Adaptive constrained mesh generation: part 1 - stripwise advancing front technique

Abstract

A study is conducted on the adaptive constrained mesh generation for two-dimensional finite element analysis, where the mesh can be adapted to point and line constraints that evolve during the analysis process. As part of the study, a new mesh generation algorithm is developed. It first divides the entire domain into parallel strips, then generates interior nodes at equidistance on the strip boundaries, and lastly applies the advancing front technique to each strip in turn with additional interior nodes put in only when required at optimum locations to generate a triangular mesh whose interior nodes are mostly on a regular grid. Nodes are numbered orderly on a strip-by-strip basis, which automatically ensures minimum bandwidth and completely eliminates the need for node renumbering. When necessary, the mesh quality is enhanced by a newly developed mesh smoothing technique of recursively moving each node to its optimum location through multi-directional searching and marching. The methodologies developed herein are applicable to arbitrary two-dimensional domains, including convex, non-convex and multi-connected ones, as will be demonstrated by examples in the paper. The techniques of adapting meshes to accommodate constraints are presented in the accompanying paper (i.e. Part 2).