately. In the study, a new remeshing algorithm using tetrahedral elements has been developed, which is adapted to the desired mesh density. At first, surface patches are extracted from the current mesh. Then, surface patches are classified according to the dihedral angle of surface elements. The surface mesh is reconstructed at each patch according to the density function. Then, the reconstructed surface mesh is projected into the original surface patch. The solid mesh is built up using a modified point insertion technique. The positions of inserted points are calculated by density weighted inner product. The element size and quality are controlled simultaneously by moving nodes according to both the mesh density function and the quality optimization function. This mesh is named the pre-constructed mesh. Usually, there still remain sliver elements and over refined elements in the pre-constructed mesh. Therefore, additional improvement scheme is necessary. At first, the object domain is divided into uniform sized sub-domains and the numbers of nodes in each ...