Adaptive meshing of 2D heterogeneous objects using material quadtree

Abstract

In finite element analysis (FEA), adaptive meshing of an object is usually preferred. With adaptive meshing, geometric accuracies of the mesh and more accurate FEA solution can be achieved while maintaining the computational efficiency. Numerous researches about adaptive meshing have been done and most of the existing schemes can generate meshes properly when the objects under meshing are homogeneously constituted. With the advent of heterogeneous objects, traditional adaptive meshing schemes become inadequate as the material heterogeneities of the mesh nodes and mesh elements are not taken into consideration. Inaccurate FEA results may result when a traditional adaptive mesh for a heterogeneous object is used as input geometry for the FEA. To cope with this problem, proper adaptive meshing schemes for heterogeneous objects should be developed. In this paper, the problem in 2D case is considered and a material quadtree is introduced. In this material quadtree, apart from the geometries of a heterogeneous object, the material heterogeneity information is also taken into account. Different types of quadrants are defined and a material composition variation threshold is introduced. This threshold and the traditional quadtree resolution are used to verify whether a quadrant should be recursively subdivided. By checking these threshold and resolution properly, the resultant material quadtree is able to represent the geometries of the heterogeneous object to predefined level of details. Moreover the material composition variation inside each quadrant should be within a preset threshold. By triangulating the quadrants of the material quadtree, an adaptive mesh can be created. © 2011 CAD Solutions, LLC.